Testing Turbines, reports, apparatus, etc.

[oneirondreamer]

Hello All,

Here's some of my research papers, created for myself and for engineers who have reviewed both the data and the test equipment.    I have more, however I'm not very organized and have had to move quite a few times, both physically and between computers, so it may take some time to dig out.   As well, I'm trying to spend most of my energy getting my latest project up and running, so thanks for your patience.

Best
Drew

[BruceDownunder]

 Gee, I would not like to be the "Judge" in this case ,,   but this is my experience.

 I live on a few acres of land and have lots of tree stumps ,from many years ago ,like 50 plus , I'd guess.

anyhow , I picked one ,around 24 inches dia by 36 or more tall .  Been there ,must be 20 years ,since the tree was cut down. 
So, I came along ,made sure it's solid all through and no termites. Poured a gallon or three of Creosote into the end grain and around the whole of the stump ,a few times to let it soak in.

 I levelled the top off ,sat a welded,galvanized "top-hat" with welded cheeks ,so a 3/4 inch bolt /azle could be attached very solidly ,with very long coach bolts, gal type.

It carries a 40 foot solid steel angle(4 inchx4 inch) back to back ,bolted and this is guyed into concrete and rock guy anchors .

Anyhow, she's been up 15 years now and still as solid as a rock.  lifts and lowers a 65 foot steel tower through 3 pulley points and a huge drum winch -used to haul a 30 foot boat up a boat ramp in its early life.

 I don't do much now in the engineering dept, because of bad health -75 yo now ,sort of like an OL battery -the terminals look ok but my insides are all corroded....still happy ,but .

well, there ya go --so this fella has had a old tree stump as a foundation for his tower for 15-20 years an she's still OK..

Cheers,
Bruce

[Adriaan Kragten]

Nice to see your papers but there is a large discrepancy in between the different papers which you have presented. In the paper of Brian Kirke, it is claimed that the turbine has an efficiency of 45 %. I assume that you mean a Cp of 0.45 because there is a difference of a factor 1.5 in between the Cp and the aerodynamic efficiency (see KD 35 page 15). I simply don't believe a Cp of 0.45 because it is impossible for a system which is partly working on drag.

In your own measurements given at the last file with performance data, you have found a Cp which varies in between 0.14 and 0.31. The highest values are found for wind speeds above 10 m/s and this must be a Reynolds effect. If I take only the measurements for wind speed higher than 10 m/s, the Cp varies in between 0.21 and 0.31 so the average value is 0.26. This is a very good value for such a turbine but it is only a factor 0.58 of the value as claimed in the paper of Brian Kirke and it shows that my suspicion for a Cp of 0.45 is right. In reality the wind speed may vary around 5 m/s, so you should not use the measurements for higher wind speeds except if the real wind turbine is much larger than the model which was tested or if the medium is water in stead of air.

The fact that there is so much variation in the measured Cp shows that something has been measured inaccurately. I expect that you have not measured at a completely windless day and that gives variation of the wind speed and so of the power depending on in what direction you drive. The mechanical power can only be measured accurately if you measure the rotational speed and the torque and measuring of the torque for a full size wind turbine is really difficult especially if you have to do it on a car. So I also doubt if this has been done correctly. So the large fluctuation in the Cp value may also be caused by inaccuracy of the torque measurement. If you have only measured the electrical power of the generator, you can derive the imput mechanical power but only if you know the generator efficiency for all load conditions. You certainly can't calculate with one generator efficiency for all measuring points.

[oneirondreamer]

Adriaan,

Thank you very much for your paper KD 35 and your review of the documents I've posted.   I also thank you for giving me the page number of your report to reference, as otherwise I'm not sure I would have been patient enough to find it (I have a lot on my plate right now).   

Thanks to your paper I finally have some idea of the real difference between Cp and Aerodynamic efficiency, which I'd always though were effectively the same, with a shifted decimal place.   Another misunderstanding banished thanks to your work.   

I had forgotten the reference to 45% by Brian.   In the dates of the reports you will see Brian's is much earlier (2008), and this was durning the time we were testing in water, and while I had just gotten started in testing.  What I read is that Brian hoped we could achieve high efficiency, but not that he saw it, or that I claimed it.  At the time that Brian wrote the letter, the best I'd had a turbine do would be around Cp 0.12 or below.   I'm sorry for the misunderstanding, and I have attached two letters from engineers who reviewed the data from 2012 testing (one of whom inspected the test platform before and after testing, and participated in testing Jon, and one from Matt, who checked over the test rig, including the calibration of the load cell, and reported on the data collected by Jon and I.   

To better understand the development and testing cycle, a bit of history may help.

From 2007-2011, I built helical versions of the turbine with tapered tops.   I built both left and right hand twist models, but without being conscious of it, I always oriented the cross section so that when twisted the convex portion ended up as the upper surface, and the convex as the lowest.    All these turbines worked (Max Cp 0.12), but their performance was disappointing as I wasn't even reaching close to the Savonius's peformance in the Blackwell report.   This is before Ian Ross's work showed the test methodology errors from Blackwell and perpetuated onward, had I been aware that the real performance of the Savonius is closer to Cp 0.05 than the Cp 0.21 claimed in the Blackwell report I would have been more excited.   

I decided to switch to testing in air, and with some awareness of the Reynolds number issues, understood that larger would work better, so built a 12ft by 6ft version version from wood.   At the time I hadn't considered moving platform testing, and so installed it on a hilltop, with a brake band dynamometer, and waited and tested.   The results were perplexing as it seemed like the max Cp and turbine speed would drop off as the wind speed picked up.    I lit flares upwind to try to visualize the path of the flow to gain a better understanding of what was going on.   What I found is that he smoke entering the blade at the centre would exit the blade much lower down.   It seemed there was a bit of an archimedean scew effect.   I began to wonder if as the wind increased, the rotor, being mounted fairly close to the ground, was building a sort of pressure bubble around it as the wind picked up.   

After this I researched using moving platforms for testing in air, hearing about how Burt Rutan used them for aircraft testing, and decided that I could test a 1m diameter version on a vehicle.   I built a 1m by 2m turbine, with the twist reversed so the convex foil surface was facing down, and concave facing up.   This turbine was the first one I tested in my moving platform, and it reached around Cp 0.16, however it did not always self start, in some positions it would weathercock to the wind, and if the right wind shift happened it would quickly start, in other positions it would start right away.   

I built another using the same cross section, but 2.25m tall, and slightly increased the angle of twist.   This was the 16 th version and is the unit you can see tested in this report.   I tested it previous to this report and believed I was reaching Cp 0.24.  For this report a local engineer, Jon Scott volunteered to look over my test equipment and procedures, then come along and collect data, and analyze the collected data.   Jon did so and concluded that the data we collected together showed a Cp of 0.29, as he reports in the letter below.    Later another engineer, Matthew Hall, examined the data set and found a max Cp of O.31.   Matthew also noted that this occurred at the highest torque load available to the test equipment I had, and that the TSR increased above that, indicating that at the highest wind speeds tested, the Cp may have been increased if we had more torque available.   

As noted in my report on the testing, we used a casting arm controlled by a tail on the wind sensor, to allow the directional wind sensor to be faced into the wind, and to make the vehicle driver aware of any significant wind shift.   Data was not collected during any time that wind shift was observed. 

I agree that the higher performance at very high speeds isn't particularly relevant to annual energy collected, however as you guess, the value is in estimating the output of a 2m diameter turbine (as you see in Matt's report attached). 

I think your reluctance to accept the Cp 0.31, or 0.29 is very reasonable, and I won't argue about your suggestion that 0.26 seems a more reasonable number.   Given what we know even it would be an extraordinary result, and should require robust evidence.   

My goal in writing here is not to convince anyone of these reports validity, but to show that I've been at this for some time, and have learned some useful things about this type of turbine, how to test them, and that much about them that is "known" may not be correct if it's based on wind tunnel data. 

My goal is to try to make this new system ready to provide the robust, repeatable evidence required for people like yourself to evaluate and I thank you for your time and assistance. 

Best Wishes,
Drew

[MattM]

Airflow over a hilltop may suffer from the Coanda effect; tendency of a fluid jet to stay attached to a convex surface.

[Adriaan Kragten]

The problem with presenting Cp values is that Cp isn't measured directly but that it is calculated from the measured mechanical power P and the measured undisturbed wind speed V. The formula for Cp is: Cp = P / (1/2 ro * V^3 * A). You only find an accurate Cp value if P and V are measured accurately and if you have used the correct values for the air density ro and the swept rotor area A.

