AE 878 Directed Project, Wichita State University, Department of Aerospace Engineering. Analysis of a Grid Tied Induction Generator Wind Turbine Steven Kreibach Wichita State University ABSTRACT A performance and structural analysis was done on parts of the Breezy 5.5 Homebuilt Wind Turbine Generator available from www.prairieturbines.com . Twisted tapered blades were analyzed and compared to the existing non-twisted-non-tapered design. The results indicate that a rotor with 3 twisted tapered blades with higher rotational speed can produce 17,000 KWh/year depending on the probability distribution of the wind. The structural analysis shows generally low stresses and a few details that uneven stress distributions. INTRODUCTION With the emphasis on renewable energy in society today, the homeowner is drawn to do his part not just for the environmental benefits, but for financial reasons also. A brief review of available wind turbines of the size needed to offset the power use of the average home shows that the cost is substantial and the pay back period long. One alternative for the homeowner is to build a wind turbine himself with a variety of plans available. One such plan is available from www.prairieturbines.com and is called the Breezy 5.5, named for its rated max output of 5.5 KW. With a few purchased components, the remaining structure is simple to build with straight cuts, drilled holes, carved wood blades, welding of mild steel, and only 1 machined part. The cost is reduced to about a tenth the price of purchasing a commercially available turbine, which reduces the payback period to years instead of decades. Other designs attempt to use clever ways of circumventing the head on force of nature, but the Breezy 5.5 design withstands nature by brute force. This paper begins an analysis of the effect of changing the blades and shows analysis results of some of the structural details undergoing some of the operating forces that the structure is subjected to. The Breezy 5.5 is grid tied and uses a 3 phase induction gear motor as a generator with a 14.5:1 gear ratio which provides a constant rotational speed of 119 rpm. The rotor consists of 4 wooden blades carved with an un-tapered un-twisted airfoil shape. Each blade is 10ft long. Primary control is achieved through stall regulation. Overspeed is sensed and auxiliary protection is achieved with a small circuit that receives a generator
Transcript
AE 878 Directed Project, Wichita State University, Department of Aerospace Engineering.
Analysis of a Grid Tied Induction Generator Wind Turbine
Steven KreibachWichita State University
ABSTRACT
A performance and structural analysis was done on parts of the Breezy 5.5 Homebuilt Wind Turbine Generator available from www.prairieturbines.com. Twisted tapered blades were analyzed and compared to the existing non-twisted-non-tapered design. The results indicate that a rotor with 3 twisted tapered blades with higher rotational speed can produce 17,000 KWh/year depending on the probability distribution of the wind. The structural analysis shows generally low stresses and a few details that uneven stress distributions.
INTRODUCTION
With the emphasis on renewable energy in society today, the homeowner is drawn to do his part not just for the environmental benefits, but for financial reasons also. A brief review of available wind turbines of the size needed to offset the power use of the average home shows that the cost is substantial and the pay back period long. One alternative for the homeowner is to build a wind turbine himself with a variety of plans available.
One such plan is available from www.prairieturbines.com and is called the Breezy 5.5, named for its rated max output of 5.5 KW. With a few purchased components, the remaining structure is simple to build with straight cuts, drilled holes, carved wood blades, welding of mild steel, and only 1 machined part. The cost is reduced to about a tenth the price of purchasing a commercially available turbine, which reduces the payback period to years instead of decades.
Other designs attempt to use clever ways of circumventing the head on force of nature, but the Breezy 5.5 design withstands nature by brute force. This paper begins an analysis of the effect of changing
the blades and shows analysis results of some of the structural details undergoing some of the operating forces that the structure is subjected to.
