Wake Wash

Sometimes it depends on the wing planform shape.
We have discussed the circular planform planar wing previously.
For that case, VLM is not reliable and nor are the induced drag estimates.

 

By the way, I have some doubts about your results in the paper on planforms.
You assumed the inviscid, potential flow even for a very small gap. That leads to optimal planforms that are closer to the full ellipse than to semi-ellipse for gaps as small as 0.01.

However, the flow through such a small gap cannot be still treated as inviscid. Consider the simplest case of an elliptic wing with the elliptic gap in its center. You can obtain the flow around it by a superposition of the wing with another wing of the span equal to the gap width, that produces a negative lift of the same circulation.

Let's analyze the wing of tha aspect ratio 4, with a gap 0.01x wing span.
Then, the downwash behind the wing will be about 1/12*V_infty, while upwash behind the gap is 100x bigger, 8x bigger than the free stream speed!
That seems to be quite unrealistic.

The assumption of potential flow means, that there is no circulation around the gap and no pressure drop between the upper and the lower side of the gap. The real flow through the small hole is, however, closer to that known in the plenum chamber hovercraft theory: the leak velocity is equal to
sqrt(2 delta p/rho),
and the effective leak area can be as small as 1/2 of the gap area. On can estimate the additional drag produced by a small gap as
D~L*A_wing/A_gap
In our case it's 0.01*L, while your result was about 0.45*total induced drag for the best planform.

It's obviosly much harder to estimate the drag of the moderate sized gap, but it should be still less than your predictions.

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It's also interesting to find the optimum planform for a sail that works in a non-uniform velocity field due to the vertical wind gradient. The variation methods presented in Mark's paper suggest that the optimal downwash distribution in the Trefftz plane should satisfy the condition:
w(y)/V_infty(y) = const.
for the less drag at a given mast height, or:
w(y)/V_infty(y) = -a*y+b
for the less drag at a given heeling moment.

What sail shapes will we obtain then?

regards

krzys

 

Don't think that's right. You need to look at the strength of the trailing vortex being formed, and that is due to changes in actual lift (rho * gamma * V), regardless of stream velocity. I think the desired lift distribution is independent of velocity gradient with respect to induced drag, but the spanwise twist in AoA created by boat speed certainly changes things. All twist being bad, and less twist being less bad.

Which brings up the nontrivial question - what is the speed ratio that produces the greatest increase in induced drag, assuming a H^1/7 gradient and the optimal pointing angle for that speed ratio? It would be an interesting plot of 'extra' induced drag vs speed ratio.

 

And well, you should, too. The simple theory isn't really valid for small gaps, as you point out. You can see this in the last figure of the report, where I compare the simple theory to Hoerner's experimental results:


For the experimental results, the ground effect sets in much earlier. This is probably due to viscous effects, as you suggest.

I'm sure there are also issues with the free surface results as the foil gets close to the surface. At some point nonlinear effects are going to become significant compared to the linearized free surface condition.

 

I noticed waves in that second video which effects the airflow, but not corresponding vessel pitch (i.e. the sail is fixed). FWIW, I think that looking at this problem without vessel motion is just bottle washing and button sorting. Too much is driven by motion effects to make CFD a meaningful touchstone except for order of magnitude. I've collected enough data to confirm the "butterfly effect" for things like this. <shrug>

Edit to add, not that some theories can be used to bound the problem, or that there aren't strange attractors, but that one should not expect a consistent answer.

 

Hmm... I don't think the "waves" you see in the sim have anything to do with chaos theory's butterflies and attractors ;-). It would rather seem to be a consequence of the mast disturbance on the sail, producing a cyclic variation in the flow pattern over the leeward luff of the sail, and hence in the whole flow domain. This is a transient, time dependent analysis - the lift & drag, too, vary in a cyclic manner at a surprisingly long period of 5 second or so, and at a large amplitude. This is a rather a low Re-nr flow, at AWS 4,4 m/s only (and a 80 mm long mast). The inflow has a considerable turbulence intensity (5%), so it might have an effect. I should re-run with less or no free stream turbulence to see what difference that makes.

As to the vessel motion, since this is a light wind simulation (TWS about 6 kn), the sea would be flat and the motions of the boat negligible. The motions do influence a lot the intantanious the forces, but much less the average, and you can simulate motions, too - see for yourself. As to the accuracy of CFD these days, we are much closer to reality than the order of magnitude, not sorting buttons anymore...

 

Exactly. It's, however, not trivial to prove that the lift is equal to rho*Gamma*V in the case of non-uniform speed.

If we assume that's true, and the drag is equal to
Int rho*Gamma*w dy
where w is the downwash velocity, we have the variational problem:

Int Gamma(y)*w(y) dy=min

with the condition:

Lift = Int Gamma(y)*V(y) dy = const

The condition leads to:

Int delta (Gamma(y)*V(y)) dy = 0

and we can rewrite the minimum drag equation in the form:

Int (Gamma(y)*V(y)) * w(y)/V(y) dy = min

which immediately gives

w(y)/V(y)=const

Similarly, you can analyze the case of constant heeling moment.