For an horizontal axis wind turbine A = pi * R^2 but for your rotor, you have to use another formula as the rotor has a certain height H and as the diameter D isn't constant. So I hope that you have used the correct value for A. If you measure the torque Q (Nm) and the rotational speed n (rpm), P is given by: P = Q * pi * n / 30. But if you have only measured the electrical output of the generator, you must must have used the correct generator efficiency.

The biggest mistake is made if the undisturbed wind speed has been measured incorrectly because Cp is proportional with V^3. Using a car for the measurements is a good way if there is absolutely no wind and if the model is positioned high enough above the roof of the car such that it is out of the boundary layer of the car. But still you can make a mistake in the wind speed. If you use the speedometer of the car, you make a mistake because all car speedometers show too high values. You can use the speedometer if it is calibrated. If you use a cup anemometer it must have been calibrated in a wind tunnel because most cup anemometers show too low values because of the bearing friction. I have seen measuring results of a Vetus cup anemometer which showed a wind speed which was 2 m/s lower than the real wind speed and so you make a very big mistake with that device especially at low wind speeds. Whatever divice you have used, it must be placed far enough from the rotor so that you really measure the undisturbed wind speed.

The density ro depends on the temperature and the pressure. In my calculations, I use a value of 1.2 kg/m^3 at 20 degrees C at sea level but it can be different. For the wind tunnel measurements which I have performed, ro was determined very accurately. The wind speed of the wind tunnel was determined with a pitot tube and the pressure difference was measured with a very accurate divice but such a divice can't be used in a car because a car isn't stable enough to read the pointer.

I have a problem with the picture of the airfoil which you have used for your rotor. It depends very much on the position of that airfoil with repect to the wind direction if the airfoil is generating lift or drag. If the airfoil is about in line with the wind direction, it will generate lift for a certain part of the airfoil. However, if it is about perpendicular to the wind direction it will only generate drag. The optimum lambda for the lift position may be different than for the drag position but the rotor can rotate only with one lambda at a certain load. Have you any idea of the torque fluctuation during one revolution if you look only at a small blade segment? I realise that the torque fluctuation of the whole rotor is flattened because the blades have a helical shape.

[Adriaan Kragten]

I have another problem with the airfoil given in your picture. You show a lift part and a drag part. Any airfoil is generating drag and lift simultaniously.

The drag D is defined as the aerodynamic force in the direction of the relative windspeed W. The drag is always positive. The drag has two causes. The first cause is that the wind speed is reduced to zero just at the airfoil nose and this gives some positive pressure at that place. The second reason is the friction of the boundary layer and this friction works around the hole circumference of the airfoil. So the whole circumference of the airfoil contributes to the drag.

The lift L is defined as the aerodynamic force perpendicular to the relative wind speed W. The lift can be positive or negative depending on the angle of attack alpha. For normal asymmetric airfoils, about 2/3 of the lift is caused by the under pressure at the convex upper side of the airfoil and about 1/3 of the lift is caused by the over pressure at the flat lower side of the airfoil. If you have an airfoil which is curved in two directions, like the airfoil which you use, there can be over pressure at a part of the upper side and under pressure at a part of the lower side. This can result in a negative lift for the back part of the airfoil if the lift for the front part of the airfoil is positive. But it isn't correct to call this negative lift drag if it would result in a negative torque.

To get a better insight in what is really happening with your rotor, I have replaced your rotor by a thin sheet which is curved in an S-shape such that a half blade has 10 % camber and that the axis of rotation lies in the middle of the sheet. It is also assumed that every half blade is a separate airfoil. Aerodynamic characteristics for a 10 % cambered sheet are given in my public report KD 398.

First it is assumed that the rotor isn't rotating and that the position of a line through both blade tips is perpendicular to the direction of the wind speed. Now we have a pure drag machine and in report KD 416 I have derived that the optimum tip speed ratio is about 1/3 for a pure drag machine. However, this derivation was done for the wind speed at the heart of the cup and if we take a tip speed ratio of 1/3 for this position of the blade, it will be about 2/3 for the blade tip. In figure 4.2 of report KD 35 you can see that there is a very large reduction of the ideal Cp for this low tip speed ratio because of wake rotation. The maximum theoretical Cp is reduced from 0.59 up to about 0.35 for lambda = 2/3, only because of this effect. The real Cp max for a pure drag machine is even much lower and only about 0.05.

Next it is assumed that the rotor isn't rotating and that the position of a line through both blade tips is in line to the direction of the wind speed. As no power is generated, the wind speed at the rotor is equal to the undisturbed wind speed V. For this position, the angle of attack alpha is zero degrees for the front part of the blade and zero degrees for the back part of the blade. The Cl-alpfa curve for 10 % camber is given in figure 3 of KD 416. The Cl value depends strongly on the Reynolds value. Assume we take the lowest Reynolds value Re = 1.2 * 10^5. This gives that Cl = 0.4 for alfpa = 0 degrees. So on the front part of the blade we have a positive lift pointing to the left and on the back part of the blade we have a positive lift pointing to the right. So both parts of the blade contribute to a positive torque.

Next it is assumed that the rotor is rotating with a very low tip speed ratio lambda = 0.1 so the tip speed is 0.1 V. It is still assumed that the wind speed at the rotor is V. The angle of attack is found from the speed diagram and it is found that tg alpha = 0.1 so alpha = - 5.7 degrees for the front part of the blade. The Cl-alpha curves are only given up to alfa = - 2 degrees but the Cl value for alpha = -5.7 degrees must be strongly negative. So the front part of the blade gives a negative torque, even for the very low value of lambda = 0.1. The airfoil nose for the back part of the blade is lying at the centre of the rotor and there the blade speed is zero. So there we have an angle of attack of 0 degrees resulting in the same lift coefficient of 0.4. So the back part of the blade still contributes to a positive torque.

If this procedure is repeated for lambda = 0.2 you will get a much larger negative angle of attack of -11.3 degrees at the front part of the blade and this will result in an ever larger negative contribution to the torque of this part of the blade. If this procedure is repeated for lambda = 0.3, you will find a negative angle of attack at the front side of the blade of 16.7 degrees and a very large negative contribution to the torque of this part of  the blade.

In reality you don't have separate airfoils for the front and the back part of the blade but even if the airfoil is seen as one airfoil you will get very large negative angles of attack at the front side. The fact that you don't use an S-shaped thin sheet but a solid body don't solves this problem so I don't understand how the lift position of your blade can contribute that strongly to the total torque that you can get a maximum Cp of about 0.26.

[oneirondreamer]

Thank you for your detailed response Adriaan, I appreciate it very much.   

I agree that measurement accuracy is key in this work, it is why I invested early in a data loggin and measurement system, is why, once I was getting interesting results,  I asked Jon Scott, a very experienced R&D engineer, and Matthew Hall, a masters in Mechanical Engineering student, to look over my test equipment and point out inadequacies.   Things like ensuring that the wind sensor would castor and alert the co-pilot - mechanical load operator of crosswind, and direct measuring of the rotor swept area (rather than rely on the CAD drawings that produced the templates for it's construction, and double checking of the load cell calibration are at least partly due to having them involved.    I am glad that they independently came to the same conclusions, and believe that itself is some validation of my attempts to measure accurately.

In terms of trying to visualize the flow over these foils, there is something about the physical geometry that adds complexity and makes the 2D visualization you are attempting difficult and perhaps impossible to be done accurately.    I'm not exactly sure how to describe it, in words, I often find it challenging to write what I see clearly in my head. 

I'll also note that I'm not convinced this is the best possible shape for this foil.   I'm no longer sold on the “bump” as much as I was at the time I designed it.   My latest work does not have the “bump”, though I have changed the cross section in the bottom 3rd to make space for an alternator and bearings.   I also noted on my turbine #15, the unit which wouldn't always self start, that by adding a bottom plate, the startup and overall performance increased. 

A difficulty with a 2D analysis of the flow in a helical solid bodied turbine is that the leading edges are longer than the center of the turbine.   So if rather than a completely 2D visualization, we consider a 10cm tall section, that's 1m in diameter we can see this complexity and consider how it may affect flow.    In this partial 3D instance the problem with 2D visualization becomes more apparent.   Here we can see that the the helical path makes the outter edge have a 15cm depth, while the inside is only 10cm.    So air attaching to the 15cm area is flowing along the foil, and as it does so, there is less foil for it to flow on.    This only partly describes the flow complexity, as it doesn't take into account the reality of vertically displaced air due to the screw pump effect.   With this amount of flow complexity, trying to reduce the model's performance to visualization of any 2D plane is challenging.   