The Breezy 5.5 is grid tied and uses a 3 phase induction gear motor as a generator with a 14.5:1 gear ratio which provides a constant rotational speed of 119 rpm. The rotor consists of 4 wooden blades carved with an un-tapered un-twisted airfoil shape. Each blade is 10ft long. Primary control is achieved through stall regulation. Overspeed is sensed and auxiliary protection is achieved with a small circuit that receives a generator rpm input and shuts the turbine down upon overspeed. Shutdown is achieved with an electromagnetic failsafe brake. The turbine nacelle yaws with the wind on its yaw bearing due to the response of the tail in the wind.
MAIN SECTION
1. Use published wind data to determine the size of wind turbine needed to produce at least 17,000
KWh/year at 11000 E 39th St S, Derby KS, which is the energy use for the residence there.
The Kansas Corporation Commission has Mean Wind Speed and Mean Wind Power Density maps available for various heights on their web site at www.kcc.state.ks.us/maps/.
The wind power density is the power available per unit rotor area in w/m2. This takes the probability density of all the various wind speeds into account and greatly simplifies wind turbine power output estimation. The average wind speed is commonly used but is less useful in that it doesn’t take into account that the amount of power available is a function of V3. The alternative is to set up a tower with wind measurement equipment on it and record the wind speeds at that particular site to get the probability distribution of the wind. And that is
indeed necessary to establish a business case for a commercial turbine. However, the costs of such a test setup is easily more than the entire costs of a homebuilt turbine. Therefore this is rarely done for the residential size wind turbine installation and instead an estimate is used and you take what you can get.
Figure 1: Mean Annual Power Density at 30 meters
The map in figure 1 reads 250 W/M2 at 30 meters above ground level at the residence address. While the map indicates “power density”, it’s not a density in the traditional sense; mass per unit volume. Instead it indicates the average power available per unit swept area of the wind turbine rotor.
The Breezy 5.5 is on a 60 ft tall tower. The lowest wind map available is for a hub height of 30 meters (98.7 ft). Because the wind speed decreases near the ground, the 1/7th power law from [3] is used to correct the power density down to the tower height of 60 ft.
Where u is the power density and z is the height above ground level of the point in question. The corrected power density is 233 w/m2.
The designers of the Breezy 5.5 use a lower resolution wind data map from www.awea.org/faq/usresource.html,
which gives a mean average wind power of 350W/m2
[1]. This is high compared to the higher resolution data available today. However, the designers use this data only to determine that Breezy 5.5 has a coefficient of performance (Cp) of 0.15 and not to predict its performance. Their measurement of output is that it
produces 12000 KWh/year as measured by the KWh meter connecting it to the grid.
If the lower power density of 233 W/m2 is used, that
would increase the Cp estimate to 0.20. It’s nice to have a super efficient turbine. But this is not the same problem that automobiles have to try and conserve an expensive fuel. Wind turbine fuel is free. The only relevant argument for having a more efficient turbine is the cost of the machinery used to capture the power you desire from the wind.
The power equation below shows how much power is available in the wind per rotor area. This is only at one wind speed though. Notice that a doubling of wind speed correlates to an 8 times increase in the power contained in that wind.
Power in the wind = ½ ρ A V3
Where ρ is the density of air at the hub, A is the area swept by the wind turbine blades, and V is the velocity of the wind.
Not all that power can be captured. A study of momentum theory and how it applies to wind turbines shows that if you capture all that power, you have reduced the wind velocity to zero and made the exit stream of air have infinite area. Therefore there is a limit to how much energy you can remove and still maintain flow. That limit is the Betz limit and is 59%. This corresponds to an axial induction factor of a=0.30. Figure 2 shows the velocity slowdown at the rotor and even more slowdown downstream.
Figure 2: Wind velocity in the stream tube and the axial induction factor a. [4]
To verify the breezy design with a 20 ft rotor diameter we use the power density and multiply by various factors to get the diameter of turbine required.
The same equation is used to determine what size rotor area or efficiency of turbine will be needed to produce 17,000 KWh/year. The first equation below shows that a Cp of .28 is needed if the rotor diameter were to remain constant.
