In this section we describe how we selected the S834 airfoil profile and talk about how we defined the blade shape parameters.

Important Note

Preliminary content from design report

The content of this article is taken from the December 2013 preliminary design report. It represents intention of design at that stage but does not necessarily show the final version of the HOLI 300 turbine design.

### Introduction

Before designing our rotor some conceptional approach has been taken. As pitch angle adjustments are quite complicated and cost intensive for small wind turbines (SWT), it was decided to design a fixed pitch rotor. In order to extract more energy at given lower wind speeds, a variable speed rotor has been chosen which is associated with permanent magnet generator selection.

The blade design parameters including airfoil shape, design tip speed ratio, blade numbers are considered in the next stage. The selection of these blade parameters is often based on blade element momentum calculations (BEM). The main reason to use BEM theory for blade calculations is that it is very fast and gives good result for steady-state conditions.

For this project, a BEM calculation script was coded in Matlab based on the algorithm described by Martin O.L. Hansen [1]. Spera correction is used for higher values of the axial induction factor. Before using the code it has been evaluated by comparing the BEM calculation result with experimental data for an old commercial wind turbine rotor. Validation gave reasonable results. Thus, the code has been used for aerodynamic analysis and performance predictions.

### Airfoil Selection

Initially, corresponding Reynolds numbers (Reynolds number $Re$) are calculated with an initial guess which is between $6.5\cdot10^{4}\ldots2\cdot10^{5}$ for a given wind speed distribution of the wind turbine. The equation $Re=\frac{U_{r}\cdot c}{v}$ is used to determine Reynolds numbers for wind turbine applications considering variations of blade chord (blade chord length $c$) and relative wind speed (relative wind speed $U_{r}$) along the blade.

Very little data is available and reliable for low $Re$ airfoils. Wind tunnel test data for several airfoils are collected. Appropriate airfoils which have reliable data for low $Re$ numbers, S834 and S822 [2] are taken as airfoil choices. They are designed for small wind turbines. The thickness of airfoils is one of the most important parameters which have affected our blade choice considering the manufacturing possibilities of structurally stiff blades. These types of airfoils have smooth stall characteristics as well which account for better off-design operation. Finally, the S834 airfoil is chosen due to its better performance during the comparison of different blade geometries. In the figure below one can observe the data obtained from wind tunnel experiments for the S834 airfoil.

Lift and Drag coefficient data for S834 for different Reynolds numbers. [3]

The data obtained from wind tunnel is limited. A wider range of data was required in order to be used in BEM algorithm while $c_{\textrm{L}}$lift coefficient and $c_{\textrm{D}}$ drag coefficient values are interpolated for given angles of attack (angle of attack $\alpha$). In accordance with this purpose a preprocessing tool, AirfoilPrep, is used which is developed by National Renewable Energy Laboratory NREL [3]. This tool extends the limited data for a given range and extrapolates the data between -180 and +180 degrees of angle of attack. This is done by Viterna’s method in AirfoilPrep. Viterna’s method is simply a kind of correlation between the post-stall characteristics of wind turbine airfoils and aspect ratio of wind turbine blades for which the post stall characteristics of airfoils are close to experimental data. Reasonable smooth airfoil data was extrapolated by using AirfoilPrep as one can see in the chart below.

### Defining the blade shape parameters

As a second step, several chord and twist distributions are determined by using formulas for optimum blade shape [4]. This step is required in order to derive approximate chord and twist distributions. Following formulas give an approximation in order to define blade geometry while taking tip-losses into account.

$\textrm{\ensuremath{\sigma_{\textrm{r}}\lambda c_{\textrm{L}}}=\ensuremath{\frac{4a(1-a)}{\sqrt{(1-\frac{a}{f})^{2}+\left[\lambda\mu\left(1+\frac{a\left(1-\frac{a}{f}\right)}{\lambda^{2}\mu^{2}f}\right)\right]^{2}}}}}$

$\textrm{\ensuremath{\tan\phi}=\ensuremath{\frac{1-\frac{a}{f}}{\lambda\mu\left(1+\frac{a\left(1-\frac{a}{f}\right)}{\lambda^{2}\mu^{2}f}\right)}}}$

For different tip speed ratios (Tip Speed Ratio TSR), blade numbers and desired $c_{\textrm{L}}$ data from airfoils are used in order to put these formulas to use. Consequently 5 different blade shapes are derived and modified considering manufacturing and structural constraints.

### Comparison

Although using different airfoils for the root and tip gives better results during the starting performance of the blades [5], both airfoils are used separately along the blade span due to the time constraints in the design process. As starting performance is important for small wind turbines, torque and power performances are evaluated together. Power performance criteria for the optimization used in this paper is the highest Annual Energy Production (AEP) based on a competition Weibull wind speed distribution.

After having reasonable blade shape parameters, their performances are evaluated for TSR between 3.5 to 5.5 considering different blade numbers, airfoils and pitch angle variations. As a result of this evaluation we obtained the optimum performing blade shape parameter with given airfoil for each TSR. Later on, their aerodynamic power curve is corrected by generator efficiency for RPMs. The Weibull distribution is used in order to obtain the probability of these RPMs taking their corresponding generator efficiencies into account.

