sail aerodynamics

Discussion in 'Hydrodynamics and Aerodynamics' started by Guest, Mar 21, 2002.

  1. tspeer
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    tspeer Senior Member

    No, you just have to figure out how to approximate the effects. I've not done the math, but maybe a vortex sheet above and below the region of interest, having opposite signs, would produce a gradient across the span. What you're doing is concentrating all of the rotational aspects into the vortex singularities. The rest of the flow is still irrotational.

    Or perhaps you could distort the geometry to get the right lift distribution in a uniform flow, shrinking the chord in proportion to the dynamic pressure, and twisting it to get the right local angles of attack. You might have to do a transformation back to the physical domain from the distorted domain to account for the right orientation of the lift vectors due to twist in the apparent wind.

    The attached paper is the only one I've seen that uses lifting line theory in a non-uniform flow. It compares the proper formulation with the geometry-distorted approach, and shows the distorted geometry is a reasonably good first approximation.
     

    Attached Files:

  2. philSweet
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    philSweet Senior Member

    I found this thesis on unsteady flow. It's a bit of a chore to follow if this isn't your day job. What it does have is an expression for the drag (or thrust) associated with a sinusoidal heave and pitch combo. That is courtesy of someone named Peters.

    http://scholar.lib.vt.edu/theses/av.../unrestricted/Walker_Thesis_final_revised.pdf

    Jamie asked -
    The above thesis has qualitative and quantitative answers to that question.

    One approach is to try to even out drag. This would be total drag, so you need a time dependent drag model of the entire boat moving in a seaway. I don't think Mikko's X35 model using borrowed motions and a seaway locked to the airflow is going to do that well enough to inform design choices. But he's obviously getting pretty close. This idea is mostly about shaping the way the motions caused by the seaway are damped. It is force management, and need not involve energy storage. Damping can not eliminate the additional drag caused by the motions or convert it to thrust, but it can reduce the amount of added drag vs undamped motion.

    The opposite of drag is a driven motion. If you store and release energy cyclically, you are damping part time and driving part time. Theoretically, this can produce thrust from a surging motion. Basically, you are trying to extract energy from the seaway itself, and deposit it in the air to make thrust.
     
  3. tspeer
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    tspeer Senior Member

    I've not started to work with it in earnest, yet, but OpenFOAM is not something you're going to just pick up and start to use without a good CFD background. It's really a system for programming CFD codes, not an application into which you can plug your configuration.

    The computational demands for any form of RANS code are pretty heavy. Like a high-performance Linux cluster crunching for days or weeks heavy. It's not something you're going to do on a laptop. You don't need to have your own computer any more, though. There are cloud computing services that will rent the cores you need to run CFD on demand.

    In a real project, the three levels of CFD you mention get used in the opposite order, with perhaps an order of magnitude ratio between each level. Most of the real design work, ie, determining the shape, is done with the simplest tools because you can quickly iterate the design. Then the intermediate level is used for generating the bulk of the VPP database. The VPP is the real workhorse of the design process, because it relates all aspects of the design, aero & hydro, and determines how the boat's components will actually be used. RANS is used for 3D effects, like the interaction between the platform and the rig, that are difficult to predict using potential flow.

    RANS is also used to "calibrate" the potential flow results. A reduced number of RANS runs are compared with the corresponding potential flow results to get a correction factor or delta, and that correction is then applied to all the other potential flow results.

    Probably more CFD is used to determine how best to operate the boat and come up with targets for the sailors, than in creating the shape itself. Of course, once the boat is built, it doesn't matter how sophisticated the analysis was that went into shaping it. It is what it is, and the sailors have to make the most of it.

    For an A cat, a lifting line or vortex lattice to shape the rig, plus empirical estimates for the windage of the hull and sailor are probably the best compromise of time, money, and accuracy. A panel code would be good for the foils, because you care about surface pressures when dealing with cavitation. XFOIL gets heavily used for the foil sections, even when RANS is available. After that, it's probably cheaper and more effective to build it and try it out on the water. A good partner to sail against would allow you to do two-boat testing, which is the gold standard for sailing yacht development.
     
  4. philSweet
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    philSweet Senior Member

    I was also wondering about this. I think you could couple the sail membrane equations (which have to be solved in the transformed space) with the aero forces in uniform flow as long as there were reasonably limits on the transform.

    The transform itself doesn't change for a particular case, so the coupling of the two sets of equations is fixed for a given state. In a seaway, you would identify the motion state and look up the transform precalculated for that motion and linearized about the operating Cl. This doesn't change the computational time at all. It may even converge faster.

    Getting the proper time dependent solutions would be trouble, though. You would need a transform that preserves forces and reduced frequency. Does anybody know of one? Don't the turbine folks have something like this?
     
