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*Report by John Perry*

Computational fluid dynamics (CFD) is the study of fluid behaviour by numerical analysis rather than by testing of physical models or prototypes. Kate Taylor, who works for a firm of specialist consulting engineers, gave us an interesting and wide ranging talk which outlined the principles behind CFD and revealed some possible applications to yacht research.

There are a handful of fluid flow situations which can be analysed to produce formulae which can be solved with a pocket calculator, but the great majority of 'real life' fluid flow problems can only be modelled theoretically by using complex numerical analysis software and powerful computers. Interest in CFD started about 50 years ago, and early applications were to predict the behaviour of nuclear explosions - a problem which is tricky to handle experimentally! The capability of CFD has advanced rapidly over the last twenty years, but it is only over the last few years that it has been marketed for use outside of research institutions and large aerospace companies. Because CFD is dependent on the availability of powerful computers, the advances which have been made in CFD over the last couple of decades have shadowed the advances which have been made in computers. Indeed the demand for CFD and other numerical analysis applications is a major incentive for improving computer performance and, in particular, for developing parallel processing computers. As Kate explained, £10,000 (minor expenditure for her client companies if not for a typical AYRS member) will now buy hardware and CFD software which will give useful predictions of fluid behaviour for simple situations. However, there are still many fluid flow problems which are either beyond the state of the art, or which can only be attempted using the most advanced computers found in specialist research institutions.

Kate started her talk by considering the methods which were used for theoretical fluid flow analysis before the advent of CFD. These methods generally required simplifying assumptions. For example, a hypothetical non-viscous fluid was often assumed: this being known as "ideal flow". In this situation the pressure gradients in the fluid are due only to the gravitational weight of the fluid and the inertial forces required to accelerate and decelerate the flow. This type of fluid flow can be predicted using continuity equations which balance the mass flow in and out of flow regions, together with Euler's equations which balance the pressure, gravitational and inertial forces on such regions. By making the regions infinitely small, the equations become partial differential equations. For a few simple geometries, such as two dimensional flow normal to the axis of a cylinder, these equations are capable of analytical solution, but for most problems numerical analysis is needed. The most used numerical analysis method is known as Finite Element Analysis (FEA), and its use for predicting ideal flow is very similar to its use for calculating the stresses in an elastic structure. Indeed much of the software code required is likely to be identical for these two types of problem.

The flow field is considered to be divided into many small regions, known as finite elements, and large numbers of simultaneous linear equations are produced to represent the balance of forces on each of these. These equations are then solved to produce a map of fluid pressure and velocity. Solutions which assume ideal flow are limited in that, because they ignore viscosity, they may predict regions with infinitely rapid shearing of the fluid flow. Although the predicted flow pattern well clear of these regions may be quite plausible, the presence of localised high shear regions can sometimes produce totally misleading conclusions. For example, if we consider an aerofoil at an angle of attack to the flow: an ideal flow will whiz around the sharp trailing edge of the aerofoil and then head upstream to meet the main flow at some point along the upper side of the aerofoil. The flow then separates from the surface at this meeting point. The pressure prediction corresponding to this unrealistic flow prediction will show that the aerofoil produces zero drag and zero lift, so no bird or plane could fly in a totally non-viscous fluid! One way of overcoming this is to keep the basic method using ideal flow analysis, but to mix some vorticity into the flow. Vorticity is a rotating effect in the fluid and is associated with the presence of viscosity. It can generate a 'circulation' around the aerofoil section, the effect of this being to move the point at which flow leaves the surface back to the trailing edge where it should be. The resulting pressure predictions will then give reasonable indications of lift and drag.

Until quite recent times ideal flow analysis with modifications to take account of viscosity was the standard method for calculating aerofoil properties. Now it has been superseded by modern CFD methods based, not on Euler, but on the Navier-Stokes equations, of which Euler's equations could be considered to be a simplified form. The Navier-Stokes equations do include terms to take account of fluid viscosity, and CFD based on the solution of these is capable of handling any fluid flow problem, since all the phenomena associated with real fluids can be taken into account. The difficulty is that, unlike the analysis of ideal flow, the solution of the Navier-Stokes equations requires an iterative finite element method - very demanding on the computer. It is also unreliable in that if the iterations do not converge no answers will be produced!

