Hello,
Just wanted to share with you a concept of wind turbine I am working on since years :
monopale_eng1.docx (2.2 MB)
Not as light as AWE, but requiring much less materials than conventional HAWT.
Waiting forward for your comments…
Pierre
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Hello Pierre,
Thanks for sharing this information publicly. The following video is in the references of the paper, and represents how an uniblade wing for pumping is working (at 5:17).
I skimmed it and will think about it and read about it later.
You obviously put a lot of effort in this so it may seem weird that I approach this as an idea that was presented without mutch thought; But isnt the wing moving rather less crosswind and then how will you «Betz out» the swept area? Ot rather, how to achieve a high induction factor with a design like this?
Anyways. I will digest my first impression then read it again later. My question above is not worthy the amount of effort you made in presenting this. Though it may make my path to understanding what we have here easier, if you were to comment.
Tallak
Thks Tallak for your input and sensitivity.
In my original idea, the mast pivot axis is oriented in the wind direction, resulting in a wing movement fully crosswind. Now, for some sites with prevalent wind directions, a fixed pivot may be used and some equivalent to turbine yawing obtained by adapting the blade pitch angle to keep the wanted angle of incidence. Imperfect yaw positioning is less impacting than for HAWT due to lower tip speed ratio.
As for Betzing out, CFD resulted in near 80% of Betz limit can be had (3d effects not accounted for), provided we keep enough oscillation frequency and fast reversals. Attached one of the main CFD study (for a blade section linear movement instead of a large arc, which makes little difference as we found in 3D CFD) :
AIAA_57-12_2019_LargeHeavingAmpl.pdf (3.1 MB)
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So I watched the videos and read the document.
It seems most natural to compare this to a HAWT.
Your blade will have a bigger chord and lower aspect ratio of the blade. This is mentioned as a benfit but I have the feeling why would you not rather have the twisted high AR high efficiency blade of a HAWT and move faster with more power output?
The twist is also mentioned as a benefit but the fixed twisted blade of a HAWT seems the better option for me because it does not need to twist during operation. It will have a designed twist that will be close to optimal at any operstional point that matters a lot. On the other hand, your reversal of the wing would require both changing camber direction and twist of the blade twice every cycle. Or settle for a symmetric blade. Or settle for no twist. Its possible but I think hardly a benefit.
The back and forth motion also does not seem to be a benefit. A lot of the time the blade is moving slower than «TSR» max speed. In these phases, its going to be hard to keep losses down as blade is moving slower and the flow over the blade is changing rapidly [hard to control blade angle vs airflow]. So all in all I would expect significantly higher losses compared to a HAWT. This comes in addition to reduced utilization of the generator electronics due to time lost in direction reversal.
Add to this that back and forth means that the blade will start each sweep directly in the wake if the prevoius sleep, compared to a HAWT blade that would always see fresh air.
About the mechanical design, and this is where my knowhow is the worst, the main difference between your design and a HAWT seems. to be that the whole tower is moving rather than a set of three smaller blades mounted at an altitude. The downwind pull and of the two designs should be similar, both huge. The beam inside your blade thus probably needs to be quite hefty given the length of the blade would be twice as long compared to a HAWT blade. But still liggtweight as the blade should have a small moment of inertia when changing direction. I think you should probably compare this turbine to a HAWT of similar size swept area, or smaller given the losses described above. You do seem to have a big benefit though in terms of most of the moving components being mounted on ground. This seems to be the one big benefit I can see clearly so I would focus on answering whether this could offset the drawbacks.
I would also like to mention that the yawing mechanism would be quite large compared to a HAWT, due to the size of the mechanism that needs to rotate.
I would be careful to not fall into wishful thinking. You seem to frame anything different as a benefit. In reality most are probably the opposite. Rather try to map out the objective benefits and then weigh them against drawbacks.
I am not sure if you are delivering on «something between AWE and HAWT» here, as I suspect this design would be as heavy or heavier than a HAWT at scale. Again, dont apply wishful thinking, rather make a mass budget for eg. a 4 MW unit installation which seems a popular size at the moment, and see how this design compares to a HAWT that your customer could easily get his/her hands on.
