The Application Of Cfd To Sails

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The Application of Computational Fluid Dynamics to Sails Arvel Gentry The Boeing Company Seattle Washington Proceedings of the Symposium on Hydrodynamic Performance Enhancement for Marine Applications Newport Rhode Island October 31 November 1 1988 December 1999 Abstract This paper presents examples of the application of seen some application to the aerodynamics of sails over Computational Fluid Dynamics CFD in understanding that same time period the aerodynamics of sails The basic principles of the Before the digital computer relied on generation of lift and the jibmainsail slot effect for thin soft basic theory supplemented by extensive wind tunnel and sails are reviewed The application of this technology to flight testing However the approximations present in the 12Meter yacht mast design problem is presented The wind tunnel testing and the high cost of both tunnel and paper concludes with an experimental study of the use of flight tests slowed the design process In physical testing CFD techniques in understanding the design problems of all flow phenomena are present so that the real effects are a multielement solidwing sail seen within the limitations of the experiment However in physical testing it is usually difficult to separate the various Nomenclature effects so that the real cause and effects of the physics can Cl section lift coefficient be understood CL wing lift coefficient By its very nature CFD is able to probe such problems Cl ccref span load coefficient Within the computer it is possible to test the sensitivity of c local chord the mathematical assumptions and the physical processes cref reference chord that they simulate The computer even provides a means Cp surface pressure coefficient pp 12rV 2 of discovering new physical phenomena In this sense oo oo 1 V V 2 CFD is closer to experimental than to theoretical fluid oo H boundary layer shape factor d u dynamics However just as with experimental fluid p surface pressure mechanics CFD has its own difficulties and limitations poo freestream static pressure Present day codes are becoming quite sophisticated Re Reynolds number per foot Everyday production tools for subsonic work such as S stagnation streamline higher order panel methods boundary V local surface velocity layer methods and coupled solutions V freestream velocity have provided unique insights into basic aerodynamic oo X longitudinal distance problems The future looks even brighter with the more Xsep location of separation point powerful Euler methods with coupled boundary layer Y span location and airfoil ycoordinate solutions The application of the ultimate the solution of a angle of attack the NavierStokes equations is becoming practical for r air density increasingly complicated geometric shapes but requires d boundary layer displacement thickness more computer speed memory and cost than is presently u boundary layer momentum thickness available to someone doing avocational research in sail aerodynamics This paper will therefore limit itself to the Introduction use of the more basic tools based on panel methods plus boundary layer solutions The digital computer plus advanced mathematical The application of CFD to sails has provided several techniques has spawned a relatively new and powerful advantages over testing With CFD we can separate and field of aerodynamics called Computational Fluid identify the physical phenomena involved The Dynamics CFD In its simplest terms CFD is the process application of CFD is much cheaper than testing of taking a physical flow problem breaking it down into a providing one has access to the appropriate computer suitable set of equations and solving them on a digital programs and a powerful computer The disadvantages computer The use of CFD in the aircraft design process has are that CFD is only as good as the mathematical equations steadily grown over the past twenty years and has also and assumptions used in representing the physical flow C 1900 Arvel Gentry Also all 23 Ranger CFD codes require Newsletter the precise input of the surface Applying the condition of zero normal velocity on geometry of the shapes to be studied In the case of soft the surface gave an integral equation for the source thin sails this is difficult Under sail the crew can adjust distribution The integral equation was replaced by a set of the sails precisely to the flow conditions but this is difficult linear algebraic equations for the values of the source to accomplish in a computer program density on the elements Once these were solved for the This paper presents the experiences of the author in source distribution all flow quantities of interest velocity exploring the use of CFD on sailing problems over a pressure etc could be calculated The body surface was number of years Early explorations were quite significant approximated by a large number of small surface segments in that they led to the correct explanation for the jib or elements over each of which the source density was mainsail interaction problem