Or, the next equation shows that we could instead increase the diameter to 23.9 ft.
Since the goal of this paper is to compare 2 different blades, the attempt is made to reach a higher efficiency.
2. Estimate the coefficient of performance of the Breezy 5.5 homebuilt wood 4 blade design and determine the viability of changing the blades to commercially produced composite 3 blade design.
The Cp of Breezy 5.5 was determined in the last section to be 0.20 and so the hope is that a twisted and tapered blade would have the performance increase that we desire for a Cp of 0.28.
The Breezy design uses a rotor with 4 blades made of wood. Each blade is carved out of a single 2x12, 10 ft long and have an un-twisted and un-tapered airfoil shape which is constant along the length of the blade similar to a NACA 4412 airfoil. This airfoil will be used to analyze both the breezy blades and is assumed to be the airfoil of the prospective new blades for comparison purposes. Blade manufacturers don’t share their design and manufacturing processes because they are of a competitive nature. Therefore this assumption is the only practical choice.
The Breezy blades are designed to be easy to produce and that is a big benefit to the home-builder. Wood is inexpensive, fatigue resistant, and easy to maintain. If a blade breaks, another one can be made the same way the originals were made to begin with. The wood blades simplicity comes from having no twist or taper which makes it easy to use a hand held portable planer to form the initial airfoil shape.
While it may be easy to conceptualize that a twisted and tapered blade would be superior, and easy to find the twist and taper calculations, it’s quite another to make a twisted tapered blade to any degree of accuracy either in wood or especially in composite due to the tooling costs and labor intensive nature. Composite blades have the disadvantage of being contrary to the spirit of home building. If the OEM composite blade manufacturer cannot be found after 5 years, then the homebuilder has some redesigning to do. And a wooden twisted tapered blade is more difficult to carve compared to un-twisted un-tapered blade and requires more material thickness to accommodate the twist.
Despite these problems, the project statement suggests the possibility of sourcing blades from a manufacturer for comparison purposes. An example of such blades are below and are available from www.magnets4less.com.
Several important differences between the Breezy blades and a possible replacement affect the performance of the 2 different blades.
4 blades vs 3 blades Twisted vs un-twisted blade Tapered chord vs un-tapered chord Tip speed ratio of 6 gives 200 rpm vs the Breezy
119 rpm rotational speed
In addition to these differences, each blade must operate at various wind speeds which make the blade operate at different angles of attack. The interactions of all the different variables at each radial location combine to produce the rotor performance vs wind speed. In this paper the Blade Element Momentum (BEM) method is used to evaluate the 4 bladed Breezy rotor and the 3 bladed composite rotor and compare their output at a variety of wind speeds. The designers of Breezy 5.5 measured the energy generation at the grid connected power meter to be 12,000 KWh/year of generation [1] and so this provides a point of reference.
The BEM method is an iterative method from [5] and this paper includes Prandtl’s Tip Loss Factor in step 3 and the Glauert Correction for High Values of the axial induction factor a in step 7.
The BEM method is as follows from [5]. Begin by dividing the blade into sections.
1. Initialize the axial induction factor a and the radial induction factor a’. These will converge to the right value upon iteration. Figure 3 shows that a max value of performance is achieved at a=0.3. a’ tends to be closer to zero.
Figure 3: Coefficient of thrust (Ct) & Coefficient of power (Cp) vs a [4]
2. Compute the flow angle Φ
Figure 4: Angles in the rotor plane showing the relative velocity of the air Vrel when rotor speed is included [4]. Where Φ is the angle of Vrel to the rotor plane, θ is the angle of the airfoil to the rotor plane, and α is the angle
of attack of the airfoil to Vrel.
3. Compute Prandtl Tip Loss Factor F
The high-pressure air on one side of a blade spills over the end of the blade seeking the low pressure on the other side making tip vortices
which waste energy and create drag on the blade. The Prandtl tip loss factor is a method of including the effects of those tip losses. A graph of those effects can be seen in figure 5.