The iterations start with an assumed pressure distribution which allows an approximate flow distribution to be predicted. This then gives a second pressure distribution which hopefully will be better than the previous one. Continued iterations may converge on an acceptable solution. If the flow is unsteady with time then the problem is even more demanding on the computer since the whole procedure has to be repeated for successive time intervals, the results for any one time interval being based on those produced for the preceding time interval.

Having explained what CFD is about, Kate then showed some examples of typical problems from her everyday work. Like any other FEA application, a CFD study falls into three parts. Firstly the problem has to be set up by generating a mesh and defining input parameters including fluid properties and mainstream velocity and pressure. The mesh is the pattern of elements which are chosen to represent the geometry of the problem and the computer will display it as a grid extending across the region under study. As I know from doing stress analysis by FEA, there is scope at this stage to ruin the results by choosing an inappropriate mesh or by making erroneous assumptions. For studying the flow around an aerofoil for example, the mesh would typically extend a few chord lengths and assume mainstream flow properties at the outer edges. Areas where the flow pattern is complex generally require smaller elements than where there is fairly uniform flow, so the elements are densely packed around any solid surfaces in contact with the fluid. The number of elements used in CFD, especially for three dimensional problems, can be huge, and computer programs are used for automated mesh generation. Often these programs produce rather strange patterns, looking like crazy paving, but which are still effective in solving the problem.

The second stage of a CFD study is to start up the equation solving program and then go away for a coffee, or perhaps come back next day ... or next week ... while the computer does the arithmetic. The third stage is to study and interpret the results, using computer graphics to display contour maps of, for example, pressure distributions. This can produce some very attractive coloured printouts.

Considering the results, the first example which Kate showed us was the two dimensional flow over a cascade of three aerofoils which appeared to have been designed for absolute maximum lift coefficient regardless of drag. The predicted lift coefficient (based on the overall chord?) was close to 4.0 - a very high value apparently confirmed by experimental work. Kate told us that CFD for aerofoils tends to produce better predictions of lift than of drag since drag is rather dependent on the exact location of the stagnation point on the leading edge.

Another example shown was the three dimensional flow of water over the stern sections of a ship. For this particular problem the sea surface was considered as a plane of symmetry, which means that there could be no waves, not even those made by the passage of the hull. This would mean that any drag prediction would not include wavemaking drag which is of course fairly significant even for large ships. It is interesting that CFD can in principle predict wave motion and wave drag, for example an initial assumption can be made for the shape of the sea surface and this used to predict an approximate pressure distribution at the surface so that the surface can then be adjusted in the next iteration to bring this pressure distribution nearer to a uniform atmospheric pressure, or presumably even to a predicted wind induced pressure distribution. This means that CFD could be used to predict the motion of yachts in a seaway and to address the interesting problem of capsize in steep waves, but to do this reliably is close to, or perhaps a little beyond, the state of the art.

Perhaps the most relevant example which Kate showed us was the flow around the mainsail and jib of an America's Cup yacht sailing to windward at 30 degrees heel. I think this 'state of the art' example quite well illustrates both the potential for CFD in yacht research and also the current limitations of the method. The lift coefficient predicted by CFD was apparently in reasonable agreement with that expected from experimental work. The pressure distribution over the sails was clearly indicated, and it was interesting that the greatest pressure was generated in the upper regions of the sails where the triangular planform of a Bermudan rig tends to cause overloading and premature stall. Similar pressure distributions have been measured with sheet metal model sails in wind tunnels, and it is reassuring to see that the theoretical and experimental methods are in agreement. However, as Ian Hannay was quick to point out, a real sail would twist so as to reduce angle of attack at the top which would move the highest pressure regions lower down the sail, improving efficiency by avoiding overloading towards the tip. To simplify the CFD model, no account was taken of sail twist or other pressure induced rig deformations. Other assumptions had been made including ignoring the mast thickness, the time varying nature of the flow due to wave action on the hull, the effect of the hull on the airflow, the effect of vertical wind gradient etc. Some of these effects could have been included but not without a lot of extra work and computer time, and it seems that even Americas Cup teams cannot afford this. For example to include the sail twist would require the CFD program to be linked to a pretty complex structural analysis so that the pressure distribution predicted by CFD could modify the structural analysis to produce a refined rig geometry for the next CFD iteration.