the slot effect CFD assumed constant Specification of the trailing edge flow technology also was applied to the problems of mast cross condition the Kutta condition could be turned on or off section shape design for Americas Cup l2Meter yachts Figure 1 shows what the flow about a simple airfoil This paper reviews this earlier work on thin soft sails and would look like if the air had no viscosity This is easily concludes with some results from an experimental study simulated with the potential flow program by turning off of the use of the latest CFD techniques on a solidwing sail the Kutta condition Without viscosity the flow would such as used on catamarans make the turn at the trailing edge as shown in Figure 1 the streamlines would be symmetrical and there would be no Aerodynamics of Sail Interaction lift and no drag In 1973 SAIL magazine published the first of a series of articles by the present author on the aerodynamics of sails 1 2 These articles were based on research reported in 1971 3 An updated version of this material was presented in 4 The basic objective of these references was to understand how two sails the jib and mainsail interact with each other the slot phenomena The accepted Figure 1 Flow if air had no viscosity explanation was that the slot between the two sails caused a highspeed venturi effect and that it energized the The real air does have viscosity but its primary effect is boundary layer on the lee side of the mainsail and kept it near the surface of an object the boundary layer The from stalling This popular explanation in the sailing thickness and of this layer depend upon literature followed the then current description for the how it is treated by the external flow and in particular by wingslat interaction problem in the aerodynamic the pressure gradient A rapidly increasing pressure will literature Both were wrong The use of CFD provided the thicken the boundary layer and eventually cause it to correct answers separate from the surface For the flow in Figure 1 the The authors coworkers in the early 70s had developed boundary layer would not be able to withstand the rapid a new multielement CFD code 5 and were beginning to increase in pressure around the trailing edge It would gain new insights into highlift design problems It seemed separate and shed the starting vortex as shown in Figure 2 clear that these same concepts must apply to the sail interaction problem With the new CFD code it was possible to separate the various phenomena and to gain a new understanding of the physical problem The Generation of Lift The fundamental problem as to how a surface such as a sail generates lift is rather difficult to understand for the average nontechnical sailor The fact that it is the viscosity of air that makes lift possible is even more difficult to grasp The concepts used in CFD codes help in explaining the principles involved as illustrated in Figures 1 through 3 Figure 2 Formation of starting vortex at Early versions of these illustrations were generated by the trailing edge the author using an analog field plotter an early and simple CFD method 3 Later the streamlines were Once we know what happens at the trailing edge we determined more accurately using a potential flow can adapt our mathematical of the flow program for twodimensional airfoils 5 This program and produce useful answers The condition of flow leaving was probably typical of the stateoftheart at the time the trailing edge the Kutta condition certainly has been 1965 However it contained no viscous interaction or understood for many years In theoretical aerodynamics separation flow modeling capabilities The method was the Kutta condition is satisfied by imposing a mathematical based on the use of a distribution of source density over the circulation about the airfoil until the flow leaves the 2 trailing edge smoothly With the Kutta condition imposed The twodimensional potential flow program 5 was the viscous effects can then be neglected and the used to study these effects and to present basic examples as mathematical tool used to explore and understand the to how the jib affects the mainsail and how the mainsail flow about shapes without separation The resulting final affects the jib Again viscous and separation effects were flow with the Kutta condition imposed is shown in Figure not included However basic potential flow results gave 3 The airfoil now generates lift the understanding that was needed The advantage of the CFD method over observing the real flow afloat was that the potential flow program could isolate and study each airfoil without the other being present and without the confusing effects of the boundary layer and separation Streamline and pressure distribution plots from the CFD code gave the data necessary to correctly explain the jib mainsail slot effect for the first time Effect of Mainsail on the Jib Figure 5 shows the effect of the mainsail on the Figure 3 Final flow field with lift streamlines about the jib The dotted line is the jib flow Although the circulation about the airfoil as generated without the mainsail The aft