User Guide

User Manual:

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Page Count: 47

License
Credit
Contents
Introduction
Installing and Uninstalling SWRDC
Folder Structure and Distributed Files
Starting SWRDC
- Source Code
- Compiled Code
Using the GUI
Running an Optimization
Notes on GUI Inputs
Building a CAD File using SolidWorks
Final Remarks
References

Small Wind-turbine Rotor Design Code (SWRDC)

User’s Guide

October 28th, 2013

License

Redistribution and use in source and binary forms, with or without modiﬁcation, are per-

mitted provided that the following conditions are met:

* Redistributions of source code must retain the above copyright notice, this list of conditions

and the following disclaimer.

* Redistributions in binary form must reproduce the above copyright notice, this list of con-

ditions and the following disclaimer in the documentation and/or other materials provided

with the distribution.

* Neither the name of the University of Calgary nor the names of its contributors may

be used to endorse or promote products derived from this software without speciﬁc prior

written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBU-

TORS ”AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT

NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND

FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL

THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, IN-

DIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES

(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS

OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)

HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CON-

TRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHER-

WISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF

ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

*********************************************************************

Credit

Please cite the following article in all published work involving the use of Small Wind-turbine

Rotor Design Code (SWRDC):

Sessarego, M and Wood, D 2015, ’Multi-dimensional optimization of small wind turbine

blades’ Renewables: Wind, Water, and Solar, vol 2, no. 1, pp. 1-11. DOI: 10.1186/s40807-

015-0009-x https://doi.org/10.1186/s40807-015-0009-x

Credit for the source code development also goes to:

NGPM – A NSGA-II Program in Matlab v1.4

by Song Lin

23 Apr 2011 (Updated 26 Jul 2011)

http://www.mathworks.com/matlabcentral/ﬁleexchange/31166-ngpm-a-nsga-ii-program-in-

matlab-v1-4

NSGA - II: A multi-objective optimization algorithm

by Aravind Seshadri

19 Mar 2006 (Updated 19 Jul 2009)

http://www.mathworks.com/matlabcentral/ﬁleexchange/10429-nsga-ii-a-multi-objective-optimization-

algorithm

polygeom.m

by H.J. Sommer

09 Oct 1998 (Updated 30 Nov 2008)

http://www.mathworks.com/matlabcentral/ﬁleexchange/319-polygeom-m

NWTC Design Codes (HARP Opt by Danny C. Sale)

http://wind.nrel.gov/designcodes/simulators/HARP Opt/. Last modiﬁed Thursday, 28-

Feb-2013 17:18:24 MST; accessed Saturday, 23-Mar-2013 12:29:38 MDT.

Multi-objective NSGA-II code in C

by Kanpur Genetic Algorithms Laboratory

Revision 1.1.6 (08 July 2011) (for Linux only- 64-bit bug for binary coding ﬁxed): NSGA-II

in C with gnuplot (Real + Binary + Constraint Handling)

http://www.iitk.ac.in/kangal/codes.shtml

XFOIL is released under the GNU General Public License:

https://web.mit.edu/drela/Public/web/gpl.txt

XFOIL:

https://web.mit.edu/drela/Public/web/xfoil/

Contents

License 2

Credit 3

Contents 5

1 Introduction 6

2 Installing and Uninstalling SWRDC 6

2.1 SourceCode..................................... 6

2.2 CompiledCode................................... 6

2.3 UninstallingSWRDC ............................... 8

3 Folder Structure and Distributed Files 8

4 Starting SWRDC 9

4.1 SourceCode..................................... 9

4.2 CompiledCode................................... 10

5 Using the GUI 10

5.1 BEMCodeSetup.................................. 10

5.2 TurbineData .................................... 11

5.3 StartingData.................................... 12

5.4 WindData ..................................... 12

5.5 DesignParameters ................................. 13

5.6 StructuralData................................... 13

5.7 LoadCaseData................................... 14

5.8 Blade Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.9 Genetic Algorithm Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5.10AirfoilData..................................... 17

5.11 XFOIL Airfoil Noise Database Calculation . . . . . . . . . . . . . . . . . . . . 18

5.12NoiseData ..................................... 19

5.13 Objective Weight Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5.14Plotting ....................................... 21