  5. philSweet
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    philSweet Senior Member

    ... And now that I've read the paper in TSpeer's post, I see they propose a method of similarity that does just that.
     
    Last edited: Jun 29, 2015
  6. Erwan
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    Erwan Senior Member

    Thank You Mr Speer for Lissaman workpaper, and your comments.

    Some time ago a friend of mmine had a termporary access to a sail software using VLM.
    Unfortunatly, either it was not possible either he was not proficient enought with the software, he could not include the teardrop mast section, which of course, is not a good representation of reality.
    As it's possible to consider the actual mast section with XFOIL, I though a cost-effective solution could be to mix XFOIL for the 2D, and modified LLT for the 3D.

    This Lissaman workpaper is realy a great one , Thanks again.


    Cheers

    Erwan
     
  7. Doug Halsey
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    Doug Halsey Senior Member

    Tom, I don't understand why it should be necessary to add vortex singularities, or anything, to produce the rotational onset flow to a vortex-lattice code. The onset flow is simply specified as input data (or programmed into the method) & affects only the right-hand side of the matrix. It shouldn't matter how that onset flow could be generated.

    If I'm correct about that, modifying the code would be almost trivial. Accounting for the twist is another matter, however. I can see that opening up a can of worms.

    But, a method with a spanwise gradient specified, without considering any twist might still be useful. It would be equivalent to the situation where you look at your rig on shore, or where a sailmaker studies a sail on a mast on the roof of his building.
     
  8. philSweet
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    philSweet Senior Member

    With respect to potential flow calculations, it does matter Doug. The method of generation has to be irrotational in order for the analytics to work, and you can't get there from here. The problem is that there is really no good way to know the errors introduced when you flatten a rotational flow into an irrotational one.

    Mathematically, the overriding requirement is that the differential of the vector field is zero. The differential consists of some scalars which combined are called the divergence and have to be 0, and some bivectors which combined we call curl, and that has to be 0 also. You can add time or any other dimension you want, but the rule is the same, the divergence-like group and the curl-like group have to be zero. A flow with an angle of attack = A(h) and a speed V(h) doesn't fulfill this requirement unless the two functions A and V are tightly constrained (Harmonic_conjugate). One determines the other.

    It is possible to model twisted and sheared inflow, even unsteady flows, but they have to have a vector derivative of zero. That gives you two separate constraints on the problem. These have been studied since 1820s and they are now just treated as operators with known properties. Basically, the notation is just a way of saying we know these have the properties we want.
     
    Last edited: Jun 29, 2015
  9. Doug Halsey
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    Doug Halsey Senior Member

    Phil : I think you are making this more complicated than it has to be.

    The flow we're talking about already has zero divergence, since physically, conservation of mass is not violated and computationally, we're using singularity-based methods with no sources or sinks.

    The flow does have curl (i.e. rotation), so it's not a potential flow, but we already knew that & are just discussing how to approximate it. Computationally, the rotation could be simulated by adding vorticity into the flow & somehow solving for the vortex density in the field.

    But I'm accepting markdrela's opinion that it's OK to break the flow into a rotational onset flow and a potential perturbation flow due to the sail. In that case, we don't need to know what the vorticity distribution might be, because we already know the velocity distribution that it creates. Basically, I'm just talking about directly implementing what markdrela says in the last sentence below.


     
  10. daiquiri
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    daiquiri Engineering and Design

    I fully agree with this. You folks are making it too difficult. The VLM requires the potential flow field, but it also introduces a series of simplifying assumptions in order to eliminate the influence of higher-order disturbances and to linearize the equations.

    The VLM formulae don't care too much about what is going on in front of the wing/sail, because all the calculations are performed at the control points on the body surface. On that regard, it behaves like a strip a theory. Therefore, the upwind flow can have any shape, as long as its effects are of the second order respect to principal local flow direction. I am pretty sure it can be demonstrated that the case of the free stream with horizontal wind gradient on a vertical sail does fall into this category.

    The fact that it uses linearized equations is also the main limitation of the VLM when it is used for the analysis of sails. It cannot handle stall, and that means that the VLM analysis is pretty much meaningless for course angles above approxim. 60°-70° (hence between close reach and running). That's where other CFD tools (like finite volume method) are necessary, besides the wind-tunnel testing.
     
  11. DCockey
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    DCockey Senior Member

    The basic potential flow assumption results in linear equations as well as an irrotational flow, not the particular potential flow solution method.

    VLM (Vortex Lattice Method) is only one type of potential flow analysis. There are other types of surface singularity methods for potential flow analysis which use sources, and doublets or vorticity distributed on the surface rather than concentrated in a lattice. Also, many different types of finite difference, finite volume and finite element methods can be used for potential flow.

