CFD sail trim optimization

[jlconger]

I have been experimenting with using a 3D OpenFOAM CFD model to 'optimize' sail trim. The test case is a J/32 fractional sloop. The CFD model has been calibrated against the performance of the real boat before starting the optimization (https://sites.google.com/site/sailcfd/home/calibration).

The concept behind the optimization was to allow the CFD model to pick the jib and mainsail sheeting angles and sail shape at each point of sail, attempting to maximize either VMG (close hauled) or boat speed (all other points of sail). Essentially the model was allowed to cut new sails as needed for each point of sail - just to see where this would take us. Simulations used moderate wind speeds and flat seas, so controlling boat heel was not a major driver.

The preliminary results are shown in the attached figures, along with a typical image from the simulation. Some comments:

1) The 'optimum' angle of attack for both sails steadily increases as the apparent wind moves aft.
2) The 'optimum' camber of both sails increases to a point, and then levels off.
3) The draft of the sails was not particularly critical, with very shallow optima. Anything around 45% of chord is fine.

Items 1 and 2 are consistent with the notion that the penalty for sail drag diminishes as the apparent wind moves aft. Increasing angle of attack and camber are moves towards a high lift/high drag foil as the wind angle increases.

More details are available at: https://sites.google.com/site/sailcfd/home/sail-trim-optimization

 

[Mikko Brummer]

Interesting... Your sails appear to be conical, ie. the camber% is the same from foot to head. That's not the case of a real sail, see for instance http://www.wb-sails.fi/Portals/209338/news/98_11_PerfectShape/Main.htm#. Due to their triangular shape, sails tend to be flatter in the foot, fuller in the head and twisted, for best performance.

At least for the upwind case, a more realistic sail trim analysis would be to keep the sheeting angles & camber at various heights unchanged (main sheeting 0-5 deg, jib 12-14 deg), and vary the twist instead. You can assume a linear twist from foot to head, even if mast bend & battens can change that a little. Also, there's a strong relation between camber & twist, but that you could assume to be able to control by design (at least partially).

You would need to check that the pressure difference near the luff of the sails remains positive or near positive (no luffing or backwinding), else the simulation is not realistic.

For fetching-reaching you would vary the main sheeting angle, keep the twist unchanged, vary camber maybe, but for the jib it's more complicated. The shape of the jib changes a lot when you ease the sheet - twist and foot depth will increase, head will flatten. No matter how how you design, you cannot prevent this from happening, and you can nowhere near achieve "any shape". There is no way you could sheet your jib conically by merely changing the sheeting angle, unless you are on a catamaran with a wide sheeting base, or you put a boom and a vang on the jib, too. Nevertheless, even in that case the conical shape would hardly be optimal.

In the attachment, a case of serious sail shape optimization.

 

[jlconger]

Thanks for your thoughtful reply. As you say, this 'optimization' takes the sails to places that I can't really go with my own boat with real sails. Some things are easily fixed, such as having too short a main sheet, but my fully battened mainsail won't go past about 15% camber. Similarly with the jib, I might get a bit closer to this idealized shape by installing a whisker pole, but the only boat I know that can really get something close to that downwind jib shape is the Alerion Express with its Hoyt boom. Those boats do seem to have excellent downwind performance, so perhaps I have a bit of better understanding of why that is.

I am not a sail maker, although I appreciate how challenging that work is. These simulations were done to help me better understand the physics of these complicated machines we sail. The most interesting outcome of letting the computer loose is that it chooses to continually change the sail's angle of attack as the relative wind goes aft. That was not at all obvious to me, and differs from the 'make all the telltales stream aft' approach to sail trim most of us tend to follow.

 

[Alik]

How do You model wind gradient in speed and direction? Real sails work at twisted flow, due to wind speed gradient and corresponding change of apparent wind direction with height.

 

[jlconger]

This model simulates a 100m x 100m x 50m high box of air with the 10m boat in the center. Drag from the water surface results in a wind speed gradient in the vertical direction. Influence of the hull and sails results in a large amount of distortion to the wind field, including well in front of the sails. This is probably what you are referring to as 'twisted flow'.

The beauty of these 3D simulations is that you do not need to make any assumptions about what the air is doing. You just put in your model, set the boundary conditions, and let the model figure out what must be happening at each location in the grid to conserve mass, momentum, etc.

 

[Alik]

This model simulates a 100m x 100m x 50m high box of air with the 10m boat in the center. Drag from the water surface results in a wind speed gradient in the vertical direction. Influence of the hull and sails results in a large amount of distortion to the wind field, including well in front of the sails. This is probably what you are referring to as 'twisted flow'.

Not really. What You model is speed gradient only. BUT there is also change of apparent wind angle with height, due to effect of boat speed. Try to make addition of vectors of boat speed and true wind speed at sea level, and at mast top level, and You will understand what I mean.

 

[jlconger]

Perhaps you are thinking of a different frame of reference? In this model the boat is fixed in the center of the grid and the airflow moves by it. Except for the effect of the sails themselves, there is no intrinsic gradient in wind direction with height.

The calculation sequence is as follows: The simulation starts with an apparent wind speed and direction. Once the model converges I calculate the boat speed and boat heel based on the forces generated by the sails. Given the boat speed and leeway I can calculate the true wind speed an direction, VMG, etc. This is probably the reverse of the way most people think about the problem, but the sequence works for CFD simulations.