Thanks again for taking the time to consider these issues and providing your reflections on them.   It's very helpful for me to understand the inadequacies in my presentation.   
Best Wishes,
Drew

[Adriaan Kragten]

I have slightly modified my previous post as the angle of attack for the back part of the blade wasn't taken correctly. You might be right that my 2D description of the flow isn't correct but then I don't understand how the lift is generated such that this lift results in a positive torque.

In my public report KD 417, I have described the rotating blade turbine. In figure 4 of this report, I have determined the angle of attack for twelve positions of the blade if the rotor is rotating with a tip speed ratio of 2/3. In this figure you see that the angle of attack is rather small for positions 2, 3, 4, 5, 6, 8, 9, 10, 11 and 12. So this machine is mainly a lift machine. Now lets assume that the optimum tip speed ratio of your rotor is also 2/3. If I compare the blade positions of the rotating blade turbine with your turbine, I see that your blade is positioned totally wrong with respect to the direction of the relative wind speed W. You may try different other tip speed ratios but I expect that you will find no tip speed ratio for which you will get reasonable angles of attack for the airfoil which you have chosen. Therefore I still doubt the high Cp values which you have measured.

[oneirondreamer]

Thank you again Adriaan, for your willingness to engage with this topic after being so clear about how you see it to be unlikely to bear fruit.   

My hope is that even if it doesn't bear fruit, our combined dialog, and that of the other participants, will be a useful tool for people in the future to recongnize a road best not traveled. 

After all the research I've done on other VAWT systems, I find your unwillingness to accept my results (at Cp 0.26 or 0.31) at face value to be reasonable, and even perhaps appropriate, given the number of major oversites in the research in this field.  If these credentialed scientists can make the major errors we see in the research, then of course I agree, I am even more likely to make errors.   

I had hoped that using proffesional engineers to validate my work would give it more credibility, however these days, in this field, I can understand how that is of limited value.   I've seen engineers make errors often enough that I no longer expect them to be mistake proof. 

My plan has been to first make a simple, quick version of the turbine, to try to determine TSR and Cp, then with that data build a slightly larger and much more durable version out of sheet metal.    With the sheet metal version, my aim is to install at least 1, near a government weather station, and ideally to then have real time results published to the internet, of course fundamental to those results having value, is a decent match to the alternator, which is at least in part why I'm here in this forum.   

I hope that you see that this work has value, even if only to show people in the future that this direction was explored, and the results of that exploration.   I think we can all agree that the technical data available on these types of high solidity turbines, and especially helical ones, leaves a lot to be desired.   

The sectional drawing I posted is part of a larger presention which I usually give in person, but I will find time to record it and post it to youtube. 

A positive factor for these turbines which I don't believe has been addressed very well in the literature, and on which you might have some interesting thoughts is this.   An advantage of the HAWT design is that the winds action on the blades is consistent around it's circle, with perhaps a small interference from the tower.   The flow over the blade is continuous and regular.   

In contrast in a straight bladed VAWT, the wind angle changes constantly, and at some points the blade will be in stall, or flooded with such turbulence, that it is in stall.   In an airplane wing that's recovering from stall, it's generally understood that even once the airplane is oriented for recovery from the stall, it takes at least the time/ distance of a wing depth, for clean flow to be established, and lift to reoccur.   It's my understanding from Dr. Bowie Keefer, that this is also a problem in H rotor VAWT's.   That geometrically and theoretically it can be determined when lift conditions will be reestblished on a VAWT blade, however practically, it will take some amount longer before this is actually in effect.   This is one opinion on why the smaller Darius turbines have much poorer results than would be expected from a calculation table using data from stationary airfoils. 

For a helical bladed VAWT, this is not as simple, as the “lift bubble” for lack of a better discriptive term, once formed, can remain attached, and travel up the turbine blade as it rotates.    No time/rotational distance is required to establish clean flow, it's already present on the blade. 

The other issue that thin bladed VAWT's face is that they are more likely to be stalled by turbulence, as the blade depth is so short. 

I'm not convinced that helical bladed Darius VAWT's are worth the extra effort to fabricate, and while they may average torque output, they face even more complex fatigue dynamics. 

Thanks again for your patience with my lack of understanding some of the technical terms you use.   I'm presently trying to understand your use of the term lambda, and I'm sure understanding it will be useful for me in the future.   I did not finish high school, so my formal mathematics training didn't go much beyond multiplication and division and while I've taught myself quite a bit, I have some significant holes in my understanding.

Best Wishes
Drew

[Adriaan Kragten]

I have made a mistake in one of my earlier posts. I have said that the optimum tip speed ratio of a pure drag machine is 1/3. This is true if you only look at the cup which is moving in the direction of the wind. But the cup which is moving against the wind consums all the power generated by the other cup for this tip speed ratio. The real optimum tip speed ratio is therefore much lower and in KD 416 I found that it is about 0.15 for a half hollow sphere and if you take the wind speed at the heart of the cup. For an S-shaped rotor the optimum tip speed ratio will be about double this value as the tip lies at the double radius of the heart of the cup and so it is about 0.3.

It might be that you have not used the correct swept area A when you calculated the Cp value. Your rotor is rather slender if you compare it with a normal Savonious rotor. So if you make a photo of the rotor you see a certain area of it. This area is not the swept area but much smaller for your rotor. The swept area is the area which you get if you make 360 photos for every degree of rotation and if you pile all these photos together. If you have used a too small area A, you will find a too high Cp value.

To get an idea for which angles of attack your airfoil supplies a positive torque, you can make a 2D wing of the airfoil and test it in the wind tunnel or on your car with the shaft of rotation horizontal and in the centre of the blade. You start with the position for which the line through the blade tips is horizontal and call the angle of attack zero degrees for this postion. You measure the torque for this position for a certain wind speed and using the correct formula, you can calculate the torque coefficient. Next you increase the angle of attack by 5 degrees and do the same. You measure the torque by taking steps of 5 degrees untill the blade has rotated 180 degrees. I expect that you will find only a positive moment for angles around 0 degrees and around 90 degrees. For the anglea around 0 degrees you have the effect of a lift machine and for the angles around 90 degrees you have the effect of a drag machine.

If the moment is negative, the rotor will consume energy when the rotor has this position with respect to the direction of the relative wind speed W. The direction of the relative wind speed depends on the chosen tip speed ratio and on the value of the absolute wind speed in the rotor plane (which is 2/3 V for the lambda which belongs to the maximum Cp). You only get a positive average moment for a whole revolution if the summarised effect of the positions for which the moment is positive is larger than the summarised effect of the positions for which the moment is negative.

[oneirondreamer]

It might be that you have not used the correct swept area A when you calculated the Cp value. Your rotor is rather slender if you compare it with a normal Savonious rotor. So if you make a photo of the rotor you see a certain area of it. This area is not the swept area but much smaller for your rotor. The swept area is the area which you get if you make 360 photos for every degree of rotation and if you pile all these photos together. If you have used a too small area A, you will find a too high Cp value.

In the reports done on it, the way the area was calculated is in the notes, but by my recollection the rotor swept area of turbine #16 was arrived at by two measures, which agreed.   The first was "as drawn in CAD", the rotor was redrawn as a 36 multiple rotations, turning it into a vaned tapering shape, the silloet or projection of this shape was done onto a flat plane, and that area was calculated by the CAD system.   The second, which was recommended by engineer Jon Scott, was to have the turbine mounted horizontally over a sheet of plywood, set to be easily rotated.  A tall 1.5 m T-Square was mounted so as to stand vertically, on small piece of plywood, with a marking hole drilled at the point the T-Square edge met the plywood.  This was positioned at the turbine tip, and was moved along the blade in 10cm (as measured along the turbine axis) increments, resulting in about 16 points measured along the blade, on both sides, and then rotated, and measured again, both sides.  These measurements were used to calculate area, using straight lines between the measured points.  I don't remember what the variance was, but it's documented somewhere in my records, and Jon's, as he insisted on it.   Mathew and Jon also insisted on taking calibration measurements on the load cell and anemometer, and may also have been the people to ask that the wind sensor be made to castor freely as directed by a wind vane.   

