Wake Wash

One problem with measuring gamma is that it becomes intense very near the tip. In fact, theoretically it's singular:
gamma(y) ~ / sqrt(y_tip - y)

One possible way around this is to assume that the spanwise loading

Delta phi(y) = Gamma(y)

is as Prandtl wrote it, with some number of Fourier modes in terms of the alternative spanwise coordinate theta:

y = (b/2) cos(theta)
Gamma = A1 sin(theta) + A2 sin(2 theta) + A3 sin(3 theta) + ... AN sin(N theta)

with N terms used in the sum. This is related to the sheet strength gamma(y) by

gamma = -d Gamma / d y
gamma = [ A1 cos(theta) + 2 A2 cos(2 theta) + 3 A3 cos(3 theta) + ...] / [ (b/2) sin(theta) ]

The idea is to use the measured gamma(y) at N stations to obtain the coefficients A1,A2... by solving a NxN linear system from the equation above applied to the N stations. Or one could use an FFT on the measured gamma(theta)*sin(theta) data. The corresponding lift and induced drag are then obtained immediately from the coefficients:

L = 0.5 rho V^2 pi b^2 A1
Di = 0.5 rho V^2 pi b^2 ( A1^2 + 2 A2^2 + 3 A3^2 + ... )

Or better yet, one could calculate the inverse of the span efficiency, which uses only the coefficient ratios and will be less sensitive to biases in the measurements.

1/e = 1 + 2(A2/A1)^2 + 3 (A3/A1)^2 + ...

 

It will be in a book coming out in about a month:

Flight Vehicle Aerodynamics
Mark Drela
ISBN 978-0-262-52644-9
MIT Press

 

As I could not wait one full month,

I Googlized: Flight Vehicle Aerodynamics

and get an info which can interest CFD rookies who look for self-education opportunities:


You can enroll in:

https://www.edx.org/course/mitx/mitx-16-110x-flight-vehicle-aerodynamics-871

It is recommended to start with 16-101x before 16-110x

Unfortunatly its a bit late for 16-101x , which began Sept 26,
but 16-110x will start early January


Please Mr Drela, is your new book a handbook for these lectures ?

Regards

Erwan

 

Thanks Erwan. I think I will want the book in any case.

If I was to give a down to earth description about the wake wash would it be correct to say:

At the luff, he sail divides the airflow into 2 sheets or layers, one on the windward and the other on the leeward side. When exiting at the leech, the two layers have a shear between them: The sheet of air on the windward side is flowing in a slightly upward direction, especially towards the head of the sail, while the layer on the leeward side is sliding downwards. The layers are also moving at slightly different speed.

You can describe the shear (velocity difference) between the two layers in terms of a vertical, up and down direction, and a horisontal, fore and aft direction.

The vertical, up and down or spanwise component of the shear between the windward and the leeward layers is the source of the trailing vorticity: Swirls extending in the direction of the wind are formed at the leech, their core more or less horisontal (in the direction of the boom), with vortices spinning around the core. These leech trailing vortices account for the inviscid, induced drag of the sail.

The horisontal, fore and aft or chordwise component of the shear between the two layers creates vortices spinning around a more or less vertical axis, in a horisontal plane. This vorticity is the source of the viscous pressure drag of the sail.

Imho, this way it would be rather easy to explain the two sources of the sail drag even to a relatively layman who is not so much into aerodynamics.

 

Thanks for the explanation Mikko,

From my candid perspective, when it comes to sail induced drag, a question arises:

Is it possible to treat sail induced drag independently from wind gradient ?

 

Here's something to think about. These illustrations are from a large-eddy simulation of an AC45-style wingsail section. They show the temporal and spatial development of eddies near the wing surface. The mean flow is fully attached - this isn't a stalled case.

The turbulent eddies can be as large as a typical sensor. Of course, the sensor readings would no doubt be time averaged to try to minimize the effects of such eddies, but it's not necessarily true that the average of the sensor readings would be the same as the measurement of the mean flow. For example, dynamic pressure would be proportional to velocity squared, and averaging the pressures would be like averaging the square of the velocity, which is not the same as squaring the average velocity.

 

Would something like this makes sense? The sensors are small cruciform vanes that are free to rotate. The rotation rate would be proportional to the vorticity being shed from that station along the trailing edge.