 

[Alik]

Perhaps you are thinking of a different frame of reference? In this model the boat is fixed in the center of the grid and the airflow moves by it. Except for the effect of the sails themselves, there is no intrinsic gradient in wind direction with height.

The calculation sequence is as follows: The simulation starts with an apparent wind speed and direction. Once the model converges I calculate the boat speed and boat heel based on the forces generated by the sails. Given the boat speed and leeway I can calculate the true wind speed an direction, VMG, etc. This is probably the reverse of the way most people think about the problem, but the sequence works for CFD simulations.

Pls see the pictures on the first page of this paper:
http://www.ignazioviola.com/ignaziomariaviola/download_files/Viola_EACWE2005.pdf

 

[Mikko Brummer]

Not really. What You model is speed gradient only. BUT there is also change of apparent wind angle with height, due to effect of boat speed. Try to make addition of vectors of boat speed and true wind speed at sea level, and at mast top level, and You will understand what I mean.

Alik is referring the the apparent wind twist that you cannot ignore - see the attachment, for instance

 

[jlconger]

OK - got it. This is the effect of the vertical wind speed gradient on the the apparent wind vs elevation. And yes, that is included in the model. The surface drag of the water layer creates a velocity gradient from zero at the surface (no slip boundary condition) to the bulk wind speed at elevation, so the model converges with this gradient established automatically at all points in the simulated cube of air.

Note that I am simulating a smooth sea condition (and only taking data with the real boat under similar conditions). The velocity gradient under these conditions happens primarily in the bottom 2m of the atmosphere - very different from conditions on the ground with vegetation, etc. There is a discussion of the depth of the gradient with references on this wikipedia page: http://en.wikipedia.org/wiki/Wind_gradient

 

[Mikko Brummer]

OK - got it. This is the effect of the vertical wind speed gradient on the the apparent wind vs elevation. And yes, that is included in the model. The surface drag of the water layer creates a velocity gradient from zero at the surface (no slip boundary condition) to the bulk wind speed at elevation, so the model converges with this gradient established automatically at all points in the simulated cube of air.

Note that I am simulating a smooth sea condition (and only taking data with the real boat under similar conditions). The velocity gradient under these conditions happens primarily in the bottom 2m of the atmosphere - very different from conditions on the ground with vegetation, etc. There is a discussion of the depth of the gradient with references on this wikipedia page: http://en.wikipedia.org/wiki/Wind_gradient

Not quite sure we understand each other... in addition to the gradient in the apparent wind speed, there is a gradient in the apparent wind direction with height. How do you define your inflow in the simulation?

Not sure where that wikipedia got its information from, but we have measured on several occasions and locations the wind gradient on the water, with a mast with anemometers at 2 m and 5 m heights. The usual difference in wind speed there is 5-10%, the largest we have measured (in a light 5 kn wind) was 26%. It's true that most of the variation happens under 10 m of height, but there is a lot happening there, especially under 5 m.

 

[jlconger]

I believe the papers on the subject you are referring to are in the case where you are simulating 2D cross sections of sails at different elevations. With a 2D approach and a large wind gradient with elevation you would need to have a different apparent wind at each elevation simulated. Up until recently we had to do 2D simulations because it took too much computer time to do a 3D simulation.

These days we can run a 3D simulation on a high-end laptop. With a 3D simulation the wind gradient happens automatically. You simulate the whole wind field right down to the surface of the water. Not only is any gradient in wind speed/direction handled, but you get the more interesting 3D impacts of air going around the sails, turbulent eddies and so on. This is particularly important in downwind cases where the action of the sails is intrinsically 3D.

The initial condition inflow in my 3D simulations is set as uniform velocity with elevation, but the CFD model immediately creates a wind gradient because of the zero air velocity at the surface of the water (no slip boundary condition). If I don't put a boat and sails into the 3D wind field, all I get is a simulation of the wind speed gradient. The best way to increase the gradient would be to add waves or other forms of roughness to the simulated water. Simulated waves would be interesting - something for future work. The literature suggests the fractional gradient is highest in light winds, so that too would need to be a variable.

BTW: Just a word of warning for anyone else reading this... Last year I held up a hand-held wind speed instrument a number of times while sailing. Since I tend to stay on the high side of the boat and can only reach up and out so far, I always got a reading that was about 80% of the mast head wind speed. Of course, what I was really measuring was the deceleration of the air on the windward side of the sails. The decelerated area extends well beyond the width of the boat and well aft, so there was no way for me to reach an unaffected area. Eventually I figured out that all of that data was useless. Sigh...

 

[Alik]

Seems You do not understand what You are modelling... Strongly recommend to study basics of sail craft dynamics first; start from wind speed vectors.

 

[tdem]

Your model does indeed exactly model the physical 3D flow, of a STATIONARY boat! Directly upwind it will make little difference but downwind, if your speed is a large percentage of wind speed, it has a huge difference.

 

[daiquiri]

These days we can run a 3D simulation on a high-end laptop.

You could have even a Cray supercomputer at your disposal, but it would be useless if you don't understand the physics of what you are simulating. Sorry for harsh words, but that's what the reality looks like here.
What Alik and Mikko are telling you is one of very basic concepts of the physics of sailing. The apparent wind direction changes with height, due to the motion of the boat.

On the positive side, this thread could become a very educative example of how a poor knowledge and powerful yet cheap analysis tools can be dangerous when hastily cobbled together.