airfoil the mainsail causes an in theoretical aerodynamics and as simulated by potential increase in the upwash flow coming into the jib A large flow programs seems like just a mathematical trick this is amount of air that originally flowed on the lower not the case The circulation is real and can be viewed by a windward side of the jib now flows on the upper lee side simple experiment using a bathtub with about two inches This matches our original view of the circulation about the of water 4 A small airfoil is placed at one end of the tub two airfoils and then moved smoothly toward the other end This will cause the formation of the starting vortex as the viscosity takes over and forces a Kutta condition at the trailing edge After a short distance the flow will adjust and there is an upwash in front of the airfoil and a downwash behind If the airfoil is then removed from the water an additional vortex is left behind This is the circulation required to satisfy the Kutta condition and its magnitude determines the amount of lift generated by the airfoil Figure 5 Effect of mainsail on jib streamlines JibMainsail Interaction When two airfoils are close to each other such as with Figure 6 shows the pressure distribution on the jib with the jib and mainsail then two circulation fields are present and without the mainsail present as calculated by the Figure 4 We may easily deduce a number of things from potential flow program The jib carries a much larger load this figure It is clear that the two circulations oppose each with the mainsail present However another phenomena other in the slot between the jib and mainsail The air is present that is not so obvious from the simple circulation speed in this region will be slowed down The two picture The flow off the trailing edge of the jib the leech is circulations should add to each other in the area to the lee faster with the mainsail present the pressure is more side of the jib In front of the jib the two circulations should negative The Kutta condition is being satisfied on both add together to increase the jib upwash If no flow airfoils by the potential flow program but the dumping separation is present the Kutta condition must be satisfied velocity at the trailing edge of the jib is determined by the at both the mainsail and jib trailing edges combined flow of the jib and mainsail and it is higher This phenomena is discussed in some detail by AMO Smith 6 and also covered by CA Marchaj 7 p635 Figure 4 Circulation directions about jib and mainsail Figure 6 Effect of mainsail on jib pressures 3 Effect of Jib on the Mainsail The Separation Bubble Figure 7 shows the streamlines about the mainsail with Early CFD applications on thin aircraft airfoils required and without the jib The jib reduces the upwash at the an understanding of the laminar separation bubble leading edge of the mainsail the mast Some of the air that problem As the angle of attack of the airfoil was increased passed between the headstay point and the mast will be the bubble grew and under certain Reynolds numbers and forced to the lee side of the jib when both sails are present angles it finally burst and the entire airfoil stalled It occurred to the author that this same phenomenon might be present on the luff of thin sails and this turned out to be the case This led to the design of a series of short tufts placed end to end near the jib luff to measure the size of the separation bubble This line of tufts is used differently than the long single telltale placed 1218 inches from the luff on most jibs With several short tufts in a row the number of tufts twirling shows the size of the bubble and how the sail angle is changing between the stalling and the luffing condition see Figure 9 Sailing experience proved that Figure 7 Effect of jib on mainsail streamlines this special tuft system or Gentry verklikkers as they are called in Holland was very useful in windward sailing Figure 8 shows the pressure distribution on the and sail trim 14 7 Almost all of the l2Meter yachts mainsail with and without the jib Without the jib the sailing in Australia in 1987 used this tuft system concept on mainsail stagnation streamline is well onto the lower their jibs windward side of the sail The flow accelerates around the mast and to the lee side of the mainsail producing high suction pressures followed by a rapidly increasing pressure This adverse pressure gradient would cause the boundary layer to separate Figure 9 Tuft system to measure separation bubble Mast Design Aerodynamics The same program used on the jibmainsail interaction problem was used in 1974 to design a new mast for the Americas Cup l2Meter COURAGEOUS 10 11 Studies Figure 8 Effect of jib on mainsail pressures with the potential flow program gave details of the mast With the CFD code we can isolate the different physical design problem that could not easily be measured afloat aspects of the problem and determine just what causes To support the analytical work sailing tests were used to what The primary effect of the jib is that it reduces the understand the separated flow regions and