Where B is the number of blades, R is the radius of the rotor, r is the radial position of
calculation, and e is the mathematical constant.
Figure 5:Prandtl tip loss factor F vs radial position for various number of blades (NB) and
wind speeds.
4. Compute the local angle of attack of the airfoil.
5. Read Cl(α) & Cd(α) from experimental data for the airfoil. These are the coefficients of lift and drag, perpendicular and parallel to the airfoil respectively.
To clarify some issues with lift and drag graphs some discussion about Reynolds number (Re) is needed. Re is a dimensionless quantity that allows comparisons to be made from one size of airfoil to another in different kinds of fluid.
For the Breezy and the composite blades Re is calculated and it’s found to be quite low compared to much of the published data for airfoils.
Additionally, the Cl & Cd change with Reynolds number as shown in the figure below. It mainly affects the response of the airfoil in the stall region. While this graph is for a different airfoil, it shows a trend. While conceptually the trend is assumed to apply to the NACA 4412 airfoil, to include that in the analysis would probably be arbitrary and especially so because both blades would use the same data making the assumption of questionable usefulness. This results in the conclusion that more accurate lift and drag is needed for more accurate results.
Figure 6: variation of Cl and Cd with angle of attack for various Re [4]
Figure 7: Cl and Cd curves from [4] for NACA 4412 at Re 1.5 x 106
The data used is from [4] and shows lift and drag at a higher angle than other data found for this report. The lift and drag curves are available in a variety of resources, however most of them were tested with aircraft in mind and tend to stop at the beginning of the stall region. A stall regulated wind turbine sometimes operates exclusively in this region during a time when this estimation is important; max power output. Unfortunately figure 7 represents the best data the author could find and while it’s at a Reynolds number that is too high, the blade comparison using this data is assumed to be useful even if not fully accurate.
6. Compute Cn & Ct which are the coefficients of force normal to and tangential to the rotor plane.
7. Calculate a & a’ with Glauert Correction for High Values of a. The Momentum theory breaks down at higher values of a, therefore some factor is needed to correct the prediction. Note that these also use the Prandtl tip loss factor F.
For a>ac, ac ~ .2
For a<ac, ac ~ .2
and a’
8. If a & a’ have changed significantly from the initial a & a’, then go to step 2, else quit.
9. Compute the forces on each blade element.
Where L is the lift on the airfoil perpendicular to the chord, and ρ is the density of the air, and c is the chord length.
Where D is the drag on the airfoil parallel with the chord.
Where Pn and Pt are the force per unit blade length normal and tangential to the rotor plane respectively at that radial distance on the blade.
Then compute the force for each section from I=1 to N. The formula below is the point slope equation for a linear assumption between
sections where A is the slope and B is the y intercept.
Sum up all the sections to get the total thrust force on the blade. Repeat for the Pn to get the bending force on the blade.
10. Calculate blade in-plane and out-of-plane moments where the moment is M.
RESULTS OF BEM method
The calculations are in an accompanying excel spreadsheet due to the large number of calculations for each blade section. The calculations at 23mph result in a Cp of the Breezy blades of 0.32, and for the twisted, tapered blades of 0.38 which is a 18% increase in power output by changing the blades twist, taper, & RPM.
The Cp at 30 mph is 0.22 & 0.37 respectively, which is a 68% increase at that wind speed.
This Cp is for the blades only and doesn’t include the other losses such as gearbox losses, electricity used to operate the wind turbine, electrical resistance losses, and other inefficiencies. These losses are assumed to be similar for either type of blade.
Changing from the Breezy blades to the twisted, tapered blade gives a projected increase from 12000KWH/ year x 1.19 = 14280 KWh/year. But since the Cp’s are so different at the higher wind speed, the new blades could
capture a significant amount of power at higher wind speeds.