The other thing we did to try to ensure the best accuracy possible, given time and money constraints, was to park the test system in the windiest place we could find, which was Clover Point, in Victoria BC.   There we experienced turbulent, but significant winds, between 10-25km/hr, and collected data while varying the load on the turbine blade.   We spent two days stationary testing, and found that the results were a close fit to the moving platform tests, at least in the low speeds measured stationary. 

My biggest concern in measurement error is also on the wind speed input sensor, and having it in the same wind stream tube as the turbine, without having turbulence from the anemometer affect the turbine.   I've done what I can to position it, and welcome advice on how I may improve this.   I do have access too, two identical instruments to the one I'm using and was  planning on mounting them in place of the turbine, one at centre of swept area and another near the top, and comparing the results.    Another thing I haven't gotten done yet.

As well, I recognize the side wind issue, however the place I test is in a mountain valley that is very calm usually at least 5-6 hours per day.   I will mount my existing sensor on a casting bracket controlled by a tail, so that it can be free to track wind direction, and I will then also be able to see it and note when/if crosswinds occur.   

To get an idea for which angles of attack your airfoil supplies a positive torque, you can make a 2D wing of the airfoil and test it in the wind tunnel or on your car with the shaft of rotation horizontal and in the centre of the blade. You start with the position for which the line through the blade tips is horizontal and call the angle of attack zero degrees for this postion.

I am familiar with this method of analysis for anticipating VAWT performance, and it seems especially on the higher Reynolds functioning Darius turbines, I think it has been shown by people like yourself, to allow for accurate projections.   

In the higher solidity VAWT's, in the work of Modi, Benesh, Rahai, this same methodology does not seem to have made accurate predictions of real world performance.  They were of course handcuffed by not understanding about radically different blockage ratio's required to test these turbine types and so trying to come to understanding of how these turbines worked from bad data.  That's not to say that A-B testing of the same size turbines in the same wind tunnel, by Modi and Benesh have no value, just that the computed Cp's and TSR's are inaccurate.   Though I used some of Rahai's CFD generated results in my turbine that worked so well, I no longer see those ideas as the features that contributed much of the power.

Another complication to visualizing the flows around the turbine is the vertical flow through the turbine due to it's achimedian screw shape.    The only good video I have of a few hours of trying to get smoke to go through one of my early rotors, it shows the smoke leaving the blade (in a 6 ft diameter turbine) about 1 ft below where it entered.  On the best version of my older turbine, and my new turbine, my best guess is that it would move up the blade.

I do have some ideas of how the flows may work and result in energy capture by the turbine, and even how it may be possible to numerically calculate some aspects of the flow, and I will find time to put that all together and into a video/document, though I'm not sure when.   

The way I've worked has been more empirically, than by projection.   I've built what was thought to be the best, found it didn't meet projections, so modified it based on my intuition and sometimes with flow visualization tools like smoke flairs, again and again, often in ways that resulted in things that didn't function well, or at all.  I think we ran about 15 different models in water, and I've done about 24 different models now for air.    I think now that I've gotten an understanding of how the flows at different TSR's interact with the blade, however I'm also aware that my mental model may not be correct.   

An issue I face around this, is how do I best transmit these idea's around 3D flows that are dynamic with the TSR.   I've done a lot of arm waving trying to explain theses very visual ideas.   I think I can do a good job of it now that I've figured out some software tools to help.   Just hasn't been the next thing on my plate yet.

[Adriaan Kragten]

So I see that you have determined the swept area A in the correct way, so this is no simple explanation for the high maximum Cp values which you have measured. If your measurements have been performed correctly then the result is what it is. But I have no idea how you have realised that the lift generates the major part of the torque. If the major part of the torque is generated by drag, a maximum Cp of 0.26 is simply impossible.

The problem which I have to understand the functioning of the lift part of your rotor also exists if I want to understand the functioning of a normal Savonious rotor with buckets made out of half hollow cylinders. Also for that rotor type, I find very large negative angles of attack when the leading edge of a cup is at the front side of the rotor and when this rotor is rotating at a tip speed ratio of 0.9. So I doubt if a normal Savonious rotor is really a combination of a drag and a lift machine like it is generally accepted. If it is only a drag machine, the high measured Cp values of about 0.2 can only be caused by wind tunnel blockage. I have the same doubts for the VAWT with many cambered blades mounted close to each other.

[oneirondreamer]

So I see that you have determined the swept area A in the correct way, so this is no simple explanation for the high maximum Cp values which you have measured. If your measurements have been performed correctly then the result is what it is. But I have no idea how you have realised that the lift generates the major part of the torque. If the major part of the torque is generated by drag, a maximum Cp of 0.26 is simply impossible.

The problem which I have to understand the functioning of the lift part of your rotor also exists if I want to understand the functioning of a normal Savonious rotor with buckets made out of half hollow cylinders. Also for that rotor type, I find very large negative angles of attack when the leading edge of a cup is at the front side of the rotor and when this rotor is rotating at a tip speed ratio of 0.9. So I doubt if a normal Savonious rotor is really a combination of a drag and a lift machine like it is generally accepted. If it is only a drag machine, the high measured Cp values of about 0.2 can only be caused by wind tunnel blockage. I have the same doubts for the VAWT with many cambered blades mounted close to each other.

I have done my best to make my tests as accurate as I can, and I've brought in professionals to check my work, as much as my budget would allow.   I had hoped to take that turbine to the large wind tunnel in Ottawa, (where it would be less than 5% of the tunnel swept area), as results measured there would seem to be incontrovertible, however the company which owned the patent was forced to sell it, and the new owners became antagonistic with each other, and me, so it's unlikely that it will move forward in the near future.   I still have the # 16 turbine blade, however I no longer have the test equipment, or suitable vehicle for to be run on.   Sadly most of my other prototypes were destroyed by the new owners of the patent. 

This was fairly crushing to my mental health and I'm not entirely over it.   It's been my opinion for 5-6 years, since 2013 anyway, that even if somehow we've over calculated the Cp, and the design were only used in Kinetic Hydro, it would still unlock many MW of untapped sustainable energy, and do so with "low tech", that doesn't require billions of dollars of infrastructure producing high purity silicon and other feed products PV requires.   

I'm more sensitive than is healthy for me, and the craziness of modern business people can be shocking.   Modern business people are the ideal example of the old saw "experts are people who know more and more about less and less", and nowhere is this more true than in MBA programs.   Money is their only lense.   

The EPRI report from 2010, a survey of Kinetic Hydro devices in development and their requirements and theoretical outputs, vs resource availability in North America was between 15,000 and 150,000MW of untapped available resource.  It's been 10 years and there is still no real solution to accessing this resource, although some success in very large ocean based systems has happened, Canada just abandoned it's latest system.   Virtually all these failed attempts take HAWT systems and immerse them, but the lack of uniformity of flow though their blade area destroys them. 

I believe the Cp of my #16 turbine has been fairly accurately measured, within +or - 10%, so I've got no problem seeing it as max measured Cp of 0.31, or 0.26, however I suspect that there is quite a bit of room in the design for optimization.   Here's my thinking.

As I see it, there's some significant design issues with the turbine #16 as tested, and I will discuss them here, in part because they will help to see why I've taken the direction I have, with my new design. 

A mistake I made early on with this design was to not listen to some engineers, in specific engineer Ryan Nichol, a principle of the company DSA in Victoria and Halifax, who argued with me about my method for caculating TSR while doing some early testing of a rotor.   

In an eggbeater/tropinskein type Darius, or a tapering Savonius type, like mine, it does not seem as simple. 

Normally TSR is simple to calculate, with HAWT's and H rotor Darius designs, it is the outer most part of the turbine vs the wind input speed.   In my #16 tapering design, the outer most part of the turbine is not functional blade, but the rim at the bottom, which is unlikely to be contributing positively, other than as a fence to keep the lower portions of the blade from sheding flow in the wrong direction.    Even the lowest part of the tubine blade, with the large bump in it's centre, is unlikely to be making large positive aerodynamic contributions.    It's my thinking that while all the parts of the turbine may be working together, the centre section, where it's truest to what I imagined as the ideal cross section, is likely providing most of the positive reaction.    This section has little taper, and if we take it's average diameter, and calculate tip speed from it, we get a very different number.    In my testing using the standard calculation, we found ideal TSR to be about 1.2 -1.3, and that the turbine could run unloaded to about 1.5 or 1.6, but at any significant wind speed TSR's of 1.4- 1.5 or above would create a strong 2 pulse per revolution aerodynamic vibration and our test system was not robust enough for us to try to explore to it's highest possible unloaded speed.   This unloaded vibration was strong, and would occur at various RPM's whenever TSR went too high.  If we revise the TSR calculation, using the average of the best working area (the middle) then our max Cp came at TSR's of closer to .8-.9 than 1.2-1.3.   