the effect of suction pressures and velocities on the lee side of the unsteady flow conditions mainsail The potential flow efficiency of the mainsail is It was important that the proper flow conditions were reduced by the jib However the real boundary layer is simulated in the CFD and in the sailing tests The mast is able to live with this revised leeside mainsail pressure the leading edge of the mainsail airfoil with its velocity and distribution without separating pressure distribution strongly influenced by the presence Note that the final trailing edge pressure on the jib of the jib and the mainsail Studies of the flow around a Figure 6 is higher than the mainsail trailing edge mast standing alone would be of no use pressure This is the result of the Kutta condition being Conventional nonrotating sailboat masts have a imposed under the combined flow fields of both the jib region of separated flow on the aft leeside of the mast In and mainsail the analytical studies the area behind the mast where the These explanations for the jib mainsail flows were flow is usually separated was smoothed over Computer used by CA Marchaj 78 with the statement that they for runs with the potential flow program and a separate the first time explained correctly the jibmainsail boundary layer analysis showed that the amount of interaction effect The results were also used by P Gutelle separation depended primarily on the condition of the 9 boundary layer as it faced the first adverse pressure 4 gradient This was verified by the sailing tests yellow to blue at the turbulent transition point A thinfilm The initial design objective was to find a mast shape gauge was also used to determine the effect of trip devices that would have reduced separation From basic boundary on the boundary layer transition layer theory it was clear that a turbulent boundary layer on The sailing tests indicated that the mast leeside the mast would reduce the amount of flow separation The separation matched the CFD calculated adverse pressure problem then became one of finding a mast section shape gradient location In the sailing tests the Msection in that would help trip the flow to the turbulent flow Figure 10 had a separation point farther aft than the other condition before it reached the first adverse pressure sections This led to the idea of developing a mast section gradient shape that would have a long region of approximately flat A series of computer runs were made to determine how pressure gradient prior to the start of the adverse gradient the pressure distributions changed with mast cross section This region of constant pressure and constant speed shape Some examples are shown in Figure 10 might provide sufficient running length for a boundary layer trip system to trip the flow to turbulent Numerous CFD analysis runs led to a shape with a flat topped pressure distribution which had the dual purpose of giving sufficient length to trip the boundary layer plus a higher leading edge thrust The final shape is shown in Figure 11 Final full scale sailing tests verified that the new shape represented an improvement over previous mast sections This shape was used on the mast for COURAGEOUS in the 1974 and 1977 Americas Cup defenses A similar mast was designed and used on FREEDOM in the 1980 Cup races Figure 10 Shapes and pressure distributions of initial mast sections The cross sections were tried in short sections in live sailing tests A variety of methods were used to visualize the flow during the tests including small tufts on the mast section and mainsail soap bubble streams generated by a special nozzle driven by a small compressor and a pressure rake The condition of the boundary layer was studied with the use of a special surface paint that changed color depending upon the amount of ammonia present in the boundary layer ammonia was pumped through small holes at the leading edge The paint color changed from Figure 11 Final Courageous mast shape 5 The author was asked to design a new mast for use on are symmetrical The wing camber is adjusted from one LIBERTY for the 1983 Cup defense and conducted some tack to the other by changing the angle between the sailing tests on board FREEDOM in the summer of 1982 forward and aft airfoils and adjusting the tab on the The mast and mainsail were tufted and observed under forward airfoil various sailing conditions Photographs were taken of the Several basic objectives were selected for this study of sails and later digitized for input to the computer analysis the wing sail The sailing tests indicated that the original mast design 1 Demonstrate that the basic theories described previ was excellent in smooth water but that the separation was ously for thin soft sails also apply to the thick wing sail a bit too sensitive to the dynamic motion of the boat in a In particular show that the improvement on the aft seaway A new mast section was designed for LIBERTY to airfoil is not due to any high speed flow in the slot improve this situation This involved the use of a new revitalizing the aft airfoil boundary layer but due to multielement