The apparent wind twist is another problem. Does it produce any additional drag, provided that the sail is correctly twisted? I have a hypothesis that it doesn't, but can't prove it yet.

Anyway, what we should maximize is the total thrust force for a given heeling moment at a desired speed and twist of the apparent wind. Not easy...

regards

krzys

ps. Tom, thanks for your comment and the picture.

 

The very meaning of lift and drag in a sheared flow is problematic. Lift is defined as being perpendicular to the freestream direction, and drag is parallel to the freestream direction. In a sheared flow, each spanwise station has a different freestream direction. So what direction should be chosen for the total lift and drag components of the entire surface?

One can, of course, abandon lift and drag entirely and go with normal force and axial force in body-fixed coordinates. This complicates performance analysis because now the body's orientation is a required variable. When the performance is analyzed using lift and drag, the actual orientation of the body frame is irrelevant.

 

As you know, I have been a proponent of body forces for sailboats... amongst others for exactly the sheared flow problem you mention. Although the convention is to measure the wind speed & direction at the 10 m height.

However, the body frame is relevant for instance when working with VPPs, to incorporate the effect of leeway on the rig & sail geometry. Most VPPs rely on lift & drag, ignore the leeway, leading to less accurate performance results. At least for existing boats, the body's orientation is a variable.

 

Tom, here's another problem with your hypothesis. In the original post of this thread, you say :

This statement is true only for an unswept lifting line. For a lifting line with specified vorticity distribution, adding sweep causes no change to the wash in the Trefftz plane, but it causes inboard filaments to have stronger influences than outboard filaments in the near field. Therefore, the shape of the wash in the near field is not always the same as the shape in the Trefftz plane.

 

Yes, that is one of the things that needs to be worked out. It's much the same problem as a planform with a curved trailing edge. Should the measurements be taken in a single plane, similar to the Trefftz plane? In that case, the near-field shape of the wake immediately behind a swept lifting surface might need to be whatever it takes so as to achieve the desired distribution in the measurement plane. The measurements might still be used as feedback to the local lift of the swept planform to achieve the desired effect.

 

Correlation between circulation & pressure field

Hi Everybody,

As you are already mentionning circulation , induced drag issues, and I would not dare to start a new thread as it could be a dummy question, that is why I first post it here but can move to another place if off-topic

So here is the dummy question.

1-Starting from a XFOIL velocity/pressure distribution (2D)

Is it possible to make a plot of pressure fields on both sides of a foil
The idea is to see how far from the foil surfaces, the low (high) pressures of the upper (lower) side of the foil can be mesurable, and how it is supposed to decay with increasing distance from the foil surfaces.

In other words, consider a foil with infinite aspect ratio in a horizontal plane
put a plate @ 90° from the foil (vertical plane) aligned with the fluid stream
just like for an end-plate effect.

If you can put pressure sensors everywhere on the vertical plane, you should get a map of the pressure fields above (negative pressure) and under(positive pressure) the foil at different distances from the foil surfaces.

I d like to find a theorical relation, to find the magnitude of the pressure & distance from the foil surfaces.

If totaly stupid , just let me know, I will not be offended.

Cheers Everybody

Erwan

 

At large distances, the flow about any 2D object looks like 2D vortex whose strength is the lift (via Kutta-Joukowsky), plus a 2D source whose strength is the profile drag. Defining x to be along the freestream V the fractional x,z perturbation velocities are:

u/V = [ cd x/c + cl z/c ] / [ (x/c)^2 + (z/c)^2] / (4 pi)
w/V = [ cd z/c - cl x/c ] / [ (x/c)^2 + (z/c)^2] / (4 pi)

and the pressure coefficient is
Cp = -2 u/V - (u/V)^2 - (w/V)^2 ~ -2 u/V

The "wake wash" angle is simply w/V.

The above relations are strictly correct only for thin airfoils, and assume the x origin is at the lift centroid. For more accuracy with thick airfoils and shifted origins, you can add an x-doublet whose strength is the normalized airfoil area, kx = A/c^2, and a z-doublet whose strength is the pitching moment coefficient cm about the x,z origin.

 

Mark, isn't the x-doublet strength also dependent on thickness or is the thickness incorporated into the definition you use of normalized airfoil area?

 

I think a 3D panel code would be better than a 2D calculation from XFOIL.

As Prof. Drela points out, the velocities drop off roughly as 1/r^2. We used this effect to estimate the position error of the wind sensors on USA 17. There were two sets of wind instruments at the head of the wingsail, separated vertically by about a meter. The difference between the sets of instruments was attributed to the perturbation of the flowfield by the wing itself, and corrections based on the difference were applied to get the apparent wind speed and angle without the effect of the rig.

There were also wind instruments mounted to each outer hull of the trimaran. In principle, the difference between the windward and leeward instruments should have given us some indication of the circulation toward the bottom of the rig. The difference between the two instruments at the top might have indicated the circulation there as well. So it should have been possible to deduce both the lift on the rig and the wind shear between bottom and top. However, this would have required a pretty good model of the distributions of lift and shear to get that much from just four measurement points.