I did wonder whether the America's Cup team who commissioned this CFD study could have gained anything other than a psychological advantage, although perhaps this alone was well worth the money. Suppose, for example, that the skipper wants to know exactly what stiffness of sail battens should be used in a particular weather situation. To find this out he would need to link very sophisticated structural FEA with CFD, and then with luck he would obtain values for lift, drag and heeling moment for a range of angles of attack, boat heel, sea state etc. However, even if these values are accurate, the effect on the race course is still unknown since more lift, for example, may or may not mean more speed, as it will be linked to changes in heeling moment and drag. Predicting the effect of all these changes on boat speed integrated around a race course is another massive computer task which no one has yet attempted seriously, despite what some yacht designers may claim.

At the present state of the art I would expect experience and intuition to be of much greater practical value to an America's Cup skipper than any CFD software, but given a few more decades of development of computer hardware and software who knows how this may change. Perhaps one day we will not need to sail around a race course since we will be able to allocate the silverware purely according to the output of a computer program!

*Report by John Perry*

The Sailboat Exhibition at Alexandra Palace is held annually around the beginning of March. This is the main UK boat show for dinghies, and it includes only sailing dinghies and sailboards whereas the better known boat-shows at Earls Court and Southampton cover all types of recreational craft. The Exhibition is organised by the Royal Yachting Association rather than by a commercial company and in the early years it was a mainly amateur effort with stands only for non-profit making organisations such as sailing clubs and dinghy class associations. This gave the show a rather attractive atmosphere of amateur enthusiasm, a bit like the AYRS. Over the years the show has become progressively more commercial and many of the exhibitors are now companies selling boats, chandlery, sailing holidays etc, and some of the class association stands are also assisted by boat manufacturers. The exhibition is now held at Alexandria Palace which is a very pleasant exhibition centre set in parkland high on a hillside looking South across central London.

Having an interest in the technical side of sailing, I wandered around the exhibition looking for new developments. There has been a trend for several years to add 'racks' or 'wings' extending out from the gunwales of dinghies to increase the righting moment which can be produced by crew weight. Such extensions are applicable to both boats which are fitted with trapezes and those which are not. It is clear that this trend is now well established with a plethora of designs offering rather similar features. I expect this could be followed by a 'shake down' with just a few designs becoming popular and the others fading into obscurity. One of the survivors is likely to be the '49er' design since this has now been selected for Olympic competition and is available from a number of manufacturers around the world. The Laser 5000/4000 and a few others will probably also survive by force of marketing power.

One boat which drew my attention was the 'Breeze' which has folding racks for sitting out and is almost a small keelboat rather than a dinghy since the pivoting centreboard is quite heavily ballasted. My own boat, which was designed specially for dinghy cruising, also has a pivoted and ballasted centreboard and when I designed it 20 years ago I did consider a folding sitting out rack but at the time this would have been an extreme option even for a pure racing dinghy. At 6m length the Breeze is much larger than my boat and it is intended for day-sailing rather than camping on board, since it has virtually no dry stowage nor anywhere flat to make a bunk. The Breeze on display appeared to have a few rather nasty design features such as a mild steel centreboard winch which looked as though it would quickly go rusty and the handle for this winch seemed to have inadequate clearance with the deck.

The International Moth class was one of the first racing classes to adopt 'wings' and they have produced many other novel ideas, for example a few years back they proposed a fully submerged hull, with only the rig and crew seating above the water. Another idea which has become popular for the Moth, but is rarely seen on other boats, is a pitch stabilising foil attached to the tip of the rudder. This generally takes the form of a horizontal symmetric section hydrofoil which is set at zero incidence when the boat is in level trim. It is reckoned to produce substantial damping of pitching motion which arguably reduces hull drag and will almost certainly improve rig aerodynamics. The obvious disadvantage is that a hydrofoil in this position is very vulnerable to damage on grounding. The recent Moth designs probably need pitch damping more than most boats since they have small waterplane areas for their length and sail area. Perhaps some multihulls would also benefit. The latest Moth hull on display looked a very strange shape having a crude looking rectangular cross section. It was very narrow, deep and sharp ended with an aft sloping stem reminiscent of the ram on a Victorian battleship. I think the idea is to have a narrow low drag hull for light winds, albeit with more wetted surface than a round bottomed Moth, whilst at high speeds it can be pitched to plane on the narrow but almost dead flat bottom.

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