airfoil program that had an inverse design the fact that the forward airfoil suppresses the leeside capability 12 An initial shape was analyzed by the pressures of the aft airfoil program and the pressure distribution plotted A new 2 Learn how the pressure distribution builds about the desired pressure distribution was then sketched and input airfoils as the angle of attack is increased to the program and the code generated a new mast shape 3 Study how the boundary layer behaves with different The process was repeated several times until the desired airfoil deflections and angles of attack results were achieved 4 Generate lift versus angle of attack data for two different camber shapes Experimental Studies of a MultiElement Wing Sail 5 If possible determine the airfoil stalling angles The material presented in the previous sections of this 6 Apply a 3dimensional panel method to the wing sail paper is a summary of work conducted by the author between 1969 and 1983 and involved only soft sails CFD The CFD computer program selected for the two codes have improved since that time and it would be dimensional part of this study was a modified version of interesting to apply the latest programs available to the the Boeing multielement airfoil program 12 recently author to the type of sail that has been built by the Sail completed by WenFan Lin of the Boeing Aerodynamics America syndicate for the 1988 defense of the Americas Research Group The program is basically a potential flow Cup against the New Zealand 90foot waterline problem solver coupled with a viscous flow problem challenger The new Sail America boat is a 60 foot catamaran solver in an iterative fashion That is the inviscid flow is christened STARS STRIPES and sports a solid multi calculated by the potential flow solver and the results element wing for its sail power The legality of this boat as input to the boundary layer The boundary layer solver a cup defender was still being challenged by New Zealand furnishes the boundary layer displacement effect which is in the courts as this is being written then fed back into the next inviscid solution The process is It should be emphasized that the present author was continued until it converges not part of the STARS STRIPES design team The wing The potential flow solver is based on a higher order sail shape and the airfoils used in this paper were derived panel method for twodimensional airfoils It can be run in from photographs of the STARS STRIPES and must be either an analysis mode direct or in a design mode viewed as only rather crude approximations of the actual inverse Only the analysis mode was used in the results design The airfoil shapes used in this exercise are probably presented here The design mode was however used in far from optimum the design of the mast for LIBERTY as previously This provides an interesting situation for the discussed application of CFD The author is applying CFD to new The viscous problem solver uses a momentum integral problems for which he is completely unfamiliar and has no approach to calculate the boundary layer test data to verify any of the findings or conclusions Also The integral boundary layer solver calculates the laminar the results presented were obtained in a very short period boundary layer laminar separation the laminar of time Therefore these data should be viewed more as a separation bubble transition based on a correlation of CFD experiment rather than as actual design data Granville and the turbulent boundary layer The However the analysis steps presented are typical of how turbulent calculations use the momentum integral CFD would be used in the first stages of an actual design method a power law velocity profile Garners equation process It will be interesting to eventually see how the for the form parameter and the LudwiegTi11man results of this very brief CFD experiment match what is equation for wall shear stress The turbulent separation found on the actual sailing catamaran point is assumed to occur when the shape factor H 28 The STARS STRIPES wing sail has a forward airfoil The program includes a simulation of any separated flow with an attached small movable tab The aft airfoil has a regions on the airfoils The boundary layer displacement slightly longer chord than the forward airfoil at least over effect between iterations is accounted for using a the lower part of the mast There is a small slot between transpiration method the forward and aft wing airfoils and of course the airfoils 6 Basic Interaction of MultiElement Wing Sail Airfoils shown in Figure 14 Note the very high pressure peak at The basic principles of the interaction between the jib the leading edge of the aft airfoil Previous discussions and mainsail as already outlined must also apply to the indicate that the boundary layer will probably separate at solidwing sail airfoils This fact will be illustrated in the the adverse pressure gradient and that is exactly what the following examples However with the new program that program tells us when we let it run for a number of includes viscous and separation effects we