This appears to validate the benefit of using a twisted tapered blade, however it doesn’t necessarily do that. An increase in RPM will give an increase in power output as shown in figure 8. This peak happens at a higher wind speed though and so to compare blades at one low wind speed gives a deceptively low number. This is a case where the probability distribution of the different wind speeds is needed to see if the shifting of the blades peak power wind speed is useful or not. This report did not pursue that analysis.
Figure 8: the effect of rpm on output for an example turbine. [4]
Figure 8 shows an increase in power output as the RPM and wind speed increases. But the faster an airfoil goes, the greater the drag. To maximize the power output at one rotational speed the turbine gives up performance at another rotational speed, so the designer will need to justify the output of his design at a variety of rotational speeds for the expected wind distribution at the particular site. For instance, in the example turbine in figure 8 above, the 45 rpm turbine is making nearly 10 KW in a 6.5 m/s wind while the 60 rpm turbine is making none. The 60 rpm turbine doesn’t match the performance of the 45 rpm turbine until 9 m/s wind speed. But after that the 60 rpm turbine greatly surpasses the slower turbine. So there is a tradeoff that only a complete analysis of all the options would show.
Ideally the turbine rpm would increase or decrease depending on the wind speed, and some turbines do
that, but it is an advanced feature for an induction turbine and certainly out of the realm of possibilities for the vast majority of homebuilders.
A further discussion of the effects on output of wind turbine configuration changes is warranted to further understand the effects of the changes between the 2 different blades.
If the wind blows constantly at low speed, then a high peak power output in high winds will not be productive since it’s rarely seen. That turbine’s peak capability would rarely be used and the significant cost increase in generator capacity would be underutilized.
The opposite is true if the site has plenty of very windy days. That extra generator capacity can capture a significant portion of the output for the year in these peak scenarios.
Figure 9.1 & 9.2 show the power output and Cp curves for the 2 different blades. The new blades show a peak and a drop off as the wind speed increases. The Breezy 5.5 turbine power output was described in [1] to rise fairly linearly and level off to 5.5 KW at 23 mph. This analysis shows an unexpected peak at 30 mph and so it doesn’t correlate very well to the observations and measurements in [1]. But the analysis of both show the power rising to a peak and falling as the airflow stalls over the airfoil and stall regulation takes over. This doesn’t mean the authors of [1] are wrong. Just that the analysis here can’t include all the factors in a simple analysis of a real wind turbine.
The Cp also rises to a peak and drops off dramatically. This is the whole point of stall regulation because this is exactly what is needed to limit the power input from the blades due to the tremendous power in the wind at high wind speeds.
To calculate the power output using the mean annual power density, the Cp of a turbine is used. It must be an average Cp over the expected normal range of power output.
Figure 9.1: Power output vs wind speed for Breezy and for the new blades.
Figure 9.2: Cp vs. wind speed for Breezy and for the new blades.
Figure 10: A classic Cp vs tip speed ratio graph for different types of turbine.
In Figure 10 each curve rises to a peak and then falls as the tip speed ratio increases. This shows that a fast rotation speed in a slow wind (high tip speed ratio) gives a lower Cp due to drag. And also a low Cp occurs for a low rpm rotor in high wind speeds (low tip speed ratio), which gives low Cp due to stall. Additionally, high rotational speeds produce more noise and stress on the blades and hub due to high centrifugal forces and gyroscopic forces. There is an optimal tip speed ratio for each rotor configuration and rotational speed.
The solidity of a rotor, which is the ratio of the blades plan area to the total swept area of the rotor, shown in Figure 11, has an effect on the operating characteristics of the turbine. Using more blades isn’t necessarily better. Higher solidity gives you slower speeds, higher torque, and less power. While lower solidity gives you higher speeds, less torque, and more power.
