Principles of Yacht Design by Larsson Lars;Eliasson Rolf;Orych Michal;

Author:Larsson, Lars;Eliasson, Rolf;Orych, Michal;
Language: eng
Format: epub
Publisher: Bloomsbury Publishing Plc
Published: 2022-08-15T00:00:00+00:00

Fig 8.13 Flow around a mast/sail combination

MEANS FOR REDUCING MAST DISTURBANCES

A well-known but seemingly paradoxical phenomenon in fluid dynamics is the reduction in drag of bluff bodies when their surface is changed from smooth to rough. As we have seen in Chapter 5 a rough bottom of a yacht causes a considerable resistance increase. The reason for the different behaviour is that the viscous resistance of the hull, which is a slender body, is essentially due to direct friction (see Fig 5.4), while the resistance of a bluff body to a large extent is due to pressure losses in the wake (viscous pressure resistance).

Let us return to Fig 5.5, showing the different regions in the flow around the hull. It can be seen that the boundary layer is laminar at the bow, but undergoes transition relatively quickly. Thereafter it is turbulent, and may, in rare cases, separate from the hull at a point near the stern. The same flow regions may exist around the cylinder, but not always. If the Reynolds number (i.e. the product of diameter and velocity, divided by viscosity, cf Fig 5.8) is small, the boundary layer never gets turbulent, but separates directly in the laminar part. This happens, in fact, before the maximum thickness (as shown in Fig 8.14). The wake then becomes quite wide and the drag is high. On the other hand, if the boundary layer gets turbulent before separation, the latter is delayed to a point well aft of the maximum thickness (see Fig 8.14). The wake is then narrower and the drag smaller. The reason why turbulence delays separation is that it has a stirring effect on the flow. High-speed fluid from outside the boundary layer is convected inwards and energizes the flow that is about to stop moving along the surface.

With this explanation in mind it is not difficult to understand why a rough cylinder may have a smaller resistance than a smooth one. If the Reynolds number is in the subcritical region, and laminar separation occurs, introducing roughness causes the boundary layer to turn turbulent earlier, maybe before separation. This is then delayed, as just explained, and the drag gets smaller. Now a mast is normally in the subcritical region and has a high drag, but it is close enough to the low drag region to make the roughness trick work. Fig 8.15 (overleaf) shows the drag coefficient of circular cylinders of around 0.1 m in diameter with different roughness heights. The height is given as a percentage of the diameter. It may be seen that at 11 m/s the drag is reduced by 50% if the roughness height is 0.5% of the diameter. The narrower wake also disturbs the sail much less, so there is a double gain. Unfortunately, the optimum roughness height varies with the wind velocity, but a height of 1% covers most of the interesting velocities quite well. Note that it is the apparent wind that is of interest.

Fig 8.16 shows results from measurements made by one of the authors and his students.

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