I now agree with Ryan, that this is a more accurate way to think about the turbine in terms of TSR.   

In the testing of #16 we didn't spend a lot of time characterizing the performance at the low TSR's where the Savonius may function maximally, however it was clear that even at low TSR's, during startup, the turbine produced plenty of torque, and would function even when loaded well past ideal speed.   This makes me think that the turbine may have two operating modes, a "drag" mode, similar to the Savonius, and another mode, which I'm reluctant to call a lift based mode, and would rather call a boundary layer mode.   The only other boundary layer turbine that I'm familiar with is the "bladeless" Tesla disk turbine.   

I don't wish to be too controversial, however I hope without too much trouble readers can accept that there are more than one way to calculate the effects of flow over surfaces, the historic, and accurate for most airplane wings and propellors, high pressure vs low pressure, lift and drag methodology, and a more complex way of thinking that's the foundation of most modern CFD software, that lift is generated by changes in vector and velocity in the medium a foil is traveling through, or mass flow reaction theory, via Newtonian physics.   That airfoils are flow turning devices, and the changes in flow direction and velocity result in torque or force on the rotor.

https://www.grc.nasa.gov/www/k-12/airplane/wrong1.html

I don't consider myself qualified to speak to either, or calculate in either, so I bring them up only to note that both have been used to successfully mathematically model real airfoils performance in a variety of circumstances.    My suspicion is that specifically in very low Reynolds numbers, the mass flow method may be more useful.   

The mass flow thinking, in my mind is easier to think through, and it allows a more direct comparison between my work, and Tesla's boundary layer turbine.    I note that the Tesla turbine is an interesting and contraversial device, as is almost anything connected to Tesla.    To the best of my knowledge, as a turbine it's found little market as the best measured efficiency seems  to have been less than 50%.   It's been theorized that larger versions might do better, however the physics of scaling them up requires large diameter, flat disks that can handle massive centripetal loads, and heat differentials, without any warping.   The only real market they have found is in oil pipelines where they are apparently used as pumps and turbines in high solids contaminated flows.   

The interesting thing about the Tesla Turbine is that it also operates at very low Reynolds numbers, and it's ideal TSR is 1, or just below.   The idea is that the flow encountering the rim of the disk should be very close to the disks speed, so that the flow attaches with minimal turbulence, and as the flow spirals inward, while the RPM stays the same, the disk's surface speed reduces, and so the boundary layer of the fluid remains attached by transferring torque to the spinning disk, as it continues to do until it reaches the ports near the disks centre, where it turns 90 deg and exits.   The turbines power transformation is limited, the energy available must be less than the difference between it's input and output speeds, just as with wind turbines.   It has other issues, like turbulence in the exhaust, which mean that it's real efficiency must be much less than the input and output speed difference, however it does operate, and does so by boundary layer friction, or at least I've never seen any research that postulates another theory of action. 

In the Savonius turbine, as considered by Benesh and Co, one of the principle observations from their A-B testing of an airfoil shaped cup, vs a hemicylindrical cup, is that they believed they observed a 50% increase in Cp between the two rotors, claiming Cp 0.2 for the Blackwell, and Cp 0.3 for their flattened rotor (similar in shape to the Hi Power rotor).   Later, Rahai, also with a rotor where the "depth" of the cup had been reduced, also in some AB testing found some apparent benefit (though his methodology was so flawed it may be that no good observations can be made.   

Also, in my hydro testing, I found some interesting results.   I tested a non helical version of my cross section, and while it had very positive torque in some angles, it was not enough to keep it in rotation, it would rapidly and vigorously"flip" between stable states.   The same cross section formed helically, had strong positive torque in all positions. 

It's my understanding, from Ian Ross's wind tunnel work, and old NRC canada, real world testing from the 70's that the Savonius turbine's ideal TSR is around .2 or .3, but that unloaded it may reach 1.1 - 1.2, which was also my experience in testing a Blackwell dimensioned rotor of about .5m diameter, and that unloaded at the higher tip speeds without the top plate, it also vibrates at 2 pulses per rev.   

From the lift vs drag perspective, the Savonius, at TSR .2-.3 and Cp of between 0.05 and 0.10  is a drag machine, however at TSR 1, it's likely something more is going on.   

This something more, could be seen as the flow attaching to the outer most edge of the bucket, matching flow velocity, and having flow adhere, to create the tension in the boundary layer, pulling the turbine blade along.   

I think it's worth keeping in mind that the characteristic difference between high Reynolds number modelling and low Reynolds number modelling is that at high Reynolds numbers inertia dominates the flow characteristics, each air molecule's path is  dominated by it's own inertia, instead of being "stuck" it is to it's neighbors.   At high Reynolds numbers air is more like a series of BB's fired through the air, they each interact with the foil almost independently of the surrounding air.   In contrast, at low Reynolds numbers, the "stickiness" or viscosity between the molecules dominates and the flow is dominated by that stickiness.

In the classic Savonius, which even at TSR 1 is a low Reynolds number turbine.   In it, the change in blade surface velocity is determined simply by the curve of the bucket, and it seems to me that it is going to be strongly non linear.   If instead of a bucket, it was a flatter rotating sheet, like the popular "flip" signs I've seen at my local ice cream store, the the change in surface speed rate would be linear as flow attaches at an edge and proceeds inward toward the centre.    This aligns with the experimental work of the Benesh/Modi team's A-B tests of a Blackwell Savonius vs a flattened Savonius.    From a lift perspective, perhaps the classic Savonius can be thought about, that while the front edge is generating lift, the depth of the foil is too tall, and flow separation occurs too early.   There is a mismatch between the change in rate of flow that can remain attached, and the geometry of the blade.

However, as I found, a flatter foil, without top and bottom plate, is a very poor turbine, so while this explation may fit both the high TSR and low TSR operation of the classic Savonius, and the innovations and improvements of Benesh and team, it does not explain the improvements I seem to be measuring.

A principle difference between the helical and non helical Savonius type turbine is that in the helical turbine, as in the Tesla turbine, the surface area available for the flow reduces as the flow moves toward the centre of the turbine.   The helical shape, if cut and flattened into sections of a disk, would show that the outer most edge has a much longer path than the centre, and that flow attached to that edge, and moving along the blade, will have less surface to remain attached to, and this is happening at the same time as the flow is transferring energy to the surface through boundary layer friction.   These three geometries, the curve of the blade, the angle of the twist, and the tip speed ratio, can be optimized so that the flow encountering the blade is closely matched to the surface speed of the blade, and with the right combination of twist and flattened profile, will remain attached and sheding velocity to the blade via friction, as long as the geometry will allow, or until it reaches close to the centre, where the flow velocity and surface velocity of the turbine are close to 0, and if the TSR is correct, this should happen within 180 degree's rotation, allowing new, energized flow, into the front of the turbine, and some of this new incoming energy is lost to sweeping out the exhaust.   

A further match of the data and theory might be that the 2x per revolution vibration, felt in my turbines 15 and 16, and in earlier hydro versions of the turbine, as well as the Savonius tested without a top plate, all occurred at unloaded or lightly loaded high TSR conditions.   In this instance the turbine is encountering the flow with a good blade speed match, so energy is transferred to maintain the high speed condition, but the surface speed drop off is not occurring at the ideal rate, and as the mismatch increases, the flow separates, and separated flow, having been slowed partially, forms an energetic vortex which is shed intermittently 2x per revolution.   It's the departure of this vortex that causes the vibration I've noted, and has been noted by others testing Savonius turbines at high speeds and light loads (noted by Mother Earth news in their plans). 

I write this all with the confidence that while none of you may find this convincing, you'll hopefully take the time to consider it as an alternative to the conventional Lift vs Drag approach for Savonius type turbines.   

I of course have ignored a large part of the cycle of the turbine, the upwind side in this explanation, which I have considered, but am less confident in and do not have more time to write about now.   As well, I think the whole thing will be much clearer when I get around to making some animations and illustrations.   