Solidity also changes the characteristics of the efficiency curves as shown in Figure 12. The more the blades, the better low tip speed performance
Figure 11: Front view of a wind turbine rotor showing the area a of a single blade in the total swept area of the
blades.
Solidity σ: The ratio of blade area to the total swept area.
Figure 12: the effects of changing solidity on a Cp vs tip speed ratio plot. [4]
Note that solidity is a factor in determining a and a’ in step 7 of the BEM method.
The twisted and tapered blades in this paper were given the optimum twist angle from [5] using the following equations.
The optimal angle of attack α is chosen based on the lift and drag curves and Φ is computed and used in the BEM method.
The chord length c is calculated with the following formula
Where x is the local tip speed ratio at r instead of R for the usual tip speed ratio.
The optimal chord value is nearly 1/3 of the length of the blade. This is impractical to build and the chord is usually trimmed linearly from a practical value and blended into the rest of the blade instead of following the optimal formula.
The twist angle in the root area is commonly adjusted also. If the twist angle is increased it helps in low wind speeds when the turbine is staring up.
For every conceivable variable there is an associated graph of the effect on the power output or the efficiency. To do a complete job in wind turbine design, each variable must be changed and the effect plotted to identify the optimal design. The BEM method can be used to do that in a simple spreadsheet, however it is time consuming and tedious and is the reason why computer programs are written to speed the process and that task is not undertaken in this paper.
3. Determine the benefits and viability of including the tail furling design found in [2].
One method of limiting power during high winds is turning the rotor at an angle to the wind as seen in figure 13. With small turbines using a tail for directional control, this can be accomplished with tail furling. Furling is when the dynamics of the system respond to the excess wind by turning the tail to the side in proportion to the excess wind speed. As the tail turns
the tail still points parallel to the wind and the rotor turns at an angle to the wind. While it’s called tail furling, the effect is a rotor that turns at an angle to the wind. This reduces the power input by reducing the effective area, and by changing the angle of attack to a lower angle on the blades at the top of the rotor and to a steeper angle at the bottom.
Figure 13: Tail Furling
Another method of controlling the max power input is stall regulation. The following quote sheds some light on this method: “Stall regulation provides the simplest means of controlling the maximum power generated by a turbine to suit the sizes of the installed generator and gearbox and until recently, at the time of writing, is the most commonly adopted control method.” [4]
Stall regulation is mechanically simple due to having no moving parts to limit the power input. The blades are at a fixed angle to the hub. Stall regulation is normally used on a constant rotational speed generator like an induction generator. Tail furling is typically used on a turbine with a permanent magnet generator because that generator does not limit the rpm and the airfoil can’t stall. The rpm would increase until something came apart.
With stall regulation the wind speed increases, and the tangential velocity remains the same. The angle of attack increases and the airfoil gradually stalls and decreases the Cp as shown in figures 14 & 15. The blade design and generator must be analyzed as a system at all wind speeds to make sure that the power output vs. wind speed curve will provide the correct balance between optimal extraction of power while limiting peak output.
Figure 14: increasing wind speed decreases tip speed ratio λ.
Figure 15: Cp vs tip speed ratio λ showing the significant impact to Cp of decreasing λ during stall regulation. [4]
While tail furling is effective and useful on some wind turbines, stall regulation is a better option on an induction generator wind turbine and an analysis of the need for tail furling is therefore concluded in this report.
4. Determine the forces acting on wind turbine system and analyze the stresses on selected components.
From the BEM method calculation spreadsheet the loads on the Breezy blades at the rated output of 5.5 Kw at 23 mph are:
Blades force on tower = 264 lbs
Torque of rotor = 409 ft lbs
Blade root bending moment (per blade) = 449 ft lbs
Centrifugal force of blade on rotor = 2.6 lbs (formula below)
Gyroscopic forces (assume 60 degrees/10 seconds from the International Electrotechnical Commission (IEC) 61400-1 load case 1.3) = 138 ft lbs (formula below)
Where Ω is the, Λ is the yaw rate, and cos Ψ is 1 and –1 to give max bending at the top and bottom position of the blades.
