# Thrust of an oscillating foil

Discussion in 'Hydrodynamics and Aerodynamics' started by passenger12358, Dec 7, 2013.

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### passenger12358Junior Member

Hello,

I have read several research papers about hydrofoils that undergo oscillating movement underwater, but I'm not entirely sure if I understood the theory correctly. Most of the research is based on testing of small scale prototypes, which are used to get accurate data about the motion of the foils, so in that sense not that many studies are concerned with the mathematical models.

Lift itself is not the main concern of a hydrofoil that oscillates, but the thrust it provides. The thrust force is exactly the thing that I'm not sure about.

Oscillating in this sense means that the hydrofoil is both heaving and pitching, so the angle and the vertical position of it is changing with time back and forth.

For example, one research paper* named 'A numerical study of the propulsive efficiency of a flapping hydrofoil' states that

'Since the hydrofoilâ€™s main task is to produce thrust, it is often more convenient to think in terms of thrust instead of drag. Thrust is equal but opposite in direction to the drag force, therefore one has'

CT = -CD = T / (0.5 * rho * U^2 * c * b)

where
CT thrust coefficient
CD drag coefficient
T thrust force
rho density
U = velocity of the flow
c chord of the foil
b span of the foil

If this holds true, then we can calculate the thrust force T for each AOA of the foil with different CD value and then get the average for one oscillation period. Of course there needs to be some power source to oscillate the foil. But is the model or my thinking valid about how to calculate the thrust?

I understand that when the hydrofoil is in the water, it causes drag because it resists the motion of the water (if there is velocity difference). In order to the foil to keep moving forward, it needs to generate at least the same amount of thrust as there is drag, in which case the velocity would stay constant. And when the foil starts from still, it needs generate more thrust than there is drag.

* http://www.engr.uvic.ca/~ndjilali/Papers/IJNMF_Pedro et al_2003.pdf)

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