Best Wishes,
Drew 

[SparWeb]

Drew,
Firstly, I have to apologize because I simply can't keep up with you.
Here is an excerpt from something you said a few days ago:

Another complication to visualizing the flows around the turbine is the vertical flow through the turbine due to it's achimedian screw shape.    The only good video I have of a few hours of trying to get smoke to go through one of my early rotors, it shows the smoke leaving the blade (in a 6 ft diameter turbine) about 1 ft below where it entered.  On the best version of my older turbine, and my new turbine, my best guess is that it would move up the blade.

Please allow me to grab onto this passage and draw out the difference between two separate things which, to me, seem essential to understanding what's going on here.

1) Local flow:
The flow will be deflected locally by the Savonius airfoil, no matter what it's shape, whether it's generating power or not.  I can tell you already are coming to grips with this phenomenon, and probably better than me since you're watching it happen before your eyes.  I like the idea to smoke test with flares.  Have you ever looked into getting an entertainment smoke generator (the kind used at dance clubs)?  The smoke can be controlled and they might not be very expensive.  Watching the smoke path from above and from the side could teach us a lot.

2) General flow:
The air flowing through an "actuator disk" that is either extracting or adding energy to the flow will experience a contracting or dilating boundary.  These boundaries are referred to as "stream-tubes" but you will also have heard of the popular term "streamlines" which represent the center-line through the middle of the tubes.  The model of the "actuator disk" is easy to work with when analyzing a HAWT, since the air really does pass through a fairly flat plane where the blades pass.  In a VAWT, this isn't so easy to say, and actually the aerodynamic model becomes a bear to wrestle if you aren't going to use CFD.

There is also more than one model to be used; one which simplifies the flow as if it's 2-dimensional, and one that incorporates rotations in the wake, known as "vorticity".  You can go pretty far analyzing a HAWT with the simple model of 2-D flow, but a VAWT pretty much doesn't get realistic unless the 3-D model is used.

This is not an excuse to despair.  Even if the details are harder to compute with a VAWT, there are some principles that remain:
a) when extracting power from the air flow, the stream tubes must dilate because the velocity is reduced,
b) the dilation of the stream tubes is proportional to the velocity change
c) this is another way to expressing Betz's law

Each of these can be worked out with basic trig and algebra.  Any time you take energy out of the air flow, it has to slow down, and that can change its path after passing by the Sav blade.  So when you say you see the flow diverging downward after passing over the blade, I think you could be seeing either effect 1 or effect 2. I wouldn't want to decide which it is right away.  You're already figuring out effect 1, but there are ways to work with effect 2 even if the heavy number crunching of CFD is out of reach.

[Adriaan Kragten]

In your report in which you present the graph with the measured Cp values, you give the Cp as a function of the wind speed V. Normally the Cp is presented as a function of the tip speed ratio lambda. For your rotor it is difficult to define lambda as the diameter isn't constant but it must be possible to find an avarage value. In a Cp-lambda curve you see that the Cp depends on lambda and that there is only one value for lambda for which the Cp is maximal. This value of lambda is called the optimum lambda. So the large variation of Cp in your Cp-V curve might be caused because the points belong to different values of lambda (for explanation of Cp-lambda curves, see report KD 35 chapter 6.4).

If you test the rotor on your car, you should do it for a constant wind speed and then vary the load from unloaded up to maximal. So you start with the maximum rotational speed and end with a stopped rotor. So in this way you measure the P-n curve for a certain wind speed and using the correct formulas, you can derive the Cp-lambda curve for that wind speed. This wind speed belongs to a certain Reynolds value for the average chord of your rotor. If you repeat this procedure for the double wind speed, you will find a P-n curve which lies much higher but if you derive the Cp-lambda curve form this second P-n curve, it will be almost the same as the first one, but it will lie only a little higher. The difference in between both Cp-lambda curves is caused by the Reynolds effect. May be you have worked this way but then my question is: are you sure that the Cp values which you present in your graph are the Cp values for the optimum lambda?

[oneirondreamer]

1) Local flow:
The flow will be deflected locally by the Savonius airfoil, no matter what it's shape, whether it's generating power or not.  I can tell you already are coming to grips with this phenomenon, and probably better than me since you're watching it happen before your eyes.  I like the idea to smoke test with flares.  Have you ever looked into getting an entertainment smoke generator (the kind used at dance clubs)?  The smoke can be controlled and they might not be very expensive.  Watching the smoke path from above and from the side could teach us a lot.

2) General flow:
The air flowing through an "actuator disk" that is either extracting or adding energy to the flow will experience a contracting or dilating boundary.  These boundaries are referred to as "stream-tubes" but you will also have heard of the popular term "streamlines" which represent the center-line through the middle of the tubes.  The model of the "actuator disk" is easy to work with when analyzing a HAWT, since the air really does pass through a fairly flat plane where the blades pass.  In a VAWT, this isn't so easy to say, and actually the aerodynamic model becomes a bear to wrestle if you aren't going to use CFD.

There is also more than one model to be used; one which simplifies the flow as if it's 2-dimensional, and one that incorporates rotations in the wake, known as "vorticity".  You can go pretty far analyzing a HAWT with the simple model of 2-D flow, but a VAWT pretty much doesn't get realistic unless the 3-D model is used.

Each of these can be worked out with basic trig and algebra.  Any time you take energy out of the air flow, it has to slow down, and that can change its path after passing by the Sav blade.  So when you say you see the flow diverging downward after passing over the blade, I think you could be seeing either effect 1 or effect 2. I wouldn't want to decide which it is right away.  You're already figuring out effect 1, but there are ways to work with effect 2 even if the heavy number crunching of CFD is out of reach.

Thanks for sharing your thoughts on these things.   I guess I come across as a bit scattered and I'm not surprised that I'm hard to follow.   I'm really just getting my head back together, though back might not be fair, in some ways I've been a scattered person for 49 years, and it's been hard on everyone, including me.  I'm taking some meds for the ADD that are useful, and I have focus and the ability to stay on track like I haven't had in a decade or more. 

I'll be brief in my response as I think I've finally reconfigured my load so that I can test more effectively.   I don't really enjoy electronics, as really it's all math.   

Your separation of local flow vs general flow is interesting, and I wonder if it might be reasonable to say that at high Reynolds numbers "local" flow is a small proportion of total flow, where at high Reynolds numbers local flow is a high proportion of total flow.

I am finding Adriaan's KD 35 paper helpful, but it's going to require careful study to really feel like I'm able to speak, or just understand that language. 

CFD, eventually will crack this nut, and allow for optimization of this rotor, however at this time, the people I've talked with, Dr. Curran Crawford (uVic), who did his Phd in the CFD study of HAWT systems at MIT, and Alana Wall, head of bluff body research at NRC, both agree that CFD is unlikely to accurately project the flows over the shape, and that trying to do CFD without a robust series of real world measurements, ideally from a range of the turbines possible shapes, to compare CFD results to, would be a waste of time and energy.  As with Rahai's work, it might look pretty, but it might be meaningless and we wouldn't have any way to know which it was.

I spent time with both of them around this, and what they explained is that CFD struggles with complex impinging flows, and the low TSR and complex, unsteady 3D flows might be modelable, but without robust data to compare it too, how could we know.   

I have made arrangements to be able to have a turbine assessed in the Ottawa wind tunnel (at my cost), and if my testing shows that I'm getting a Cp of 0.25 then I will try to get it in for proper characterization.   The right expertise behind me and my results at that time, may get some of the cost funded.  This is one reason I'm here, to understand what questions and standards should I be expecting.

I will get a better understanding of all this math, however my first priority is to get this system set up so it measures what people like Adriaan and yourself agree that needs proper measurements,  Wind input, torque of turbine, and speed of turbine.   I have found a heavy duty 1-4 ohm variable resistor, and I'm looking at using it with a heavier resistor, so that I have closer to infinite control over the load.   

I also just reread some of the Dan B old post about adding resistance to the load, and his bedspring variable resistor system, helps me to remember to keep it simple. 

[oneirondreamer]

In your report in which you present the graph with the measured Cp values, you give the Cp as a function of the wind speed V. Normally the Cp is presented as a function of the tip speed ratio lambda. For your rotor it is difficult to define lambda as the diameter isn't constant but it must be possible to find an avarage value. In a Cp-lambda curve you see that the Cp depends on lambda and that there is only one value for lambda for which the Cp is maximal. This value of lambda is called the optimum lambda. So the large variation of Cp in your Cp-V curve might be caused because the points belong to different values of lambda (for explanation of Cp-lambda curves, see report KD 35 chapter 6.4).