 

The V1,V2 velocities I was talking about are in the potential flow. The sensor which measures the angle between them needs to be outside the BL and wake and all the mess in there. The largest eddies inside the BL will still produce unsteady pressures for some distance outside the BL, but they cannot change the time-averaged V1 and V2.

 

Maybe. The vane blades need to be out on radial spokes so that they spend most of their time outside the BL. What needs to be measured is not vorticity (omega), but the integral of vorticity across the BL. This integral is V2-V1, turned 90 degrees.

I still think two 2-hole probes with a diff. pressure sensor would be better. No moving parts.

 

Um.. guys, referring to my post #3, seems I was on the right track then?

 

I think a bigger question here is why do you want to take measurements? Is it for code/theory validation, or is it to be acted on near real time? After spending a decade or so developing near real time measurements of the near body ocean hydrodynamic conditions, I wrote (with what I feel is some authority) in a technical guidance manual that:

"It must be remembered that all (...instrument recorded and processed...) measurements are in the past, never to happen again, and are only tenuously connected with future conditions".

Today, even with the best sensors and processes, 8hz data/display updates, and another decade of operationl use; we can only offer max/min limit predictions, based on stoichastic prameters, just ~100 cycles/~20min into the future. And some environmental effects just cannot be predicted based on onboard sensors, they are not connected with any leading measurable factor.

 

It sounds like you're looking for a simple way for a wing trimmer to know when they've got the right combination of sheeting and twist. What an interesting problem!

The rotatory vanes are a cool concept. Given that a wing would operate without stalling for a lot of the time, particularly when overpowered - you can't change the skin friction / parasitic drag by reducing sail area - the only variable remaining is the induced drag of the rig and heeling moment.

My guess (having never had the luxury of trimming a wing!) is that currently they'd compute twist (or record experimentally, from VPP runs for eg.) for each given wind strength and boat heading. The twist would be pre-set for a given wind strength and heading ie upwind or downwind.
From that point all the wing trimmer has to do is balance the heeling moment and check that he doesn't accidentally stall it if he loses pressure.

So you can see the benefit of having a simple indicator of induced drag. From a trimmer's point of view, you'd only want to deal with say 2 or 3 rotating vanes (or differential pressure tappings) to compare. So before setting them up, it would be best to run some CFD to establish the correlation of spanwise velocity at those points so the trimmer gets the right information.

So what would they do with this information? I would guess -
- in lighter winds, where heeling moment is not an issue: all vanes would spin at the same speed due a constant downwash[in a perfect world]
- in moderate winds, where induced drag is minimised for a given heeling moment, the top vanes would almost stop rotating - because the downwash varies to zero at the tip
- in heavy winds, the top vane would spin in reverse, as the twist at the top would be such that the tip of the wing is providing righting moment

 

Ideally, both. At the design stage, it's all well and good to use a lifting line calculation to get the planform shape or twist, but for a complex configuration it would be good to have a method that could offer design guidance or even an inverse capability based on more sophisticated CFD.

When sailing, it would be very useful to have some kind of indication as to how to trim the sails. Induced drag is the largest source of drag and the only one that is under the direct control of the crew. But it's invisible - streaming telltales don't tell you if the twist is correct.

In aviation, the measurements could be used as feedback signals to optimize the performance or even maneuver the aircraft in a minimum drag manner.

 

My advice would be to tread cautiously here for near real time applications.

What can I measure? How accurate can I measure it? What is the meaning of the measurement? Should I control with this measurement? Those are all different questions that need to fitted into and automatic or agumented system.

Aircraft for years have had automated/agumented systems for economy at cruise. These are fairly straightforward because thrust velocity is much, much larger than encountered vairations in inflow. Similar systems for takeoff/landing have not been so successful because flight velocity is only 2-3 times significant environmental velocity. Sailing, soaring, and dynamic position keeping of ships have similiar issues, variations in environment are large compared to thrust velocity.

Of course, for ditch run speed sailing, it gets simpler if you limit wind speed to between 7 and 9 knots and seas to less than 0.25m. But for "any day, any condition, run-what-you-brought" type of sailing, it is much more difficult.

 

"Induced drag is the largest source of drag"

Are you using the strict aerodynamics definition of induced drag as the drag due to trailing vorticity? Or are you using the popular definition of induced drag as the increase in drag associated with lift which includes the increase in sectional viscous drag?