CFD sail trim optimization

Clearly hit a nerve here...

Always interesting when new approaches receive such loud criticisms. Rather than defend the Navier-Stokes equations, I'll just attach a couple of plots that compare the output of the 3D simulations to results captured from the boat being modeled under the same conditions. This is entirely close-hauled data. The vertical bars show one standard deviation in one second collection periods. The measured (apparent) wind speed is from the mast head. Data was collected over several days on both tacks with calm sea states.

 

I don't think the plots you show reflect the CFD solution as much as they do the basic trigonometry of the so-called velocity triangle (with boatspeed, true windspeed & apparent windspeed forming the 3 sides).

One simple relationship from applying the law of sines to this triangle is the following :

(Boatspeed) = (Apparent windspeed) * (Cos(Beta)- Sin(Beta)/Tan(Gamma)) where Beta = Apparent wind angle & Gamma = True wind angle

Setting Beta=30 degrees (which you do in plot #1) & assuming Gamma=45 degrees (which is approximately true, since you say all data were taken close-hauled), gives a straight line for boatspeed versus apparent windspeed, which matches your line for the CFD calculation pretty closely.

I agree with the previous posters that the variation in apparent wind angle can be an important factor & it certainly complicates the application of simple relationships like I've given.

 

What topic started is looking at is typical wind tunnel solution. It was state-of-the-art method until twisted flow wind tunnel was built in Auckland, and later in Milan; not sure maybe there are more. I had chance to visit the one in Auckland during HPYD2006. The system they use is wind tunnel coupled with immediate VPP analysis, so aerodynamics data from wind tunnel comes into VPP giving sailing parameters, thus affecting the apparent wind and twist adjustment of the flow in tunnel, settings of sails, etc. So it is actually iteration process through VPP.

 

You will not get the wind gradient from convergence. You need to set it up as a boundary condition. Yes something will happen at the water surface, but it takes much longer than 100 m to build up the wind gradient, if you start with constant speed.

And as many others have already pointed out, you need to calculate AWA at different heights and put that as your boundary conditions. Note that this is apparent wind thus it is not stable in CFD (or in a wind tunnel). If you set up the boundary conditions too far away you loose part of the twist.

 

Thanks - Setting an a boundary condition with more wind sheer makes sense and is easy to do.

I'm afraid I still do not follow your second point for a 3D case. Isn't the change in apparent wind angle solely due to the vertical gradient in wind speed?

 

It is due to the vertical gradient in true wind speed AND due to the boat speed.
So it will depend on both.

 

Why would you need to? Nobody has questioned the validity of the N-S equations, only your way of using them in the present context.

 

This reference here explains quite well what the twisted flow wind tunnel does:

http://www.ignazioviola.com/ignaziomariaviola/download_files/Viola_EACWE2005.pdf

Your CFD situation is basically the same as a wind tunnel. You are blowing air over a stationary boat, but simulating as if it were moving. This means you need both a velocity profile, and a twist profile.

As posted before it is a vector addition between the boat velocity and wind velocity (which is variable with height)

The wind as seen by the boat can be expressed as an apparent wind speed and apparent wind angle, given by:

Beta_A = tan^-1 ((V_T * sin(Beta_T + lambda))/(V_T*cos(Beta_T+lambda)+V_S)) - lambda

V_A = sqrt(V_S^2 + V_T^2 + 2*V_S*V_T*cos(Beta_T+lambda))

Where Beta_A and V_A are apparent wind angle and speed. Beta_T and V_T are true wind angle and speed. V_S is the boat speed and lambda the leeway angle.

Wind angles are measure relative to the boat centreline. Leeway angle is also measured from the centreline, but is considered positive in the opposite direction (eg with wind from the right, your positive leeway angle is to the left of centreline, as expected).

(reference: Enhanced wind tunnel techniques and aerodynamic force models for yacht sails by Heikki Hansen)

Your input into the CFD model should be apparent wind speed and angle.

 

How are you optimising the model, is it a manual process?

 

Let me propose this thought experiment, and see if it can help resolve my conceptual problem.

1) I want to estimate the force created by a sail 'by hand' by estimating lift using a table for thin airfoils. I would need to estimate the true angle of attack of the sail at each elevation and the apparent wind speed. To do this I would consider the wind speed, boat speed, wind speed difference with elevation, and also the relatively lifted air flow the sail experience as compared to the ambient air flow well away from the sail. That difference in wind speed and direction is a function of elevation as mentioned above. If I do this calculation correctly at every elevation I should be able to integrate to get the correct total force from the sail.

