Hi,
I’ve been busy the last weeks with a project I wanted to tackle since tufting woolen strings into Ilvy’s sail in the Swedish archipelago: CFD calculations of junk rigs.
A little bit of background
CFD (computational fluid dynamics) is basically the possibility to have a virtual wind tunnel, simulated and calculated purely by numerical means with a computer. While this may sound high-tec, it absolutely is: Lots of math (solving several differential equations like the famous Navier-Stokes-equations), programming (scripting and coding for multi-core machines/high performance clusters) and data evaluation. I do not want to go into detail here. However, setting up and running those fluiddynamic calculations is one of the things I do in my profession as a shipbuilding engineer. So, I thought I might as well set up a simulation of the junk rig(s). So far, it took me about the same time as sewing a new sail. But it is interesting, and I hope we could learn a lot from the outcome!
How is it done? I define a geometry (junk rig) that I want to simulate, and a “room” around it – wide enough to not interfere with the flow around the geometry. Then, the space inside the room is filled with cells. The cells are arranged in a way to snap exactly to the junk rig and as such resemble its geometry. They are very small close to the surface, and bigger far away. All those cells are called a mesh, and it is a science for itself to create a good mesh. Have a look at a slice of the mesh in the middle of a panel:
For each of those cells about ten equations (some differential) have to be solved, for each time step. The time step has to be very low, about 1e-5 sec, to give accurate results. The simulation is running for 15 sec simulated time. The amount of cells only in that 2D figure above is about 150000. If you do the math, there are quite some numbers to be juggled to solve that simulation. Now, as we live in the fantastic modern times of 2024, my Laptop – I admit, it is a rather strong one with 6 cores – is able to calculate such a 2D slice in about 1-2 hours (running full speed and drawing quite some power).
The output of such a simulation would be all forces acting on the geometry, as well as the full image of flow – for one state of flow: one air velocity and one angle of attack of the junk to the wind. From that, I can then (rather easily) calculate Lift and Drag, Cl, Cd, L/D, Cl/Cd, and the like – for that one state of flow. However, only that one point doesn’t help that much. Therefore, I do need to run several simulations to simulate several angle of attacks or velocities. And suddenly, my laptop keeps hard working for days nonstop before all results are calculated.
Now imagine a 3D simulation: all those thin 2D slices would have to be stacked upon each other and calculated. I estimate the amount of cells to about 30-50 millions. I did simulations like those regularly for industrie applications in the past - but not on my laptop. For such things, you need high performance clusters (also called supercomputers) which are nothing to put into your living room or cellar. It is possible to rent such high computational capabilities, and run it “in the cloud”. AWS from Amazon would be an example. But - you may have guessed it - at a price: the bill to rent their computational power for each simulation would have 3 trailing zeros…
Conclusion: Privately, I am only able to do 2D simulations. Thus, I will only be able to simulate “profiles” rather than “rigs”. Drawback: Those 2D simulations cannot include 3D effects like i.e. the tip vortex. Thus, the results I am going to present further down are not to be simply extrapolated to actual rigs. However, there are still a lot of information to be derived from the 2D calculations. More later.
Oh, I forgot to mention: over the years, CFD has become so accurate that it is widely used in industrial applications. Cars, planes, ships, pipings, pumps, meteorology, sea currents, i.e. are designed by CFD results. CFD is way cheaper than wind tunnel tests or towing tests – and in general the results are so close to reality that those real world testings can often be omitted. There are exceptions, but they are far from this case I present here. What I did with the junk rig, a 2D case of a profile in air, at Reynoldsnumbers of about 1e6, is quite a standard application.
Geometries
To start with, I set up a standard case: a flat cut rig. The dimensions I borrowed from Ilvy: 4.9 m batten length, which is the same profile chord length for a flat cut rig. The mast is set 1.5 m aft of the luff, which is about 31% mast balance. Mast diameter is 180 mm, batten thickness is 40 mm.
Second case: a cambered panel. Same batten length, same mast, but cambered profile with 9% camber. Now it gets fiddly: I do not actually now the real camber shape in an inflated junk rig panel. It surely is not the sewn in curve. For a start, I assumed a curve – there is room for discussion and improvement. It gets even more fiddly: I also had to assume a curve of the distorted profile on port tack. Again, please throw in critics, hopefully ideas to improve or even best: real world measurements of the horizontal profile distribution! However, I watched out to have the length of the profile curve the same as the flat cut one: 4.9 m – which naturally lets the leech end of the profile slip a bit forward due to camber.
Have look at the following profiles. The flat cut profile is naturally the same for port and starboard tack, the cambered not. (Please be aware, these are rather ideal, academic test cases yet. Just to prove it is working. It has to be fine-tuned! For example, a flat cut rig is not really flat in reality…)
Results
I’ve been running those geometries at 10 kn, for a variety of angle of attacks (AoA). AoA here means angle of the batten line to the incoming airflow (apparent wind). It is NOT the sheeting angle on a boat. Each data point in the following graph is derived from one single simulation.
Where the tangent hits the Cl/Cd curve, the profile is working at its most efficient point. At this point, the L/D ratio is at max.
It is interesting, that although the curves are different for port and starboard tack, the most efficient AoA of the profile is about the same for both tacks (5° for flat cut, 4° for cambered). However, it now gets also very clear that there is a good and a bad tack! There is a difference observable in L/D_max as well as in the shape of the Cl/CD curves, which describes alpha-tolerance. What I find most interesting, is that the bad tack of a flat cut sail is the good tack of the cambered tack.
It gets also quite clear, that a flat cut sail is way way way behind a cambered sail regarding upwind performance. L/D_max is 2-3x better with a cambered sail than with a flat cut sail.
To give some context, this is what the flow around the cambered profile looks like, at L/D_max with +-4° AoA respectively.
One can observe, that the flow at those AoAs and profiles is fully attached – at least where the mast does not interfere. If you compare that to the flat cut profile at max L/D (+- 5° AoA), you see a huge detached bubble on the suction side, which reattaches towards the leech end.
I could go on, posting Cd/AoA curves, Cl/AoA curves, pressure distributions on the profile etc, but this post has already gotten way too long. This very first results have already put numbers to some things. The steps to do more calculations are relatively small, now that I already did put in all the upfront work to setup the simulation.
Outlook
What can this now existing 2D CFD-setup be used for next? I could use this to investigate:
- · Different velocities
- · More realistic cambered profile shapes
- · Performance comparison of SJR to single cambered profile to flat cut to wingsail to aero junk to …
- · Performance comparison of more/less camber and different camber shapes
- · Influence of small wrinkles or large creases on performance
- · Influence of mast diameter on performance
- · Influence of mast balance on performance
- · Influence of distorted luff shape
- · And so on and so on…
Cheers,
Paul
PS: Sorry for being so sloppy about details, format, labelling etc. If I would put this into a scientific paper, it would definitely have a more professional format and be more detailed. However, I know from experience that the amount of time to do such professional formatting is not following the 80/20 principle. Not at all.