I do think the design is interesting though. Its well thought out, and the actual build is very impressive. I do find it interesting that some
of the heavy components are placed on ground rather than at the top if a tower.
I think there are options like rotating the blade in circular or maybe elliptical motions (looking at the tip of the blade) that could make a lot more sense as the speed of the blade would vary but never change direction. That would maybe give a smoother power output with less time losses. It would look a little bit like a «half height» Darrieus turbine…
Anyways, my 5 cents, youre welcome
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Many thanks for your thoughts !
I think that having a lower TSR is necessary to avoid too high accelerations upon reversals.
And that in order to compensate for lower apparent wind, and extract as much energy, the blade chord must be larger which is somewhat wanted to carry the bendings loads more distant and thus ligther spar caps. I also like the idea of lower blade speeds for noise and bats reasons. I am not sure how light we can make the blade strong enough to withstand its loads and also storms…
So let me try to compare HAWT and single blade for a 4MW turbine @9.2m/s
Reference HAWT (from V150)
Mast height: 125m - Rotor Diam: 150m - Swept area 17671m²
Wind speed: 9.2 m/s - Efficiency 80% of Betz - Pout: 4.0 MW
TSR (estimated): 7 Tip speed: 64.4 m/s
Single blade
Mast (blade root) 70m + Single Blade length 80m (vs 75m) → total height 150m (vs 200m)
Sweep angle: 55 +/- degrees from vertical - Swept area: 21598m²
Wind speed: 9.2 m/s - Efficiency 66% of Betz - Pout 4.0 MW
TSR 3.5 Tip speed: 32.6 m/s
I estimated the blade root moments and spar caps requirements using 10 sections for the blades, in the XL file I hopefully attached below :
dim_large2.xls (56 KB)
The average chord of the single blade is 7 times that of each HAWT blade, and uses a bit thicker profile, to carry the bending loads more easily -
The spar caps weight required for each blade of the HAWT would be more than twice that of the single blade. So 5/6th of blade structural materials are saved and more costy materials (Carbn) can be used to lower the weight. There is also a need for lightweight internal structure of the larger blade, which has not yet been evaluated.
The blade root section is a truss (possibly streamlined using a fixed elliptical profile facing incoming wind in order to reduce drag) carries little load since it uses cables to prevent bending and feed the winches for counterweighing the movement and ground energy extraction.
All in all, it seems to me that the single blade weight is an order of magnitude lower than equivalent HAWT (not account for the winches and counterweights). But maybe I am overoptimistic somewhere…
Yes, the single blade has a lower aspect ratio. We made some 3D CFD of the single blade (unpublished), we found simlar 3D losses than usual HAWT althought using AR=7 only. There are several differences in the airflows, more centrifugal effect for a HAWT, possibly leading to more unwanted air speed component in the longitudinal axis of the blade ? Also keeping reversing direction seem to prevent this longitudinal flow to get established. Nevertheless we tried adding symetrical blade tip winglet and this allowed to recover most of the losses at the expense of more structural loads due to increased span. I can try to dig into the 3D CFD results again in case someone is interested.
CFD gave an idea of how the air flow is affected by the single blade energy extraction. For highest yield, we got a wake with approx half the original wind speed in the main (symetry) axis - see picture below. The airflow upstream the blade is much less affected, especially where reversals do occur.
The induced air speed as I understood from BEM theory has here a sinewave shape with peak value around 0.3 in the main axis of incoming wind. The angled a’ induction factor seem here to be negligeable due to reversals.
I would not say the blade flights in its own wake just after reversal, but still uses “fresh” air, which speed is mostly unaffected by energy extraction in that area.
Anyway, this all relies on CFD, that yielded potential encouraging efficiencies, but has to be checked in practice at large enough scale - hopefully I can finish develop a 18m version in the months to come.
As for twist, I think of using symetrical and rigid profiles for small scale prototypes.