2) Now I attempt to do the same problem with a 3D N-S simulation. I'll put in a exact same wind speed gradient with elevation as a starting condition. I simulate the boat's relative speed through the air mass containing this wind gradient, looking for a solution that obeys the N-S conditions at every point.

Without doing anything else the 3D simulation will converge on a solution that shows a wind field around the sails that includes the substantial change in wind speed and direction with elevation mentioned before. The primary factors influencing the lifted condition are the wind speed gradient with elevation and the influence of the sails themselves, which extends well in front and to the sides of the sail. Careful examination of the solution will indeed show that the air flow into the sail's leading edge was significantly lifted relative to the ambient conditions, varying with elevation. The N-S calculation gives me the lift generation of the sail, which should add up to the same result done by hand since the relative wind and airfoil shape are identical at each elevation.

Do those two examples sound comparable?

 

Yes this is the same, if you are doing a transient simulation (e.g. the boat is actually moving through the domain).

 

My 'optimization' is only partially automated. The input defines a series of sail shapes to run at one apparent wind speed and direction. I've limited this to six parameters, three per sail, so I have to put up with funky sail shapes for now.

For each case Python code generates an STL model for the sails, adds this to the hull/mast model. A mesh is then generated and the CFD model run. Once complete (~25 min/case) I use more Python code to extract the pressures and normals from the model surface to calculate the forces generated. This process repeats for the range of sail shapes I've selected. I use direct measurements from tow and heel tests on the test boat to convert from aerodynamic force to boat speed and heel. I only have a crude leeway calculation method at this time.

I have then been manually plotting the results, selecting the local optima, and rerun the next set of cases closer to the last high point. It takes quite a few tries, and I don't claim to have found any true optima - I was just interested in where an unconstrained simulation would take the sails. I have certainly learned a lot in the process.

 

I don't claim to be an expert in CFD (I'm a beginner if anything), but I think it would be helpful if you added a page to your website with details of how you actually ran the simulation. Boundary conditions, turbulence model used etc. This has a huge effect on the results. The real experts could then give you better advice. It sounds like you have a few misunderstandings about CFD.

You may have learned a lot, but is it real? GIGO as they say.

I'm really interested in your project, as I'd like to learn how to use OpenFOAM. Unfortunately I don't have much play time at the moment. I think it's great you are documenting your efforts!

 

I concur with tdem, you should not be too harsh on jl. But jl, to get meaningful results you need to allow for the twist in apparent wind in the inlet boundary conditions. It's not difficult at all, once you understand the principle:

- Say you assume a boatspeed (BS) of 6 kn.
- Say at 2 m height the true wind speed (TWS) is 10 kn and the true wind angle 45 degrees
- At 2 m height you add the BS vector 6kn to the TWS vector 10 kn/45 deg. This gives you apparent wind at 2 m height up the mast.
- Say at 5 m height TWS is 12 kn, and the boatspeed is still the same 6 kn. Now you add those vectors and get the apparent wind at 5 m height, where it is both stronger and more from the side than at 2 m height.

And so on up the mast. In practise, you don't guess the TWS at various heights but use one of the well known functions for wind shear, with parameters of your choice.

At the inlet, you define 2 velocity components: one in the X-direction and another in the Z-direction (assuming height up the mast is in Y-direction). Velocities in both directions are functions of height (Y in my coord. system, some use Z for height).

Also, I would like you to consider my suggestion about the sail shape: Use twist as a parameter, rather than draft position. The 3 parameters per sail would be: Camber, twist and sheeting angle. The camber should vary with height, flatter foot and fuller head, but you could still adjust camber in your Python script with a constant multiplier. Or the multiplier could be larger for the foot, to simulate sail strim more realistically. Then I think you would get results that are more of general interest.

 

Re: wind gradient in speed and direction

As far as I know, the wind gradient in typical conditions for a typical mast height is extremely small. Yes, it could be impotant for racing competiitions. But it can be neglected in ordinary life.

Typical data for the open sea.
If at height 10...15m the wind is 10m/s, then at height 2m the wind is 8m/s.

For the problem "catamaran is moving with speed 10m/s perdincular to the true wind 10m/s" the change in the direction of the apparent wind (on the mentioned above heights) would be 3 degrees.

Meteorological data:
www.dtic.mil/dtic/tr/fulltext/u2/734670.pdf
www.publish.csiro.au/?act=view_file&file_id=PH560511.pdf