should be able inviscid viscous iteration cycles Figure 15 The aft airfoil to study the flow right up through the airfoil stall is clearly stalled without the forward airfoil The solid wing is certainly much easier to simulate than When both airfoils are present we get a different the thin soft sails since it does not change its shape luff at picture Figure 16 The forward airfoil suppresses the the lower angles of attack For all of these studies the wing peak pressure on the lee side of the aft airfoil The angle of attack will be measured relative to the centerline boundary layer on the aft airfoil is able to handle this new of the forward wing airfoil The aft airfoil angle will be pressure distribution the air does not separate and the measured relative to the forward wing centerline the airfoil is no longer stalled The aft airfoil has a strong flap deflection angle Since the wing sail has a wide influence on the forward airfoil Even though the forward range of angle adjustments relative to the true wind and airfoil is at zero angle of attack itself the flow induced by since the boat spends most of its time either beating or the aft airfoil causes a strong upwash in the streamlines close reaching no attempt has been made in these studies coming into the forward airfoil leading edge and the front to identify the angle that the wing sail system makes airfoil now generates considerable lift relative to the boat direction All of these effects are exactly as we would expect from The dimensions of the airfoils studied are only the much earlier completely inviscid work on the jib approximate as they were taken from available photos of mainsail interaction problem However with a more STARS STRIPES For the twodimensional studies the sophisticated code that includes viscous and separation chord length of the forward airfoil was taken as 89 feet and effects we are able to see the complete process in more the flap chord was set at 112 feet All of the results detail presented are for a unit Reynolds of 0265x106 which represents an apparent wind speed of 25 knots The program was allowed to calculate its own transition and separation points The Boeing Aero Grid Paneling System AGPS 13 was used to generate all the geometry data needed for input to the CFD code and for much of the output post processing The basic airfoils are shown in Figure 12 In this example the flap is deflected 20 degrees Runs were made with both a zero and 10 degree tab rotation about the 80 chord point Analysis runs were also made with a 5 degree tab and 10 degree flap combination These angles are not optimum but were selected merely as typical starting points for the design process Inviscid results for the forward airfoil alone at zero angle of attack are shown in Figure 13 The inviscid results for the aft airfoil alone at its 20 degree deflection angle are Figure 13 Inviscid results for forward airfoil Figure 12 Experimental airfoils used for solid wing study 7 Figure 15 Converged solution for aft airfoil only Figure 14 Inviscid results for aft airfoil only On a highly cambered single element airfoil the boundary layer has a hard time withstanding the adverse pressure gradient over the entire length of the upper surface flow With two airfoil components and a slot between we have a much better design The circulation fields about the two airfoils tend to cancel each other in the slot and the air slows down The peak pressure gradient on the aft airfoil is reduced by the presence of the forward airfoil The boundary layer on the lee side of the aft airfoil is starting fresh at the stagnation point rather than having suffered through the adverse pressure gradient on the forward airfoil The boundary layer on the aft airfoil is not energized by any highspeed slot flow As with the jibmainsail interaction the load on the front airfoil is much higher because of the upwash due to the aft airfoil and because its trailing edge Kutta condition is satisfied in a higher speed region on the lee side of the aft airfoil Figure 16 Converged solution for both airfoils 8 The Inviscid Viscous Convergence Problem The CFD program used for this study calculates the inviscid and viscous flows using completely different sets of equations Their interaction effects are accounted for by repeating the calculations through several iteration cycles The basic problems with such an approach are when is the flow converged and does it converge to the correct solution A good example of the iteration process is shown in Figure 17 In this case the angle of attack was 12 degrees the tab was deflected downward 10 degrees and the flap was deflected 20 degrees to give a highly cambered configuration On cycle one there is a peak velocity at the tab hinge point at X08 In the next few cycles the flow is separated off of the tab By the 6th and 7th cycles the separation has become stable at X055 As the separation on the front airfoil moves forward it is not as efficient in suppressing the peak pressure on the aft airfoil and the separation on the aft airfoil starts to move forward also Figure 17 Changes in Cp with iteration