For a 4MW turbine, it seems to me that torsion loads would be hard to deal with, so I would favor a configuration using an internal truss mast to carry the bending loads only, and several blade profile sections rotating freely (ie no motorized pitch control) around this structure. But each blade profile section having an actively pitched tail, made of symetrical profile too, just like Elkaim (brilliantly) did two decades ago for a catamaran rigid wing sail :
https://www.boatdesign.net/attachments/wingsail-project-pdf.15147/ (Elkaim thesis)
As for yawing, yes, cables would make it painfull. For larger scales, I prefer either a floating version, or selecting wind sites that do not suffer much from loosing some angles the wind rose - so without yaw system at all, just improving pitch control to accomodate the times when air flow is not perpendicular to the swept area.
As for generator inefficiency upon reversals, and also due to doubling generators (one for each winch), I think this is mainly overcome by the high winch speeds; No gearbox required and possible use of relatively high speed generators. Probably even lower cost than for AWE winches, where speeds are only half that of wind speed at best, versus more than 1.5x here.
Thanks for warning wishfull thinking. Please do not hesitate to point where I still lack adequate argumentation, this is really helpfull.
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Sorry there were large mistakes in the XL file.
Please use that one instead :
dim_large2b.xls (56 KB)
Single blade
Mast (blade root) 90m + Single Blade length 80m (vs 75m) → total height 170m (vs 200m)
Sweep angle: 55 +/- degrees from vertical - Swept area: 21598m²
Wind speed: 9.2 m/s - Efficiency 66% of Betz - Pout 4.0 MW
TSR 3.5 Tip speed: 32.6 m/s
Could you explain the ratio of mass between your 150 m blade vs three 75 m blades sweeping the same area?
ChatGPT gived me this, without considering that you need a bigger camber and adjustable twist:
Note: I am adding the chatgpt output just to indicate that the mass may scale in a bad way. The calculation is not validated by myself in any way
Me:
I have a cantilever beam scaled to withstand a force of 100 kN at the end. The beam is 75 m long. if I scale the length to 150 m and the force to 300 kN, what would the mass of the scaled beam be, relative to the original beam
ChatGPT:
To estimate the mass of the scaled cantilever beam compared to the original, we need to consider how the beam’s dimensions must change to support the increased force and length. The bending moment in a cantilever beam, which is a critical factor for design, is given by the formula M = F \times L, where (M) is the bending moment, (F) is the force applied at the end of the beam, and (L) is the length of the beam.
For the original beam:
- The maximum bending moment M_1 is 100 \, \text{kN} \times 75 \, \text{m} = 7500 \, \text{kNm}.
For the scaled beam:
- The maximum bending moment M_2 is 300 \, \text{kN} \times 150 \, \text{m} = 45000 \, \text{kNm}.
The strength of a beam, or its ability to resist bending, is proportional to its cross-sectional area and the square of its depth (for a rectangular cross-section, for example). Therefore, if the bending moment increases, the beam’s cross-sectional area and/or the depth must increase to support that moment.
Given the bending moment for the scaled beam is 6 times that of the original beam 45000 \, \text{kNm} vs. 7500 \, \text{kNm}, the cross-sectional area and the depth must significantly increase. However, without specific details on the cross-sectional shape and material properties, we can’t precisely calculate the new mass.
Assuming a linear relationship between mass and the required material (which is a simplification), and knowing that the bending moment capacity needs to increase by a factor of 6, the mass of the beam would likely need to increase by a similar factor to maintain structural integrity under the new conditions. This factor could be even larger due to the longer span and higher force, which require a disproportionately larger increase in thickness and material due to the squared relationship of depth to bending moment resistance.
Therefore, as a rough approximation, if the original beam’s mass was scaled up just by the bending moment increase, you might expect the new mass to be at least 6 times greater than the original mass. This estimation doesn’t account for the complex interplay of structural engineering principles, including buckling, material properties, and the specific geometry of the beam’s cross-section, which could all significantly affect the actual mass required.
