# Airfoil CD and CL values in air and water

Discussion in 'Hydrodynamics and Aerodynamics' started by passenger12358, Dec 6, 2013.

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### passenger12358Junior Member

Hello everyone,

I'm doing some calculations related to hydrofoil thrust generation, but due to the lack of my experience in fluid dynamics there are slight problems I hope you guys could help.

We have selected a hydrofoil profile which is symmetrical NACA 0012. We have also found a document, which lists coefficient of drag and lift (C.D and C.L) values as a function of Reynold's number and AOA.

Coefficients: http://mac6.ma.psu.edu/VAWT/Sand80-2114.pdf

The problem is that we don't know if those values are correct for water as a medium (as they are for air), and if not, is there a standard way to scale them? Or is the difference in medium taken into account with the Reynold's number and the coefficient can apply to any medium that has the same Re value?

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### johneckSenior Member

The Cl and Cd values are independent of the fluid that the foil is operating in. As long as they are appropriate with regards to Reynolds number and Aspect ratio, when you re-dimensionalize you will get the correct lift and drag.

The only additional parameter to be aware of is cavitation in water. If that occurs it will lead to a change in the lift and drag coefficients.

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### passenger12358Junior Member

Great, thank you sir!

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### passenger12358Junior Member

Sorry to bother again, but one more thing about drag and lift coefficients.

Most tables and graphs I have seen list C.L and C.D as a function of AOA which ranges from 0° degrees to higher. But in a case of an oscillating foil for example, the AOA can also be negative. How would the C.L and C.D be determined in that case? If the foil is symmetrical, are the coefficients also symmetrical around 0°

For example, if C.D+α5 = 0,01 then C.D-α5 = 0,01? If this is the case, how are the drag coefficients of negative AOAs defined for asymmetrical foils? Does same apply for lift coefficients too?

Thanks again

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### DCockeySenior Member

For symmetric airfoils:
CL(-alpha) = CL(alpha)
CD(-alpha) = CD(alpha)

If the hydrofoil angle of attack is changing rapidly the instantaneous lift and drag will not be the same as the steady state lift and drag of an airfoil at the same angle of attack.

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### jehardimanSenior Member

For a NACA 00xx shape they, Cl and Cd are symetric about AoA = 0. Which is why the are generally not used for load supporting hydrofoils, but rather for control surfaces. If you use it for a load supporting hydrofoil (as opposed to say an oscillating propulsor), you need to make sure you account for/control for any variation in AoA due to wave orbitals and dynamics or you will have a very painful "crash and burn".

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### DCockeySenior Member

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### passenger12358Junior Member

Thanks for the quick answers, helped a lot

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### Jim CaldwellSenior Member

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### tspeerSenior Member

The published data are for steady-state conditions. For a symmetrical section, the data would be symmetrical about the origin for positive and negative angles of attack.

However, for your application, you are not talking about steady state conditions - just the opposite. There will be a significant difference in lift and drag/thrust at a given angle of attack depending on the history of the rotation and translation of the foil. This is especially true if you are oscillating at a frequency fast enough that the starting vortices shed into the wake due to the change in lift haven't had time to convect to a large distance away from the trailing edge. (High reduced frequencies.) In such a case, coefficients will be frequency dependent. Look up Theodorsen and Wagner functions.

In addition, particularly at low Reynolds numbers, there can be significant aerodynamic hysteresis. This is when there is a difference in the lift and drag when sweeping in a positive direction vs sweeping in a negative direction. It is usually due to some form of flow separation. For example, when starting with attached flow, if you sweep in a positive direction past stall, the separation can persist as the angle of attack is reduced to well below stall. At some point, the flow may reattach and the lift curve will jump back to the same value it had when sweeping in the positive direction.

Take a look at http://ho.seas.ucla.edu/wp-content/uploads/2011/04/237.pdf for an integrated look at unsteady aerodynamics and structural flexibility on thrust from flapping wings.

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### passenger12358Junior Member

Interesting, I didn't think about the effect of the oscillation frequency to the steadiness of the flow but it makes sense now that you mentioned it. I'll look into that as well.

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