Wake Wash

Thank you very much Mr Drela,

It will be very helpfull, I have to chew it a little bit then and I'll try to make some calculation to appraise the pressure on an end-plate on both sides of the foil.

I guess the assumption: "At large distances" means distances that are >> than the boundary layer thickness.

Thanks Mr Speer,
As above-mentionned, I'd like to understand the pressure effects of circulation on an end-plate, that is why, the velocities/pressures (2D) datas from XFOIL seem OK for me.

Or presented differently, you put your foil in the wind-tunnel, and use the wind-tunnel walls as end-plate in order to work in 2D (neglecting the boundary layer effect on the walls, or using some "boundary layer traps", like those could be seen at the entrance on some jet-engines).

Thank again for taking time to post these very precious and pedagogic comments.

Cheers Everybody

Erwan

 

"Large distances" in the context Mark Drela used means large compared to the airfoils chord. The relationships he gave are based on potential flow and do not consider boundary layer effects.

 

Some airfoil codes allow the user to specify closer "off-body points" where the flow can be calculated. I don't know about XFOIL specifically, but I'd be surprised if it did not have this option.

Actually, by including a source term proportional to the drag, boundary layer effects are accounted for (at least in the region outside the boundary layer).

 

Not necessarily. A source term proportional to drag models the wake displacement effect which are caused by the velocity deficit in the wake due to viscous effects. If the flow is attached the entire length of the airfoil to a thin trailing edge then the wake velocity deficit is due to boundary layer effects only. But if there is separation upstream of the trailing edge, or if there is a blunt trailing edge/base then the wake velocity deficit will be larger than that of the attached boundary layer.

Also, the source term proportional to the drag is only a good approximation at distances which are large compared to the airfoil chord, not just the boundary layer thickness.

 

It's more complicated.

For distances greater than the chord but smaller than the span, the wing looks like a 2D vortex line and a source line along the span. Their velocity perturbations decay as 1/r , which is what I gave.

For distances much greater than the span, the wing and its wake looks like a semi-infinite z-doublet line trailing back from the wing. It's velocity perturbations decay as 1/r^2. The expressions are messier, but still analytic.

For intermediate distances there is no analytic relation for the perturbation velocities, and a panel code or a vortex lattice code is needed to quantify them.

 

Ok, so the visualization shows an airflow sheet just above a fixed smooth surface to which the vessel model is fixed, which is why there can be an upstream distrubance driven by control volume limits. Have you actualy done a sensitivity analysis on your input conditions? You mention cyclic variations in L&D, have you correlated those to any inputs? I have been involved with several CFD codes/projects where everybody thought the model was performing correctly until we started in on a sensitivity analysis.

FWIW, from an engineering perspective, even with a perfect model, loads will vary 10% just from the local environment. You get very different loads in the Barrents in January than from the Cebu in July even in dead flat seas.

 

Thank you very much for all your contributions for this question.

Sorry, I should have mentionned I'd like to focuse on distances between 0 and 1 chord lenght perpendicular to the wing section.

May be at this distance, pressure coefficients from XFOIL could provide a good starting point?

Or the above-mentionned equations par Pr Drela, could be a good proxy for Cp calculations?

Thanks again

Cheers

Erwan

 

So do we have to conclude there is nothing we could measure in the real world or simulated wake wash that would help us optimizing the sail for induced drag? On the other hand, is it certain that minimum induced drag, for say a given heeling moment, will result in max performance for the the boat?

 

I recall a thread several years ago which discussed research on wing shapes for minimum induced drag when the wing root bending moment is constrained. The lift distribution was considerably different than elliptical in some cases.

Mathematical rather than real world, a 1950 NACA Technical Note by RT Jones on:
The spanwise distribution of lift for minimum induced drag of wings having a given lift and a given bending moment http://digital.library.unt.edu/ark:/67531/metadc53315/m2/1/high_res_d/19760012005.pdf

 

I'd like to rephrase the first question as, "Is there a sufficient condition for minimum induced drag that can be determined from near-field measurements?" My original idea may not be valid, but I'm still not convinced that nothing can be done is this direction.