    The reason surface boundary methods for solving potential flow, including VLM, cannot directly model a sheared far field flow has nothing to do with "all the calculations are performed at the control points on the body surface". Rather is has to do with the use of a velocity potential which does not allow flows with vorticity distributed though out the flow field such as sheared far field flow. It is possible to model a non-uniform far field flow using potential flow as long as the far field flow is irrotational.

    Also, a proper 3D VLM code does not use "strip theory".

    All potential flow methods, not just VLM, cannot handle stall directly due to the rotational nature of the flow which results from stall.
     
  12. markdrela
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    markdrela Senior Member

    That's not quite correct. The velocity field assumed by VLM does not directly invoke the potential.

    Lets examine the velocity field representation used by VLM from scratch. The total velocity vector at any point x,y,z in the flow is assumed to have the form

    V(x,y,z) = Vpot(x,y,z) + Vvor(x,y,z)

    where Vpot is the gradient of some potential function, and Vvor is shorthand for a Biot-Savart integration over all the vorticity present in the flow. In the case of a sail, there are two types of vorticity present:
    1) distributed (volume) vorticity of the wind-shear profile, and
    2) concentrated (sheet) vorticity of the sail and its wake.

    If we choose to include the images of 1) and 2) below the water surface in the Biot-Savart integrals, then Vpot must be a spatial constant, and is equal to the wind velocity Vinf above the surface boundary layer. Furthermore, we can split the Biot-Savart integrals into the wind-vorticity (+image) part, and the sail/wake (+image) part. The velocity at each point then has the form

    V(x,y,z) = Vinf + Vvor_shear(x,y,z) + Vvor_sail(x,y,z)

    where Vinf is now a spatial constant as indicated.

    The key simplification I mentioned earlier is to assume that Vvor_shear is not modified by the disturbance of the sail. This is equivalent to assuming that the wind-shear vorticity is not significantly redistributed by the sail, by the time it arrives at the sail. With this assumption we can say that Vvor_shear only depends on the vertical height z. So now we have:

    V(x,y,z) = Vinf + Vvor_shear(z) + Vvor_sail(x,y,z)


    But the first two terms on the r.h.s. can be combined, Vinf + Vvor_shear = V_wind, which is nothing more than the full wind profile in the absence of the sail.

    V(x,y,z) = V_wind(z) + Vvor_sail(x,y,z)

    This final result is the same as what's assumed by a standard VLM, except that the usual constant Vinf has been replaced by a V_wind(z) function which is specified a-priori. The resulting complication in the VLM formulation is very minimal. But it's essential to note that Vvor_sail(x,y,z) includes the Biot-Savart integration over the sail image below the water surface, which also must be assumed to be flat. But again, this accounting for a wing image is nothing new for most VLM formulations.
     
  13. DCockey
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    DCockey Senior Member

    While the VLM method may not explicitly invoke a velocity potential, it is based on the assumption of an inviscid, irrotational flow (other than at/across boundaries); and an inviscid, irrotational flow can be represented by a velocity potential.

    The modified VLM method described above will not converge to the exact solution for the inviscid but rotational (Euler equation) solution for a thin airfoil in a sheared, rotational onset flow. That is not to say the modified VLM method will not provide a useful solution as long as the assumption of minimal interaction between the irrotational portion of the flow due to vorticity distributed on the sail and its wake and the rotational onset flow is valid.
     
    Last edited: Jun 30, 2015
  14. Doug Halsey
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    Doug Halsey Senior Member

    Thus, the use of the word "approximation" in most of the posts on this subject.
     

  15. Mikko Brummer
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    Mikko Brummer Senior Member

    In the attachment, graphs of Cl and CD for the X-35 pitching in waves more or less or not at all. The average CL and CD for both pitching cases (which also include heave/yaw/roll) is in nearly the same as for the "no motion" case represented by the straight line - L/D for no motion is 5.12, smaller pitch 5.07 and larger pich 5.03.

    The sail trim for the case is for smooth water, and the motions borrowed from the Star, with hardly an optimal steering for this case. There's no rig dynamics in the simulation, the sails and rig are "stiff", which would be very much true for this type of boat in this small waves. Allowing for the rig dynamics for boats like the Star & Finn, I'm convinced that the "pitched" numbers for the sails of these boats can be better than the static ones, actually extracting energy from the waves as philSweet suggests.

    This would be in contrast with all the VPPs that I know of (including my own personal VPP), which assume the sail aerodynamics deteriorate quickly in a seaway (up to 20% or so).

    Also, it makes you think something similar is happening under the water, with the keel tip pitching fore & aft and rollin sideways, even more complicated by the circular motion of the water inside the waves. The "apparent water angle" and speed is ever changing.
     

    Attached Files:

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