Gust Loads thrust on rotor (50 year extreme wind from IEC 61400-1 load case 1.6) = 656 lbs per blade and 2622 lbs total. Cd of 1.3 for a flat plate is used in the standard drag formula below.
The IEC standard defines the Mean Annual Wind Speed as an input to determine the 50 year extreme wind. Figure 16 shows this map from www.kcc.state.ks.us/maps/ and 6.5 m/s is found at the target site. The 50 year extreme wind is 1.4 times the annual extreme wind, which is 5 times the mean annual wind speed. This is 102 mph for this site.
Root moment on each blade from 50 year extreme wind loads; M = 999 ft lbs. The formula below is the standard formula for determining the moment from a cantilevered beam with distributed load w.
These loads will be combined and used to analyze the operating conditions of selected components. Due to the complexity of some of the structure, the FEA workbench in CATIA was used to analyze the structure.
a. Tower and yaw bearing assembly.
Under normal operating loads with gyroscopic forces, the stress level in the tower is quite low at only about 5 ksi as shown in figures 17 & 18. Under gust loads the stress increases to 10 ksi. The higher stress shown in the color scale correspond to stresses in the cables, which isn’t analyzed here.
Figure 17: FEA of tower under operational and gyroscopic loads.
Figure 18: Tower close-up under operational and gyroscopic loads. Tower stress ~5 ksi
The rotor hub is a complex weldment and benefits greatly from FEA.
The stress in the hub reaches >10ksi at certain locations during normal steady state operation. Assuming mild steel with Ftu = 30ksi, and a fatigue limit of 1/3 Ftu, there could be fatigue cracking at certain highly loaded locations.
Figure 20: rotor under operating loads.
Figure 21: rotor under operating loads with gyroscopic forces.
In figure 21 the rotor has gyroscopic forces applied, which bend the top blade one way and the bottom blade the other way. They result from yawing of the turbine while the rotor is spinning. The forces can be significant for a fast yaw rate. The yaw rate of 60 degree/10 seconds in the IEC standard is noted at being the minimum. Further investigation or testing is needed to see if that is a suitable number. Prior to finding the IEC standard, this author initially assumed a higher yaw rate of 90 degrees/second was a suitable number for a tail pointed turbine. The high gyroscopic forces were high enough to yield the driveshaft and hub and prompted further investigation into a suitable yaw rate.
The cyclic gyroscopic forces exemplify that fatigue is a driving factor in the design of wind turbines. In addition, each blade undergoes a load reversal from gravity at each revolution. The wind itself is cyclical with gust here and there driving various cyclical loads in all components.
Figure 22: Close-up of hub with operating loads and gyroscopic forces. Max stress ~12.6 ksi.
Figure 23: hub with substantial gyroscopic forces causing high stresses. Max stress 32 ksi.
Figure 24: Blades with 50 year extreme wind. Stress ~ 31 ksi.
Figure 25: Hub with 50 year extreme wind. Stress ~ 31 ksi
c. Drive shaft
Figure 26: drive shaft with normal operating forces. Stress ~ 1 ksi.
Figure 27: Driveshaft with normal operating forces and gyroscopic forces. Stress ~ 1.5 ksi
Figure 28: Driveshaft with gyroscopic forces from 90 deg per sec yaw rate. Stresses ~ 46 ksi.
The high stresses resulting from an assumed load case indicates the need to determine the actual yaw rate seen in service on a small wind turbine. It also underscores
the importance of appropriate radii on the driveshaft where the diameter changes so as to reduce stress concentrations.
d. Tail boom
The tail force is assumed to come from a 10m/s side gust on a flat plate. This only produced a force of 26 lbs and stresses of 6ksi. While this isn’t much, it showed the weak spot in the structure. Also included is a downward force of 50 lbs to account for the mass of the tail structure.