cycle One means of monitoring the convergence process is to watch the changes in the total lift coefficient Cl and the forward airfoil flow separation point This is illustrated in Figure 18 However some computer runs at high angles of attack were slow to converge The separation point just slowly marched forward on the forward airfoil This situation means that the airfoil is probably stalled or will stall if enough cycles are run once this was identified the case could be rerun with a flag set to force a more rapid forward movement of the separation point A few other runs would converge to what was apparently the correct solution and then oscillate about that solution until the iterations were stopped It is obvious that convergence plots must be made for every run to be sure that the solution converges properly and that the correct final solution is being selected from the iteration cycles Prediction of Airfoil Stall A series of runs were made to see if the CFD method could calculate the airfoil stall point The results are presented in Figure 19 Two different tabflap angle combinations were studied to see how total effective Figure 18 Convergence history camber influenced Cl and the stall The tab and flap angles were selected quite arbitrarily and may not represent what is actually used on the real catamaran At 16 degrees angle of attack for both configurations the final flow separation point was close to the leading edge of the forward airfoil and at about the midpoint on the aft airfoil The calculated Cls had also dropped off sharply at 16 degrees Considerable separation was also already present on both systems at 12 degrees angle of attack For the 20 degree flap system the converged separation point was at X05l on the upper surface of the forward airfoil The 10 degree flap system had a converged separation point at X066 Computed streamlines are shown in Figure 20 at 8 degrees angle of attack for the tab5 flap10 camber Figure 19 Prediction of airfoil stall 9 condition program A502 This program was selected because of its At zero degrees angle of attack the flow on both camber many capabilities and because it is available for general use configurations was unseparated except for the tab region by the public 14 on the forward airfoil These results indicate that tab Program A502 solves the general deflections of 10 degrees for the 20 degree flap case and 5 problem for arbitrary degrees for the 10 degree flap case might be too high This configurations The program uses a higherorder panel suggests that the flow on the tab on the real catamaran method based on the solution of the linearized potential should be watched carefully with the aid of several rows of flow boundaryvalue problem Results from A502 alone very short tufts Longer conventional telltales on the tab are not usually applicable to cases where viscous effects might not show the actual tab separation and separation are dominant Viscous results can be For these calculations the program input freestream obtained using a separate 3D finite difference boundary turbulence level was set to zero The transition was left free layer program However time was not available to include to be calculated by the program Changes in these 3D boundary layer results for this study assumptions would probably give different output results The A502 panel geometry used for this study is shown in Figure 22 The aft airfoil of the real wing is broken into a WingSail ThrustDrag Loops number of flap sections so that twist and camber can be The term lift is normally defined as a force adjusted spanwise For simplicity this study used a smooth perpendicular to the freestream velocity vector How variation of the angle of the flap from 20 degrees at the root much of this force is available to produce forward to 10 degrees at the tip The airfoil sections were the same boatspeed depends upon the angle that the boat centerline as used for the 2D analysis except that the forward airfoil makes with the wing sail reference line and the direction of tab deflection was zero the freestream velocity vector The integration of the The 3D geometry and paneling were generated using pressures on the sail in a direction perpendicular to the the Boeing Aero Grid and Paneling System AGPS 15 The boat centerline gives the boat driving force This thrust wing root airfoil was assumed to be 54 feet off the water drag loop method is useful in understanding the driving which was taken as the reflection plane The wing was force generated by the wing sail A sample thrustdrag plot represented by 1434 panels plus a wake system extending for a 30 degree angle is shown in Figure 21 for the 10 degree downstream The A502 program was run on a Cray XMP flap deflection case In this case both airfoils are producing computer forward thrust At lower angles the forward airfoil The span load calculated by the A502 program is shown produces almost all of the thrust with the aft airfoil serving in Figure 23 The gap between the wing root and the the purpose of loading up the forward airfoil reflection plane the water causes a rapid loss in load on the lower