If you test the rotor on your car, you should do it for a constant wind speed and then vary the load from unloaded up to maximal. So you start with the maximum rotational speed and end with a stopped rotor. So in this way you measure the P-n curve for a certain wind speed and using the correct formulas, you can derive the Cp-lambda curve for that wind speed. This wind speed belongs to a certain Reynolds value for the average chord of your rotor. If you repeat this procedure for the double wind speed, you will find a P-n curve which lies much higher but if you derive the Cp-lambda curve form this second P-n curve, it will be almost the same as the first one, but it will lie only a little higher. The difference in between both Cp-lambda curves is caused by the Reynolds effect. May be you have worked this way but then my question is: are you sure that the Cp values which you present in your graph are the Cp values for the optimum lambda?

Thanks for the advice Adriaan, 

In the testing 2011-12 I used a large cast iron drum and a leather and wood brake band to apply load to the turbine, and although this was cooled by the airflow, it got quite hot at times, charring some of the wood.  It wasn't ideal, but it allowed me to avoid the alternator/building matching problem.   I also considered using a water pump load with a variable outlet, but decided it would be too messy.  The brake was adjusted remotely with a small 9V gear motor, and while it was infinite in theory, it's adjustment was quite coarse, a push of the button gave a bit of a random amount of change in force, so what we did was start driving, and add load as the turbine began to cause vibration from overspeeding (unloaded vibration starts at around 25km).   The data logging system was set up to give near instantaneous readouts of TSR and Cp, so the driver could be directed to speed up or slow down, to achieve max Cp, and that speed would be maintained in attempt to get a large stable set of data.   

With my new electronic load, I should be able to vary it to match load to windspeed, rather than matching wind speed to load.   I could produce a velocity to TSR graph from the old Data, but I think my time is better spent on the new turbine.

With the new turbine, I'm surprised by the unloaded TSR of 1.2, and I'm not yet confident that everything is being measured adequately.    My thinking was that the ideal TSR should be between .75 and 1, as in the Tesla, the rim speed and jet velocity should match fairly closely as the jet needs to attach smoothy to the disk.   I was a bit shocked to see that I reached almost 700rpm, that's more than 3x faster than I ever ran that 3D printed alternator, and I'm glad it stayed together.   

One thing I'm struggling with is how best to use this heavy duty variable resistor I have.   It's about 1-4 ohms, and it looks like it could easily handle 50-100W for quite a while, if I use it with other resistors, I should be able to tune the load.    I've got an old heavy duty 8 position rotary switch that's good for quite high voltages, and a 4 ohm heavy duty resistor (part of dryer element as suggested), and a 10 ohm heater, and I'm trying to figure out how best to wire it up so I've got position A, 10 ohm load+ varible (series/parallel?), B 4 ohm load and 0-4 variable resistor (series/parallel) and just 0-4 variable.     I think I've got it figured out, it's a bit Frankenstein/Steampunk looking but should do the job.

 A last thing about the flow modelling around these turbines.   In my smoke testing I noticed that the exhaust from the turbine seemed to be ejected at a slight angle from the wind input, and that the angle seemed to vary with the turbine loading.   As noted in the blackwell report, Savonius turbines produce a side force when in operation, just like the Flettner rotor.    In the NASA FoilSim program you can select a cylinder instead of an airfoil, and you can give it spin, and see lift and drag change.   It also provides a flow simulation visualization which is very interesting.   At TSR 0.3 roughly, it can be seen that the flow ejects at a strong angle, and that on the "upper" side of the rotating cylinder the flow is strongly affected, 3 rotor diameters away, lateral from the edge of the cylinder.   I did some screen capture around this some years back when I had a PC that played OK with the Java Foilsim is written in, it's attached below. 

[MagnetJuice]

If you are going to use a rotary switch to switch the load, the rotary has to be able to handle a lot of current. If you switch to a very low resistance, the rotary switch can burn up. You might want to consider using solenoids as in the circuit I gave you in the other post.

Have you thought about the possibility of using a large fan to test your turbine? That way the wind speed will be constant. You can get a close value of wind speed by taking several readings with your anemometer close to the turbine, and then get the average of the total number of readings.

I just bought a used 3-speed 30-inch fan for $100. I plan to use it for testing whatever turbine I build. It pushes 7800 cfm. It blows like a hurricane.



If you can do the tests in your garage, you don't have to wait for days when the wind outside is still so you can test with your truck. You can use a cheap digital Tachometer to measure the turbine RPM more accurately and with both of your hands free, you can do many other measurements.

Also very important, it would help a lot if you had an alternator built specifically for the RPM that you anticipate with your turbine. That way you can get real watts and you don't have to guess what the output is.

I offered to design a proper alternator for you before, but maybe you though that is going to cost a lot. You said that you have some ceramic magnets, if you have enough of them, you can use those. All you need is an alternator with an output of about 800 watts.

I think that you should get as much good accurate data on your own before you commit to other more expensive tests.

Ed

[Adriaan Kragten]

Have you thought about the possibility of using a large fan to test your turbine? That way the wind speed will be constant.
Ed

In 1998 I have designed a small wind turbine (the VIRYA-0.45) which could be tested by students in the class room. I have used a normal room fan to simulate the wind speed. I have measured the wind speed behind the fan and found that it depends very much on the position where you measure. It is almost zero at the centre of the fan and maximal at the fan tip. It is reduced at increasing distance from the fan. The fan could be used for the VIRYA-0.45 windmill because the only goal was to generator some power but a fan can't be used to simulate a constant wind speed. In a wind tunnel one also uses a fan but behind the fan there is an expansion and compression room and a lot of small tubes to flatten the turbulance and this makes that the wind speed is very constant at the measuring section.

[Adriaan Kragten]

With the new turbine, I'm surprised by the unloaded TSR of 1.2, and I'm not yet confident that everything is being measured adequately.   

The derivation of the maximum Cp and the optimum tip speed ratio for a pure drag machine as given in report KD 416, is done for a cup which isn't rotating. If the cup is moving linear, it is clear that only one cup can't move faster than the wind if it moves unloaded. However, if the cup is rotating, this counts for the heart of the cup. But the tip speed ratio is determined for the most outer point of the rotor. If the diameter of the cup is large with respect to the rotor radius at the heart of the cup, this can result in an unloaded tip speed ratio larger than 1. If a normal Savonius rotor would have an optimum tip speed ratio of 0.9, the unloaded tip speed ratio can be about 1.6 because of this effect.

If the main torque isn't supplied bij drag but by lift, the optimum tip speed ratio can be larger than for a pure drag machine but certainly not higher than 1 because in this case, a large part of the power generated during the lift phase will be consumed by the blade during the drag phase. So that you have measured an uloaded tip speed ratio of 1.2 isn't impossible. Accurate measuring of the unloaded tip speed ratio is much easier than measuring of the maximum Cp as you have to measure only the rotational speed and the wind speed.

[MagnetJuice]

Adriaan, big mistake for me to use the word CONSTANT in a place where an engineer can see it. 

I can see your point, constant is invariable, unchanging. When we are talking about the wind, whatever the source that is causing that air to move, it is never constant.

What I meant to say is that using a fan, properly, to spin the turbine, could result in better readings that using a vehicle and it is also more convenient.

When you use a vehicle, there are too many variables. Is the wind totally still? Are there small updrafts or downdrafts when you go over road surfaces that have been heated by the sun or cooled by shades? What about crosswinds when you drive up or down a hill, or close to a hill or when you pass a large tree, or a building? How well does the vehicle speedometer match the actual speed?  How do you consider all those variables when you do your calculations?

When you used a fan to test the .45-meter (18 inch) turbine, it was probably a small fan.

I did a test with my large fan, not a very scientific test but good enough to do some observations. I tied a string to the end of a long thin pole. Then I tied a small bolt to the string and another string to the bolt, and that string was free to move in a slight breeze. That way I could observe a strong wind speed by watching the bolt deviations, and a lesser wind speed by watching the loose string.

I positioned the fan to make sure that there were not any obstructions in front of the fan for 15 Ft. (4.57 meters). I turned on the fan in my garage with the door closed and let it run for about five minutes to allow for the air currents to equalize throughout the room.