For precise calculations, detailed analysis using structural engineering formulas or finite element analysis (FEA) software would be necessary, considering the specific materials, cross-sectional geometry, and loading conditions.
Sorry I wasn’t clear enough.
The Single blade has a non-pitching section I called “blade root” (90m long in the latest XL file) followed by the pitching blade (80m long). There are cables attached to the highest point of the blade root section to drive the winches on both sides, but also (moving) stay cables attached to anchors located on the pivot axis, approx 100m in front and behind the blade. Theses cables (possibly rigid and profiled for largers turbines) carry most of the bending load due to blade lift for the blade root section.
As a result, the blade root bending moment experienced by the single blade cannot be extrapolated directly from the 75m HAWT blades.
Secondly, as pointed by GPT, the beam spar caps requirements depend upon the cross-sectional area. As the Single blade is approximately 8 times thicker than reference HAWT blades, the bending forces translate into spar caps constraints reduced by the same factor 8. This is the reason why I say the Single blade (profiled section) is lighter than each of the reference HAWT blade. I am aware that there are higher requirements for shear webs, profile panels… due to increased surfaces (but 4times lower pressures due to lower TSR)
Now modeling the blade lift with a single force at the end of the beam is somewhat different from reality, where each section (spanwise) of the blade contributes to bending forces, to an extend that depends mostly upon apparent wind speed and induction factors, blade area, lift coefficient… For HAWT, apparent wind speed (which must be squared) ranges from 0 to tip speed from root to tip, and most of the bending forces are located near tip. When for the Single blade, the apparent wind speed variation range is lower due to the root section.
Additionally, HAWT blades have to be very stiff in all directions and also torsionnally (to keep a precise angle of attack, which is needed at more than double TSR). This all contributes to more structural material requirements, more mass, and more constraints due to mass (the constraints due to the blade mass now outweights the aerodynamic constraints for larger blades to my knowledge)
Also the blade manufacturing would be different. HAWT blades typically use molds, and consequently gluing several blade parts, when the Single blade would possibly use a continuous main spar made of tubes (carbon truss, possibly isotruss), and hollow blade sections made of curved sandwich panels with reinforcements and pivoting around the main spar. This makes the bill of material and weights quite different, all the more as reducing spar caps volumes make it possible to use more expensive and lighter materials like carbon fibers.
The XL file I attached was just an attempt to estimate roughly the bending moments and spar caps requirements (which I think is a main driver of the blade weight, even if it seems to typically account for only 30% of very large HAWT blades)
Below I explain how the calculations are made (refer to line 10 of each blade calculation tab)
Section: height of the middle point of this section (from root to tip)
Cord: chord length in meters (decreases linearly from root to tip)
Area: area of this blade section (m²) = chord x section height
Lift coef: assumed constant (can be on average higher for single blade, due to reversals that prevent stall, even with symetric profiles)
F lift (N): force due to lift on this blade section
Moment (Nm): Product of force by distance to root (of profiled blade), assuming perpendicular lift force.
Cumulative (Nm): cumulated moment calculated from the tip
max power (W) : power extracted from this blade section (without inefficiencies taken into account - optimistic but same for both cases)
Spar caps gap (m) : avg distance between spar caps
Spar tension (N) : Cumulating bending moment basically translated into the spar caps (compression in one cap, tension in the other)
spar mm²: required cap area to carry the tension given the material strenght (max MPa)
Spar MPa: max strenght used to calculate spar area
Spar mass (kg) both caps : from spar area,section length and density… (carbon fiber assumed, which is not the case for usual HAWT blades)
But I agree, I have yet to design a large Single blade and estimate precisely how heavy it would be. If someone feels capable of proposing:
- load cases (at least for nominal wind speed, vertical blade, and upon reversal - highest acceleration)
- main spar design (carbon fiber truss ?)
- rotating profile design (sandwich panels, ribs attached to cercle rails rotating over the truss …)
and making preliminary structural calculations (probably using FEM), I am interested, possibly with some finance…
I uploaded another video of the airflow simulation (from 3D simulations)
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