Left: a vortex lattice model (VLM or panel code) used to obtain pressure distribution and so forces generated from two sails. This model is well suited to analyse sails in upwind conditions when the importance of viscous effects (flow separation, stall) is limited. So VLM, for example, provides an excellent means to quickly assess many different geometries and upwind trims. Below: RANS CFD can quickly reveal flow details that are accessible to physical experiments only with great effort. Here we look at an over-trimmed headsail. Left: we are using a fine mesh and can see the resulting vortex shedding (the blue low-pressure region). Right: we still have the same wind and trim, but solved on a coarser mesh. Now the vortex is lost in the grid resolution and the sails would appear to be well trimmed; this demonstrates the critical effects of different discretisations
the boundary layer development and the possible pressure loss due to separation. Another trick, particularly well suited
for long and thin geometries like aircraft wings or sails, is to use two-dimensional experimental data to correct the lift and drag terms in the VLM equations. Through this data we can introduce skin friction, pressure drag and boundary layer effects (like separation) back into the originally inviscid model. These add-ons improve the vortex method significantly and lead in many cases to accurate results with very reasonable effort. In fact, often VLM results that are very comparable with RANS, but at a fraction of the effort. But this only holds for specific circumstances when the assumptions are valid. Again choice and judgement are left to the user.
interested in – sails, hulls etc) means missing out on the core strength of RANS: being able to model turbulence and with it separation and such. To do this we will not get around including the fluctuating part and going one step further.
Tweaking the models Since Reynolds presented his averaging idea in 1895 engineers and physicists have been scratching their heads about how to deal with the fluctuating part. They came up with some clever solutions: the so- called turbulence models, add-ons to plug into the RANS equation dedicated to deal- ing with the fluctuating part. However, none of these turbulence models is mathe- matically exact for anything but the simplest academic cases. While the most popular turbulence mod-
els are all based on a mathematical simplifi- cation of the problem, they eventually rely on empirical fitting to experimental data. Nevertheless these models provide a wel- come means which turns solving the RANS
equation with turbulence into a manage- able task – much easier than DNS, yet still much more complicated than VLM. The trick for turbulent RANS is to
make sure that an adequate model with adequate turbulence fitting parameters is used. This model must be selected from a large pool of methods furnished through those 125 years of head scratching over the RANS equations. If the right models are chosen, RANS simulations can achieve very accurate results with a high level of detail for almost all situations of interest for sailboat design. However, even with access to a supercomputer cluster, turbu- lent RANS simulations on boat-scale prob- lems usually take several hours to solve. Turning back to the vortex methods (eg
VLM), a similar add-on exists. Since the big deficit of vortex models is their igno- rance of viscous effects (friction), add-ons have been fabricated to bring some of the friction back into the inviscid equations. One approach is to use a correction term in the simulation that accounts for
Health warning The VLM equations, just like all the CFD models we discussed, are a remedy to the fact that the Navier-Stokes equation itself is too complicated to solve in its entirety over space and time. Hence, the basis of every CFD method is simplifying the equation. In the end it is some version of Navier-Stokes, together with a specific set of assumptions and simplifications, that is being solved by CFD to calculate results. It is these simplifications that make CFD possible at all and distinguish individual CFD incarnations. It is also these simplifi- cations that constitute the limits of CFD. To choose the right set of simplifica-
tions means to run an efficient CFD simu- lation and obtaining meaningful and very accurate results. Choosing the wrong ones means at best wasted effort. It might, how- ever, also lead to a set of beautiful results that are nothing more than colourful pictures without physical relevance – a very dangerous outcome for the innocent.
Dr Manuel Fluck’s PhD dissertation was on Stochastic Methods for Unsteady Aerodynamic Analysis of Wings and Wind Turbine Blades. His work has since extended further across fluid dynamics taking in sail optimisation, wind power and a new study of bird wings. Born in Munich, Manuel now lives in Brittany q
SEAHORSE 53
NORTH SAILS
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