part of the wing Some sort of wing root end plate would help this situation if a practical design could be made Figure 21 ThrustDrag loops Effects All of the results presented to this point have been based on twodimensional analysis One reason for this is that the solidwing sail has a high aspect ratio so the 2D results should be close to the real physical flow Also the 2 D method included iterative viscous and separation effects However a 3D inviscid analysis should shed light on root and tip effects plus give some idea of the efficiency of the wing from the spanload distribution standpoint For this study the direction of the freestream velocity vector was assumed to be constant and was not varied spanwise along the wing as would be the situation on the real boat The 3D panel method used for these calculations was Figure 22 Wing paneling used for A502 program the Boeing PAN AIR Technology code identified as Boeing 10 Detailed results for the zero angle of attack case are shown in Figure 24 on Page 12 The data presented include pressure distributions at se1ected wing stations and constant pressure contour lines for the top leeward and bottom windward surfaces of the wing The pressure contour plot originals are in color and give a quick view of the aspects of the flow Conclusions Although the computational fluid dynamic tools used in these studies were developed only for aircraft design purposes they are capable of providing useful results when applied to a variety of sail aerodynamic problems These tools led to the development of the correct explanation for the jibmainsail slot effect and to the Figure 23 Span load distribution discovery and use of the laminar separation bubble for windward sailing Mast sections developed using CFD References were used on the Americas Cup defenders 1 Gentry AE How Sails Work SAIL Magazine April COURAGEOUS 1974 1977 FREEDOM 1980 and 1973 thru January 1974 LIBERTY 1983 2 Anthology The Best of SAIL Trim SAIL Books Inc An experimental study of the use of both two 1975 dimensional and CFD methods has 3 Gentry AE The Aerodynamics of Sail Interaction indicated that such tools probably would be useful in the Ancient Interface III The 3rd AIAA Symposium on design process for solidwing sails such as those being Sailing Nov 20 1971 Redondo Beach Calif used on modern high technology catamarans 4 Gentry AE A Review of Modern Sail Theory The The basic problems in applying CFD to sails are about Ancient Interface XI 11th Annual AIAA Symposium what one would expect the tools were developed for on Sailing Sept 12 1981 Seattle Washington aircraft and sometimes do not contain certain capabilities 5 Giesing JP Potential Flow About TwoDimensional needed in the analysis of sails For example the standard Airfoils McDonnell Douglas Report NO LB31946 programs do not provide a means for changing the December 1965 freestream velocity vector to represent wind shear from 6 SmithAMO High Lift Aerodynamics AIAA Paper the deck to the top of a sail No 74939 Los Angeles1974 A basic problem exists in that the sailor is able to change 7 Marchaj CA of Sailing Dodd the shape of his sails to match the real airflow conditions Mead Company New York 1979 and the computer cannot The CFD programs require that 8 Marchaj CA Sailing Theory and Practice Revised the complete sail shapes be input at the beginning of the Dodd Mead Company 1982 solution Providing shapes that match both realistic sailing 9 Gutelle P The Design of Sailing Yachts International conditions plus what the CFD program sees is a difficult Marine Publishing Company Camden Maine 1979 task This is particuu1ar1y true when attempting to model from the French edition thin soft sails but also applies to the wing sail 10 Gentry AE Studies of Mast Section Aerodynamics The Ancient Interface VII 7th Annual AIAA Symposium on Sailing Jan 31 1976 Long Beach This paper was prepared as a research project under California the Flight Research Institute FRI Seattle Washington 11 Gentry AE Design of the COURAGEOUS Mast Approval to use the Boeing CFD codes and access to the Yachting Magazine Feb 1975 necessary computer time was arranged through the FRI 12 Henderson ML A Solution to the 2D Separated The author is indebted to WenFan Lin of the Boeing Wake Modeling Problem and Its Use to Predict Aerodynamics Research Group for his guidance on the use Maximum Lift Coefficient of Arbitrary Airfoil of his new version of the Boeing 2D Multielement Airfoil Sections AIAA Paper No 78156 Jan 1978 Program and to Jim Thompson for his photographs of the 13 Snepp DK Pomeroy RC A Geometry System new STARS STRIPES catamaran for Aerodynamic Design AlAA872902 AIAAAHAASEE Aircraft Design Systems and This paper is dedicated to the memory of David K Operations Meeting St Louis Missouri Sept 1987 Snepp who lived life with style courage and a great 14 Saaris GR A502F Users Guide PAN AIR Technology sense of humor Program for Solving Problems of Potential Flow about Arbitrary configurations Boeing Report D6538l8 June 1987 11 Figure 24 A502 results for the solid wing 12

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