The answer to the second question is, "No." Nothing is certain in yacht performance when optimizing a portion of the boat. I learned that when I created a simple landyacht VPP and arranged it so the maximum aerodynamic lift/drag ratio occurred below stall. I was surprised to see that maximum performance still happened at maximum lift, even though the rig was over-trimmed. The reason turned out to be that although the aerodynamic L/D was sub-optimal, the added side force improved the L/D of the chassis, and that improved the performance of the yacht.

However, minimum drag for a given heeling moment is a darned good place to start. If you can vary the lift while maintaining minimum drag within the stability constraints, then you can search for the global combination of lift and center of effort that does maximize the performance. And the ability to know what to do to minimize the drag under non-uniform/non-standard conditions would be of immense value. As would the ability to know where to make local corrections to reduce the drag.

 

I'd say yes. The appropriate near-field measurement is the spanwise load distribution. This gives the wake potential jump (= circulation = 0.5 V c cl ),
which is sufficient to determine induced drag via Trefftz-Plane relations. The necessary calculations are in the PDF I posted a while back.

Incidentally, the way Boeing extracts induced drag from CFD solutions is precisely this way. In a potential code like PANAIR or TRANAIR, they have the potential jump explicitly. In an Euler or Navier-Stokes code they integrate the surface pressures to get the potential jump.

 

OK, let's say one can make, say, 50 measurements within 1 m of the surface. The measurements can be pressure (static, total or impact), velocity via ultrasonic sensor, or some other - you specify. There would also be some auxiliary measurements, such as apparent wind speed and direction at, say, 1 - 5 locations. As well as the positions of all the relevant structure (wing/mast rotation, flap angles, sail shapes via photogrametry, etc.)

It's not practical to capture the pressure distribution over the surface with sufficient resolution to integrate the pressures to get the spanwise load distribution.

So what measurement regime would allow the real-time optimization of induced drag? It's not necessary to determine what the drag actually is, provided that one can determine a sufficient condition to know how to correct toward the minimum and to know when one has arrived at the minimum.

Would it be possible to take the difference between pairs of velocity measurements on opposite sides of the wing (outside the boundary layer) to get the circulation at that spanwise station? The velocity perturbation due to thickness would be symmetrical and cancel out. What about a wake measurement in conjunction with velocities further forward?

 

Ok, thank you, I will try to take a thorough read at that PDF to understand it better. Which brings to mind, is there somewhere more of this excellent reading available?

 

Yet that's exactly what David LePelley & co are trying to achieve in Auckland, with some success. That would give a new motivation for direct pressure measurement?

 

Yes. I mentioned this some time ago. The PDF figure shows the two velocities V1,V2 on both sides of the wing wake. Their difference is the trailing vortex sheet strength gamma, rotated 90 degrees. We also know that
gamma = [ -d(Delta phi)/dy ] x_hat
so in principle you could integrate the measured gamma(y) to get the loading Delta phi (y).

The best place to measure (V2 - V1) would be at the trailing edge. In fact, I think this is precisely the "wake wash" velocity that you're after in this thread. It's not affected by the wing airfoil's near-field velocities, because those disappear when you take the difference. It also persists unchanged into the Trefftz Plane, because Delta phi persists along average streamlines.

Because V2-V1 is small compared to their magnitudes
V1 ~ V2 ~ V_inf
you're really trying to measure the flow angle between V1 and V2. On average the angle is comparable to the wing induced angle
alpha_i ~ CL / (pi AR)
Ideally you want something like a "differential alpha sensor" with two vanes -- one vane above the wing and one vane below. The sensor measures the misalignment between the two vanes. Instead of the vanes, one could use two 2-hole probes together with a differential pressure sensor.