Left: a family tree of a small selection of the different CFD methods now available. Below: Solid Particle Hydrodynamics (SPH) model simulating an underwater rockslide. SPH models, an example of a so-called grid-free method, are particularly powerful when dealing with splashing and wave effects. However, they often lack accuracy dealing with typical lift and drag problems (for example, forces on a sail)
assumption: inviscid flow. This means no boundary layer, no separation, no turbu- lence. Often, for example for well-trimmed upwind sails, these assumptions are not far off reality and with additional tweaking the limitation can be softened. Sometimes, however, neglecting friction will be simply wrong for a particular task at hand. In these cases we have to go back to the full Navier-Stokes equation – but pull out a few other tricks to make it solvable.
RANS – an efficient means of dealing with friction The challenge with friction in fluid flows is that it generates turbulence on so many different length scales: eddies shed from objects of all different sizes interact with each other (remember the initial example: the Superyacht to weather, as well as the micro-scratch in the mast). If you decide that all these eddies matter
are so called grid-based methods. These cut the physical space into a grid of little boxes or cells (see illustrations). Since the calculation of the CFD solu-
tion assumes that the properties of the flow do not change within a cell it is implicit that the cells are small enough to justify this assumption. If the cells are too big, vital information about the flow will be lost within this assumption. For big geometries, fine details in the geometry and/or big changes of the flow throughout the domain, this requirement is not always easily met. And of course, the more cells we use the more demanding the equations become to solve. (It is interesting to note that once the equations are discretised the number of cells does not directly relate to the complexity of the resulting equations. However, the number of cells determines the number of equations to be solved and thus the computational effort. This effort quickly becomes so big that we’re talking about hours of supercomputer time). The alternative is to not cut the space
into boxes, but to separate the fluid itself into little balls or bubbles. Since this approach doesn’t require generating a grid of boxes it is called a grid-free method. One example is Solid Particle Hydro - dynamics (SPH). Here each ball is free to move through the domain and each holds the properties of the fluid at its specific location. The balls then interact just like densely packed peas in a jar. SPH is very powerful when dealing with
two different media in a rather large-scale setting. For example, waves splashing over an offshore platform, sediment transport in a harbour, a coastal landslide triggering a tsunami… But SPH is limited when
52 SEAHORSE
small-scale details (such as turbulence or flow separation) are important and thus the majority of sailing-related CFD relies on grid-based methods. But SPH certainly has its niche for special applications.
Friction: the big challenge The next challenge when simplifying the Navier-Stokes equation is how to deal with friction. Friction in fluids causes fluid molecules to ‘stick’ to each other or to any bounding surfaces. This sticking is called viscosity. In a highly viscous fluid the molecules stick a lot – low viscosity means little sticking. Water and air are somehow in the middle, and again it is up to us CFD users to decide how much we want (or can afford) to care about viscosity. Neglecting friction, that is setting the
viscosity to zero, immediately cancels a couple of terms from the Navier-Stokes equation (for the ones who don’t mind a bit of maths: the weird terms with µ). This inviscid case makes its solution much easier right away and leads to a whole family of very elegant methods known as potential flow methods. One kind of potential flow method is vortex methods, and one of these is the Vortex Lattice Method (VLM), also referred to as Panel Code. The VLM is particularly elegant
because (again due to some fancy maths) it does not even require a grid over the whole fluid domain. A two-dimensional mesh on the model surface (for example, the sail) and in the immediate wake will suffice. This makes VLM very convenient for the modeller to set up. Moreover, solutions can usually be obtained within seconds. On the flip side, potential flow methods are of course limited by their principal
you could dig down deep into the maths, get a massive supercomputer and try to carve out a direct solution to the Navier- Stokes equation in its full beauty. With a solid set of skills this is do-able. It is called Direct Numerical Simulation (DNS) which calculates all the turbulence in the whole domain directly – a massive effort. I personally consider DNS the crown
jewel of CFD, but it is incredibly compli- cated, finicky to set up, and still extremely resource intensive (both brain power and supercomputer time) to wrestle with the equations. DNS is left mainly to academic purposes. Luckily there is one more alternative:
neglecting parts of the turbulence, particu- larly the very small ones, but not ignoring the effects this minor turbulence has on the larger-scale flow. Of course, simply pre- tending that the little turbulence is not there will not be any good. A better approach was put forward by the British engineer and physicist Osborne Reynolds (yes, the same one the Reynolds number is named after). Reynolds suggested, as early as 1895, decomposing the fluid motion into two parts: a time-averaged part, and a fluctuating part. This leads us to the Reynolds Averaged Navier-Stokes equa- tion – the famous RANS. The beauty of this approach is the averaged part becomes much easier to deal with, while the nasti- ness of the turbulence and its little eddies is hidden in the fluctuating part. If for a start we ignore the fluctuating part, we include some of the viscous effect, but largely ignore the effects of small-scale turbulence. Again this may be sufficient and even
very efficient in some cases. But it often (and most likely for the cases we are
DR. SHAHAB YEYLAGHI
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74 |
Page 75 |
Page 76 |
Page 77 |
Page 78 |
Page 79 |
Page 80 |
Page 81 |
Page 82 |
Page 83 |
Page 84 |
Page 85 |
Page 86 |
Page 87 |
Page 88 |
Page 89 |
Page 90 |
Page 91 |
Page 92 |
Page 93 |
Page 94 |
Page 95 |
Page 96 |
Page 97 |
Page 98 |
Page 99 |
Page 100 |
Page 101 |
Page 102 |
Page 103 |
Page 104 |
Page 105 |
Page 106 |
Page 107 |
Page 108 |
Page 109 |
Page 110
