Hydrofoil Design

Hello everybody,
I have been designing a hydrofoil lately and have tried to optimize it for the lift over drag ratio. Up to this point, I have only been designing the main wing. I am designing this hydrofoil for a surfboard. The requirements for the main wing is for it to have a wingspan of 1m and an area of 0.1m^2. I have also designed it to have an elliptical lift distribution to minimize induced drag. The root cord is 12.7cm and I am designing it to foil at 5m/s.

For the airfoil initially, I was using the airfoil with the highest L/D at my Reynolds number (which goes from 280 000 to 650 000, since the chord of the wing changes along the wingspan). The airfoil that had the best L/D ratio was the FX76MP120 for Reynolds numbers around 500 000. Therefore I designed the wing with the FX76MP120 airfoil.
However, when I simulate this wing in XFLR5 I get a L/D ratio of 26 which is quite a low value.
Then I simulated the exact same wing with the NACA4412 airfoil (which has a lower L/D ratio than the FX76MP120) and this wing surprisingly had a L/D ratio of 31. I have added screenshots of the simulations from XFLR5.
This result confused me since I expected the wing with the FX76MP120 airfoil to have a better L/D ratio. I am not sure how to select the right airfoil for my wing now.

Does anybody know why these strange results appear?

 

First, the Wortmann sections were designed for aircraft and assumed more laminar flow than you will probably experience in water. In XFLR5 I would set 1<Ncrit<3 instead of the default Ncrit=9.

Second, I would be more inclined to keep the trailing edge straight and put all of the planform curvature into the leading edge instead of the curing the trailing edge the way you've done. And while an elliptical lift distribution has minimum induced drag for an isolated wing, a wing with a constant chord center panel and straight tapered outer panels has a drag that is very close to the minimum and is far easier to construct.

But getting to your question, the FX 76-MP-120 is a highly cambered section, intended for high-lift applications. Your best section L/D is occurring at a lift coefficient around 0.4 or 0.5, and the FX 76-MP-120 is just getting started at that lift coefficient. At lower lift coefficients, the FX 76-MP-12o produces a suction peak on the underside of the leading edge that is draggy. When I run the FX 76-MP-120 with Re=500,000 and Ncrit=1, the NACA 4412 has less drag across the whole lift range. You need to match your section to your operating conditions, and I'd say the NACA 4412 is the better choice for you.

You've said you want to take off at 5 m/s. What lift coefficient is that at the maximum weight of board and rider? What is the lift coefficient at your maximum speed for the minimum weight rider? The section should be selected to suit that range of lift coefficients. Your wing area and span appear to have been determined by picking numbers arbitrarily. You may want to consider span and chord separately, putting the span at the maximum you think you can stand from a safety, operability or structural standpoint, and setting the chord to give you the area that results in operating about the best section L/D lift coefficient.

 

Thanks very much for the explanation of the Wortmann airfoil.
I saw that in fact, the drag is lower on the NACA4412 at ncrit=1. However, the L/D ratio of the FXMP120 remains higher at this ncrit value. What also still is not clear to me is why XFLR5 calculates the L/D of the FX76MP120 airfoil to be higher than the NACA4412 but then in the wing at the exact same flow conditions, the wing with the NACA4412 has a higher L/D ratio.

Further, I didn't pick the numbers arbitrarily, the wingspan needs to stay under 1m for ease of carrying it around. Further, the weight of the board and the rider would be around 80kg. With a Foil with an area of 0.1m^2 riding at a velocity of 5m/s, a lift coefficient of 0.63 would be needed which is generally a good range for airfoils.

 

The only elliptic wing that satisfies both the Kutta condition and optimal L/D is a flat wing. If you add camber, e.g. parabolic camber, then the vorticity density is no longer elliptic (it's a sum of elliptic and parabolic) and L/D is no longer a maximum. You can calculate the integrals for the induced drag but they are tedious. I would guess you're still near optimality but that's only a guess. There are other factors than optimal L/D that affect performance. E.g., flat propeller blades are a thing of the past.

 

Hi, sorry to interfere with your questiin. Regarding my earlier post to this forum, how do you determine the needed lift coefficient, in relation to weight? It relates to foil loading(area)?

 

Lift coeff. is weight-independent. My lift coefficient that works for 3 dimensional flows is acosb where a=trim angle and b
deadrise angle. There's also a factor for aspect ratio.

 

You assume equilibrium in level flight.

For an upright foil, Lift = weight, so CL = weight/(0.5*density*speed^2*reference area)
The foil loading is weight/(reference area), so CL = loading/(0.5*density*speed^2)

For a kite foil that is heeled over, you have to include the force from the kite as well. If theta_kite is the angle the kite's tow line from the horizontal at the board, the vertical component is weight - tension*sin(theta_kite). The horizontal force is tension*cos(theta_kite). The foil's lift vector needs to be oriented from the vertical by
phi_foil = arctan(cos(theta_kite)/[weight/tension-sin(theta_kite)])
and the magnitude of the lift increased accordingly when estimating the lift coefficient.

 

Steady running. The boat is neither lopping nor wave jumping. I wrote about a boat, not a kite on a cord.

 

Sorry, I didn't look back through the thread to find your original question. The same thing goes - lift=weight, and you get the lift coefficient from that.

 

The lift coefficient is defined independently of weight. E.g., the lift coefficient for a wing is the same whether the wing carries more than the plane's weight and lifts off or whether it only accelerates down the runway. In planing, lift≈weight when buoyancy is negligible but the lift coefficient is the same in all cases.