### Results

Ultimately, a 4 bladed rotor with a TSR of 4 is chosen with an airfoil choice of S834. This was a compromise between the evaluated blade shape parameters by taking their starting and power extraction performance. The final blade shape is evaluated with more sections until the results are not changing significantly. Also off-design performance is assessed by varying pitch angle and rotational speed parameters. Resulting loads from the selected blade are acquired by BEM code which is then used for structural integrity calculations.

[1] M. O. L. Hansen, Aerodynamics of wind turbines, Taylor & Francis, 2013.
[Bibtex]
@BOOK{Hansen2013,
title = {Aerodynamics of Wind Turbines},
publisher = {Taylor \& Francis},
year = {2013},
author = {Hansen, M.O.L.},
isbn = {9781136572265},
}
[2] B. D. McGranahan and M. S. Selig, “Wind tunnel aerodynamic tests of six airfoils for use on small wind turbine,” Journal of solar energy engineering, vol. vol. 126, p. pp. 986-1001, 2004.
[Bibtex]
@ARTICLE{McGranahan2004,
author = {McGranahan, B.D. and Selig, M.S.},
title = {Wind tunnel aerodynamic tests of six airfoils for use on small wind
turbine},
journal = {Journal of solar energy engineering},
year = {2004},
volume = {vol. 126},
pages = {pp. 986-1001},
note = {NREL/SR-500-34515},
abstract = {This paper presents detailed wind tunnel tests data taken on six airfoils
having application to small wind turbines. In particular, lift, drag
and moment measurements were taken at Reynolds numbers of 100,000,
200,000, 350,000 and 500,000 for both clean and rough conditions.
In some cases, data were also taken at a Reynolds number of 150,000.
The airfoils included the E387, FX 63-137, S822, S834, SD2030, and
SH3055. Prior to carrying out the tests, wind tunnel flow quality
measurements were taken to document the low Reynolds number test
environment. Oil flow visualization data and performance data taken
on the E387 compare favorably with measurements taken at NASA Langley
in the Low Turbulence Pressure Tunnel. Highlights of the performance
characteristics of the other five airfoils are presented.},
owner = {helgehamann},
timestamp = {2013.12.15}
}
[3] D. C. Hansen, “Nwtc computer-aided engineering tools,” NWTSC 2012.
[Bibtex]
@TECHREPORT{Hansen2012,
author = {Dr. Craig Hansen},
title = {NWTC Computer-Aided Engineering Tools},
institution = {NWTSC},
year = {2012},
owner = {helgehamann},
timestamp = {2013.12.15},
url = {http://wind.nrel.gov/designcodes/preprocessors/airfoilprep/}
}
[4] T. Burton, N. Jenkins, D. Sharpe, and E. Bossanyi, Wind energy handbook, Wiley, 2011.
[Bibtex]
@BOOK{Burton2011,
title = {Wind Energy Handbook},
publisher = {Wiley},
year = {2011},
author = {Burton, T. and Jenkins, N. and Sharpe, D. and Bossanyi, E.},
isbn = {9781119992721},
lccn = {2010053397},
}
[5] S. Worasinchai, “Small wind turbine starting behaviour,” Doctoral thesis PhD Thesis, 2012.
[Bibtex]
@PHDTHESIS{Worasinchai2012,
author = {Worasinchai, Supakit},
title = {Small Wind Turbine Starting Behaviour},
school = {Durham University},
year = {2012},
type = {Doctoral thesis},
abstract = {Small wind turbines that operate in low-wind environments are prone
to suffer performance degradation as they often fail to accelerate
condition. The behaviour during this process is called “starting behaviour”
and it is the subject of this present work.
This thesis evaluates potential benefits that can be obtained from
the improvement of starting behaviour, investigates, in particular,
small wind turbine starting
behaviour (both horizontal- and vertical-axis), and presents aerofoil
the analysis.
All of the investigations were conducted using a new set of aerodynamic
performance data of six aerofoils (NACA0012, SG6043, SD7062, DU06-W-200,
S1223, and S1223B). All of the data were obtained at flow conditions
that small wind turbine blades have to operate with during the startup
- low Reynolds number (from 65000 to 150000), high angle of attack
(through 360◦), and high reduced frequency (from
0.05 to 0.20). In order to obtain accurate aerodynamic data at high
incidences, a series of CFD simulations were undertaken to illustrate
effects of wall proximity and
to determine test section sizes that offer minimum proximity effects.
A study was carried out on the entire horizontal-axis wind turbine
generation system to understand its starting characteristics and
to estimate potential benefits
of improved starting. Comparisons of three different blade configurations
increase in starting capability.
The improved starting capability effectively reduces the time that
the turbine takes to reach its power-extraction period and, hence,
an increase in overall energy yield.
The increase can be as high as 40%.
Investigations into H-Darriues turbine self-starting capability were
made through the analogy between the aerofoil in Darrieus motion
and flapping-wing flow mechanisms. The investigations reveal that
the unsteadiness associated with the rotor is key to predicting its
starting behaviour and the accurate prediction can be made
when this transient aerofoil behaviour is correctly modelled. The
investigations based upon the analogy also indicate that the unsteadiness
can be exploited to promote
the turbine ability to self-start. Aerodynamically, this exploitation
is related to the rotor geometry itself.},
owner = {helgehamann},
timestamp = {2013.12.15},
url = {http://etheses.dur.ac.uk/4436}
}

Erol Ozan Bulut
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