Standing to the side of the fan, I was able to position the bolt/strings 8 Ft. (2.44 meters) directly in front of the fan. I slowly moved the bolt/strings around to observe air currents and probed a circle with a diameter of 5 Ft. (1.52 meters) perpendicular to the fan.

There were hardly any observable differences in the movement of the bolt/strings within the 5 Ft. circle. Only at the edges of the circle, there was an indication that the wind speed was declining, and the lack of wind speed that was observable very close to the center of the fan, was not present in the center of the circle 8 Ft. from the fan.

That might not be a very scientific way to test the speed of the wind, but if there is a 10% margin of error, it will be good enough for the testing that I am going to do.

I ordered two anemometers online today. When I get those, I can run another series of tests.

Ed

[Adriaan Kragten]

Using a car to test your wind turbine is a good way, at least if there is no wind at all, because you simulate real wind or an open wind tunnel. But there can be vibration problems if the road isn't flat. Measuring is also difficult because you have to take an energy source with you to power your measuring equipment but this can be solved. Using a simple open fan is a bad way as the wind speed varies very much depending on where you measure it and also because the fan creates a lot of turbulance. So any result you get from the fan measurements will be unreliable and you can prove nothing with these measurements.

The fan which I used had three blades and a diameter of 0.4 m. The nominal absorbed power was 60 W at the maximum speed. The windmill rotor had four square flat blades and a diameter of 0.45 m, so larger than the fan diameter. Only with this large rotor, I could get enough torque to overcome the friction torque of the planetairy gear box in between the rotor and the DC PM-generator. The maximum electrical power depends on the load but was only about 1 W which shows how much energy is lost in all components.

[MagnetJuice]

Since Drew already has a testing platform, he could improve and use that. As for me, I'm not concern so much about very accurate readings on wind speed. I will be interested mostly in finding out how much power in watts I can get at different RPM. The fan I have is good for that.

Nevertheless, I already sent Santa Claus a letter asking for a wind tunnel for Christmas. 

Ed

[oneirondreamer]

What I meant to say is that using a fan, properly, to spin the turbine, could result in better readings that using a vehicle and it is also more convenient.

When you use a vehicle, there are too many variables. Is the wind totally still? Are there small updrafts or downdrafts when you go over road surfaces that have been heated by the sun or cooled by shades? What about crosswinds when you drive up or down a hill, or close to a hill or when you pass a large tree, or a building? How well does the vehicle speedometer match the actual speed?  How do you consider all those variables when you do your calculations?

When you used a fan to test the .45-meter (18 inch) turbine, it was probably a small fan.

I did a test with my large fan, not a very scientific test but good enough to do some observations. I tied a string to the end of a long thin pole. Then I tied a small bolt to the string and another string to the bolt, and that string was free to move in a slight breeze. That way I could observe a strong wind speed by watching the bolt deviations, and a lesser wind speed by watching the loose string.

I positioned the fan to make sure that there were not any obstructions in front of the fan for 15 Ft. (4.57 meters). I turned on the fan in my garage with the door closed and let it run for about five minutes to allow for the air currents to equalize throughout the room.

Standing to the side of the fan, I was able to position the bolt/strings 8 Ft. (2.44 meters) directly in front of the fan. I slowly moved the bolt/strings around to observe air currents and probed a circle with a diameter of 5 Ft. (1.52 meters) perpendicular to the fan.

There were hardly any observable differences in the movement of the bolt/strings within the 5 Ft. circle. Only at the edges of the circle, there was an indication that the wind speed was declining, and the lack of wind speed that was observable very close to the center of the fan, was not present in the center of the circle 8 Ft. from the fan.

That might not be a very scientific way to test the speed of the wind, but if there is a 10% margin of error, it will be good enough for the testing that I am going to do.

I ordered two anemometers online today. When I get those, I can run another series of tests.

Ed

These are very similar to idea's I had before understanding Reynolds numbers, and turbulence intensity.    It makes sense the way you've explained it, why would anyone do anything differently?   

However we see wind tunnel based report after report, of wind tunnel data that doesn't line up with the real world.   The characters collecting the data are real engineers, and even they seem to have trouble converting what's learned in a “controlled” atmosphere, to the real world. 

I think the first issue is Reynolds number scaling.    What engineers have figured out is a way to test something small, and figure out what it's performance would be when it's large.   This works in the real world, and it works in wind tunnels.  The key is that as you 1/2 the size of your object, to get representitive output results, you double the flow speed over it.   So if you make a 1/2 scale turbine that is 0.5 m diameter, and you want to know what it's performance would be like at 40km/hr if it were 1m.    This means you need a wind velocity of 80km/hr.    If you expand out this math, what you see is that for small testing of objects you want to make large, you may need very high wind inputs, fan, or vehicle.     On top of this issue is the turbulence issue.   Turbulence comes in many forms, and it's not always easy to visualize.   What a fan puts out is a layered stream of air, layers of high intensity energy with lots of turbulence, which has been close to the fan blade, and the air in between.   Eventually this averages out, I think usually 5-6 fan diameters downstream.   This is why wind tunnels have a large distance between the fan and the test object, and always have a flow straightener at least a few diameters downstream of the fan, and upstream of the test section.    When you read your anometer, what layer of the cake is it reading?   The layer cake, or candy cane of wind turbulence will read differently in different stripes, but the stripes are moving so fast, we can't percieve them.   It's a bit like trying to read rapidly fluctuating voltage from an alternator, will your meter average, read peak or?     

It seems like the simplist way, but once you get your head around the velocities needed to scale to useful sizes, and the distance from the fan to get relaxed, non turbulent flow, mounting on a car makes more sense.    There's an additional benefit.   If you get a useful result, your whole test system is portable, you can take it anywhere and demo it for anyone. 

Best wishes
Drew

[oneirondreamer]

Hello All,

I've been sitting on these results, going over the formula's and the test rig, and I haven't any found errors of significance.   I think the load cell needs calibration, but that doesn't affect TSR or RPM, just my shaft Watt's calculation.   The load setup needs improvement, but the TSR/RPM's I'm getting are higher than I expected, so I may be able to use the midnite solar controller I have. 

The results are so good, that I am not willing to accept them at face value and so I don't expect any of you too.   These kind of results need professional validation.   I'll refine my test setup a bit, but largely I'm moving on to the drawings for a .5m x 2m version, to be made from cut and folded aluminum sheet.    My alternator might actually be a better match for something a bit bigger, though it would be better if the Volts/rpm could be raised.   



Best Wishes,
Drew

[SparWeb]

Hello Drew!
That's a lot of data.
My blunt opinion is that you won't see the forest for the trees.
The data needs to be filtered and handled in histograms.  It will be so much easier to work with than this.

When I do a datalogger run, I just let it go collect data and I don't try processing anything simultaneously.  Yes, it is possible, and with certain systems it would seem easy, but the point is not to rush through this.  Filtering chaotic data points and transitions isn't easy "on the spot" but doing so afterward is pretty straightforward.  In fact, if you are collecting good clean data all along, you may not need any filtering at all. 

In my years playing with wind turbines, I've built a number of dataloggers.  I always built them - rather than buying them; that was part of the challenge.  My first dataloggers had very poor data. I found myself filtering the data heavily - then not trusting the results because of all the filtering I had done.  I was also not using good statistical tools to sort the data.  I couldn't understand what was going on because the data was bad and I didn't know how to clean it up either (if that was even possible).  This is how bad it was:



Eventually I learned how to collect data that I could trust before I could do calculations on it.  Once I had trustworthy data, it all started lining up neatly.



I recognize the same thing going on in the data you just posted.  There is probably some good data in there, but 90% of it is in transition or unsteady. 

• Cut off the parts where the vehicle is speeding up or slowing down; don't waste time processing them at all. 
• Sort the data into bins.  You can use vehicle speed bins such as "0m/s, "1-2m/s", "2-3m/s" etc.  or "0-100RPM", 100-200RPM" etc.
• Plot on the same graph data that is related, eg. Vehicle speed, RPM, and TSR.  Since the first two are used to calculate the third, they make a clear picture when all plotted together.
• Document your apparatus.  Make sure you can set it up the next time the same way it was set up this time, otherwise the data collected on your next run won't match this run.
• Spot data is useless.  Calculations based on spot data are misleading. 
• Use statistical averages or median values while the parameters are steady to provide inputs to your calculations.