Hydrofoils 4. Drag

a) Principle

Drag is the force which opposes the movement of hydrofoils and should therefore be minimum. There are two ways of achieving this goal : either by reducing the profil drag or by reducing the induced drag.

• The profil drag is due to the viscosity of the fluid which creates friction. Indeed, close to walls, the flow is slowed down by the friction of the fluid on these walls. This zone, (in our case, close to the hull and the foil) is called boundary layer.
• The induced drag is due to the fact that a wing (or a foil) is never infinitely long. Consequently, at the trailling edge the fluid coming from the upper surface and the one coming from the under surface have neither the same speed nor the same pressure. The homogenization of these quantities downstream from the wing creates spanwise eddies which dissipate energy. They form what is called the wake.

b) Experiments

How to mesure drag?
In order to mesure the drag created by a foil, we had to seperate it from the hull so that we could fix it onto a balance dedicated to the mesurement of drag.

Principle of the mesurement
We then proceeded in two steps. First, we had to adjust the balance (ie. adjust the position of its left weight) in its reference state which defined when there is no flow. In order counterbalance the effects of the foils, we moved the left weight horizontaly until the top rod was horizontal again. This settled the reference state.
We then could measure drag for different flow rates. For each measurement, we added weights on the right part on the top rod in order to maintain the equilibrium.

Vidéo 2.31 Mo

Knowing the added weight, the drag intensity can be calculated by using the equality of the moments which reads :

• M is the added weight
• g is the acceleration of gravity
• 0.590 and 0.200 are respectively the distances (in meters) from the profil and the added weights to the axis of the balance

Thus, we can calculate the drag coefficient :

• Sref is a reference surface of the foil. Nous prendrons ici la surface représentée par la largeur du foil fois sa longueur. Now, as we have already seen in en Insérer Lien vers III.2 Notre hydroptère, our two foils have a 230 mm width and a 200 mm length, which implies a Sref=0.230*0.200=0.046 m2 surface of reference.
• Q the flow rate of the canal.
• Scanal, the section of the canal (we will have to note the water height after each measurement).
• the x vector corresponds to the represent the unit leading vector of the horizontal axis.

Visualization of the wake
In order to study the wake created by a foil (here, by the asymetrical foil), we injected a colorant in the upstream section. In theory, this method can be used to see a potential burbling phenomenon, but also to see the eddies created at the trailling edge. Unfortunately, the colorant disperses too quickly and we can, therefore, not draw any conclusions from these experiments.

No incidence Vidéo 3.35 Mo

Strong incidence Vidéo 3.72 Mo

c) Results

After some calculations, we obtained the following graphs. The coordinates of all the points are also available.

Evolution of Cx function of the incidence of the NACA 0015 profile

Comments:
First, let us note that the general aspect of the graph is more or less the same as the one we took as a reference (the one from the Rebuffet). Yet, all the values obtained experimentaly are ten times too big. We checked all are calculations and did not find any mistake. This wide gap can maybe be explained by the fact that Cx is always obtained through experiements. The conditions of the experiments that led to our reference values were perhaps quite different from our conditions. Moreover, the reference surface used in the calculations are not always specified, and it is very difficult to estimate the section of the flow since the foil reduces it.

Evolution of Cx function of the incidence of the EPPLER 817 profile

Comments:
As for the NACA profile, the general aspect of the graph is correct but a values should be divided by ten to fit with the reference values.
Anyway, we should bare in mind that the Cz and Cx coefficient are always determinded thanks to experiements and therefore depend from the conditions of the experiment. In our case, for example, the size of the canal creates side effects that can not be neglected. Moreover, Cz and Cx are not really constant : they vary with the Reynolds number. Finally, our profile were not perfectly smooth and small eddies were maybe created, thus modifying the drag.

Comparison of the lift/drag ratios for both foils :
We had decided to make the second foil (Eppler 817) in order to obtain better performances. Indeed, the NACA 0015 was already efficient but raised technical problems linked with the incidence adjustment.
As regards to the drag and lift results for both studied foils, we decided to compare the lift/drag ratios for the same run-off in the canal and the same incidence. We thought we would have obtain a higher ratio in the optimized Eppler 817 case .
Two examples are presented in the following table :

In both cases, we have a higher lift/drag ratio with the Eppler than with the Naca.

It must anyway be taken into account that the "protocole de mesure" for lift was not very reliable and that we didn't have many results with the same conditions for incidence and run-off , it seems difficult to find any law which would link the lift/drag ratios of both profiles together.