Reynolds number dependence of AFT performance?

[petebachant]

Chamorro et al. (2012) showed that an AFT wake became Re-independent at Re_D ~ 10^5. I haven't see much about the performance of AFTs though. I know that a low-Re model will need a different blade, which I guess shows it right there. Any concrete references for purely scaled HAWTs at low Re?

[wosnik]

Have you looked at the blade profiles used in:

Walker JM; Flack KA; Lust EE; Schultz MP; Luznik L (2013) Experimental and numerical studies of blade roughness and fouling on marine current turbine performance. Renewable Energy, 06/2014; 66:257-267.

[petebachant]

Note this paper was published in 2014. The Reynolds number was actually quite high--Re_c = 4 x 10^5. Not seeing much on the Re effects on performance either unfortunately.

[wosnik]

Yes it is quite a high Re# - but here is the Reynolds number dependence bit: They selected a NACA 63-618 foil instead of the one specified for the RM1 design, since the lift coefficient is Reynolds number independent in their operating range for this foil.

[petebachant]

I have that Miley paper and they test a 63_1-412, not a 63-618. Not sure if that matters.

[wosnik]

I did not read the Miley paper, but do recall that Karen Flack mentioned that they struggled to find a foil shape that is Re# indep't at the scale and Re#.

[petebachant]

Interesting. I guess Re dependence of an AFT is basically just that of a fixed wing. If you check out the paper, I think I am showing that for a CFT the kinematics of the blade motion matter, and that CFT Re-independence is driven by more than just Cl/Cd of the foil.

[petebachant]

So I went through and calculated the torque contribution from an AFT blade element, searching for the highest value for many angles of attack and pitches. I got this:

The conclusion being that you can design an AFT for to be much less Re-dependent than a CFT by dropping the angle of attack (raise TSR), since it's constant. This logic may be messed up though since it doesn't take into account the relative velocity.

Getting these values for optimal angle of attack and pitch:

12.5 80.0
13.5 78.5
14.5 78.0
15.0 77.5
16.0 76.5
17.5 76.0
17.0 76.0
17.0 76.0
17.5 75.5
17.5 75.5
17.0 76.0

[wosnik]

See attached notes for definition of relative velocity and blade angles. It is a bit more complicated, with axial and angular induction, although a=1/3 and a’=0 are reasonable values for outer blade segments.

[petebachant]

My logic was that all things being equal, induction factors really wouldn't change that much between Reynolds numbers. That's really what I'm trying to predict--the Re-dependence of AFT performance, not the absolute values or whatever. I took the formulas from the MMR book. Here's a code snippet:

    alpha = np.linspace(0, 20, num=81)
    pitch = np.linspace(-90, 90, num=361)
    alpha_rad = alpha*np.pi/180.0
    pitch_rad = pitch*np.pi/180.0
    ctorque = np.zeros((len(alpha), len(pitch)))
    for n, ai in enumerate(alpha_rad):
        coeffs = lookup(ai/np.pi*180.0, Re, foil=foil)
        ctorque[n, :] = coeffs["cl"]*np.sin(pitch_rad + ai) \
                      - coeffs["cd"]*np.cos(pitch_rad + ai)

[petebachant]

Similar Re dependence for an AFT was seen in Krogstad and Lund (2012): https://drive.google.com/file/d/0BwMVIAlxIxfZZm0zWlM2M3lXQVk/view?usp=sharing

[petebachant]

This was described in Krogstad and Adaramola (2012) in more detail.