Concerning the curvature of an airfoil (shape)

I am wondering about the reasons for the shape of a turbine blade airfoil, see here

Do you know the reason for this shape? Usually, very large curvatures like this are to extract high lift from LOW speed environments. But the conditions inside a turbine is the most strenuous for any object, and the speeds are certainly not low (right?)

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Thanks to Rory for the great picture. The difference between a turbine blade and a wing is that.

1. A wing has to impart no more momentum per second to the fluid than the aircraft weighs, or a small multiple of that, in either a positive or negative direction, so it is not changing the direction of flow by much of an angle. During landing, the effective curvature of the wing is increased by using flaps and slats, so the same momentum per second can be gotten at a slower speed.

2. A turbine blade needs to impart maximum momentum per second to the fluid, turning it through as large an angle as possible. What's more, it has to do it at a range of input velocities, from cruising speed down to near zero.

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I just read about wind turbine blades. I think the same principle holds here. Please correct me if I am wrong. The shape of a wind turbine blade seems to rotate from the root to the tip, i.e. the angle of attack varies along the blade. The reason is a varying speed over the blade (speed increases from root to tip, v=wr) and the angle of attack providing maximum lift depends on airspeed. Therefore the blade cross-section varies, but I am not sure the shape itself varies, only the angle of attack. But the angle of attack varies to extract maximum work from the fluid. – l3win Apr 15 '13 at 18:21
@l3win: I think you're basically right. The camber of the airfoil controls how much the flow can be diverted, and momentum flux generated, especially at low velocity and/or angle of attack, without stalling. Check here. – Mike Dunlavey Apr 16 '13 at 0:40

Turbine blades can actually have a very complex shape, which changes dramatically from the root to the tip. That diagram is a little misleading as it only shows one cross section.

The shape at the root is indeed at a high angle of attack, and is quite broad - partly as it needs the strength to cope with the large forces at work in a rapidly spinning blade. Towards the tip the angle reduces dramatically, and the cross section thins out a lot as speed increases.

From blog.nikonmetrology.com

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Very good picture Rory! You mentioned the cross-section is highest at the root. Why are the forces so high in the root? The speed of the blade is lowest towards the root over the entire blade section...? – l3win Apr 15 '13 at 19:54
The force is because the blade is spinning. A wing is travelling in a straight line, but a rotating blade has all the mass of the blade trying to fly outwards! – Rory Alsop Apr 15 '13 at 20:00
Makes sense, all that mass on the rest of the blade is pulling that section outwards, so it has to withstand those forces. In some wind turbine blade designs, this section is circular or elliptical and at high angle of attack, so lift is very low at this section (the relative wind speed is smallest there?) and they focus on withstanding large forces at the root by making the cross section circular/ elliptical. Does the same principle hold here? Don't they pick the shape at the bottom right to maximize lift in low (relative) speeds while withstanding high stresses via large cross-section. – l3win Apr 16 '13 at 3:13
The high force at the root is not entirely due to axial stresses from the centripetal acceleration. A very large portion of the stress is from blade bending. Think about holding a ruler cantilevered over the edge of a desk. If you push down on the free end, the ruler bends. Push down hard enough and the ruler will break at the root. This is the location of maximum bending moment. – OSE Apr 16 '13 at 14:33
Also turbine blades are made to extract energy from the flow. Typically jet engines have many more (axial) compressor stages than turbine stages. This is because the adverse pressure gradient in the compressor makes compressor stall a possibility. In other words, if the compressor tries to turn the flow too much or increase the pressure to much in one stage, the compressor could fail. In turbines, the situation is the opposite. The pressure gradient is favorable allowing large angle changes in the flow without separation. – OSE Apr 16 '13 at 14:38