The high stresses in figure 30 occur on the aft standing leg of an angle iron support in bending. A quick fix for this is to use a square channel section. This will add stiffness as well as reducing the peak loads in that piece. This isn’t necessary depending on the confidence
that this analysis represents the maximum load on the part.
Figure 31: Tail without side support. Stress ~ 4.5 ksi
The high stress above caused me to investigate whether this angle was even needed and figure 31 shows the stresses without it. While this reduced the stress to 4.5 ksi, the deflection doubled and further treatment is needed to investigate weather vibrations are a problem due to the structure being less stiff.
e. Structure connecting low speed driveshaft bearings to yaw bearing.
This is another complicated structure that benefits from FEA. The bedplate provides a mounting base for the generator and the driveshaft bearings so that they remain properly aligned to each other.
Figure 32: yaw structure under operating and gyroscopic loads. Stress ~ < 3ksi.
The stresses in this structure under operating and gyroscopic loads is quite low at 3 ksi. The deflection is about .020”. What isn’t shown is the nacelle cover that’s made of 16 gage sheet metal (.060 thick). It is fastened along the sides of the bedplate to the upstanding leg of angle iron. It’s also fastened along the entire front and back creating a tension and shear member. The inclusion of such a substantial stiffening member can only be assumed to make the stresses and deflections irrelevant.
CONCLUSION
The coefficient of performance of Breezy 5.5 output was found to be .20 at 23 mph.
The size of blades was determined to be 23.9 ft, or the same size but with a Cp of .28 in order to achieve the 17,000 kwh/year goal.
The blades of Breezy 5.5 were analyzed and compared to a twisted tapered design of the same diameter but at an increased rpm. The efficiency increase coupled with an rpm increase caused their output to be predicted at the target 14280 kwh/year. This is short of the goal at face value. A further investigation of the complete power curve combined with the probability distribution at various wind speeds will determine if their performance is suitable for this stall regulated design.
The tail furling concept was abandoned in light of the investigation into stall regulation. Stall regulation is well suited to induction generators and is therefore the preferred choice over tail furling which is more suited to permanent magnet generator equipped wind turbines.
Loads on the blades were determined for the operating loads, gyroscopic loads during yaw, and for the 50 year extreme wind. Some structural details of the Breezy 5.5 were analyzed and the peak stresses identified. Some peak loads were found to be excessive and this may lead the builder to modify certain details to avoid high stresses.
REFERENCES
1. Timothy McCall and Alan Plunkett, Breezy 5.5, Derby KS, Prairie Turbines, LLC, 2005
2. Dan Bartman & Dan Fink, Homebrew Wind Power, Masonville, CO, Buckville Publications LLC, 2009.
3. Gary L. Johnson, Wind Energy Systems, Electronic Edition, 2001.
4. Tony Burton, David Sharpe, Nick Jenkins, & Ervin Bossanyi, Wind Energy Handbook, England, John Wiley & Sons, 2001.
5. Martin O. L. Hansen, Aerodynamics of Wind Turbines, 2nd Edition, Sterling, VA, 2008.
CONTACT
Steven Kreibach is a design engineer at Spirit Aerosystems. He has a BS in mechanical engineering from the University of Kansas (1995) and is working on a master’s degree in aerospace structures at Wichita State University. He lives at 11000 E 39th St. S, Derby KS 67037 (where he intends to build a wind turbine) and can be reached at [email protected], or 316-686-1611.
DEFINITIONS, ACRONYMS, ABBREVIATIONS
a: axial induction factor (AKA, slowdown factor)
a’: radial induction factor
A: area of rotor
ρ: density of air
z: height above the ground
u: power density
V: wind speed
V0: far upstream wind speed
Vrel: apparent wind speed in rotating airfoil frame of reference
Φ: angle between apparent wind and the rotor plane