5.15 Parallel Computing Toolbox - MATLAB - MathWorks . . . . . . . . . . . . . 25

5.16ResultsFile ..................................... 25

5.17 Annual Energy Production (AEP) . . . . . . . . . . . . . . . . . . . . . . . . 26

5.18BaselineBlade ................................... 27

5.19 Saving and Loading GUI Settings . . . . . . . . . . . . . . . . . . . . . . . . . 28

6 Running an Optimization 28

6.1 Clicking the Run Optimization button . . . . . . . . . . . . . . . . . . . . . . 28

6.2 OptimizationHeadings............................... 31

6.3 Optimization Finished: Analysing the Outputs . . . . . . . . . . . . . . . . . 32

7 Notes on GUI Inputs 34

7.1 Objective Weight Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

7.2 Genetic Algorithm Data: Population Size . . . . . . . . . . . . . . . . . . . . 34

7.3 NoiseData ..................................... 34

7.3.1 PowerLawFactor ............................. 34

7.3.2 Bluntness Thickness at Trailing Edge . . . . . . . . . . . . . . . . . . 35

7.3.3 TipFactor ................................. 35

7.3.4 Sound Pressure Level at Diﬀerent Observer Positions . . . . . . . . . . 35

7.4 XFOIL Airfoil Noise Database Calculation: Transition Criterion . . . . . . . 36

8 Building a CAD File using SolidWorks 36

9 Final Remarks 47

References 47

1 Introduction

The Small Wind-turbine Rotor Design Code (SWRDC) uses a genetic algorithm, blade

element momentum (BEM) theory, simple Euler-Bernoulli beam theory, a model for starting

from Wood [1], and a noise model of Zhu [2] to design small-scale, variable-speed and ﬁxed-

pitch horizontal-axis wind-turbine rotors. The code is based on the work of a M.Sc. project

done at the University of Calgary designed for large-scale wind-turbines, which has been

recoded for the purpose of designing small-scale wind-turbine rotors.

The genetic algorithm used in SWRDC is a search heuristic that mimics the process of

natural selection. This heuristic (also called metaheuristic) can be used to solve optimiza-

tion problems such as the design of wind-turbine rotors. Genetic algorithms belong to a

larger family called evolutionary algorithms (EA), which generate solutions to optimization

problems using techniques inspired by natural evolution, such as selection, crossover and

mutation. A set of solutions is called a population and undergoes selection, crossover and

mutation to create subsequent generations of superior solutions (or individuals). SWRDC

uses a genetic algorithm as described in Deb’s book [3] and BEM and beam theory models

described in Hansen [4].

SWRDC can optimize rotors based on a single or multiple criteria. Each criteria is called

an objective and is optimized by either minimizing or maximizing its objective function. The

rotor design optimization is formulated as a weighted min-max problem:

minimize q

max

i=1 wi

fi(x)−zmin

zmax

i−zmin

i

subject to x∈S

(1)

where qis the number of objectives, wiare weights that satisfy wi≥0 and Pq

i=1 wi= 1,

fi(x) are the objective functions, zmax

iand zmin

iare the maximum and minimum objective

values of the population in the current iteration (or generation), and Sis the feasible region

(i.e. region where constraints are satisﬁed). The objective functions for the small-scale rotor

optimization are the power coeﬃcient CPor annual energy production AEP , starting time

ts, blade mass mblade, and noise SP Ltotal. Note CPand AEP are maximized by minimizing

the inverse of their objective functions.

2 Installing and Uninstalling SWRDC

SWRDC is only supported for Windows operating systems and Microsoft Excel must be in-

stalled for outputting the SWRDC optimization results. Furthermore, the GUI of SWRDC

requires a minimum screen resolution of 1280 x 768, but a much higher resolution is recom-

mended.

2.1 Source Code

If you have the original source code and not the compiled version, you will need an installed

version of MATLAB with associated licensing. Toolboxes that do not accompany the stan-

dard MATLAB license are not required, with the exception being the “MATLAB Parallel

Computing Toolbox” if executing the code in parallel is desired.

2.2 Compiled Code

If you have the compiled version of the code, you must have MATLAB Component Runtime

(MCR) installed on your computer. The MCR is a standalone set of shared libraries that

will allow you to execute MATLAB code on computers without MATLAB installed and

associated licensing. The compiled code must be executed using MCR v7.17, which should

accompany the compiled code in a package named SWRDC pkg.exe.

Locate SWRDC pkg.exe and open it to extract the contents of the package.

Figure 1: Open the SWRDC package.

The package will automatically extract all of its contents into the directory where the

SWRDC pkg.exe is held.

Figure 2: Extracting SWRDC package contents.

The MATLAB MCR installation window should appear automatically. Please follow the

instructions to complete the MCR installation.

Figure 3: MATLAB MCR installation window.

2.3 Uninstalling SWRDC

If you have the original source code, simply delete all ﬁles and folders pertaining to the

SWRDC program.

If you have the compiled version of the code, delete all contents that came with the

SWRDC pkg.exe package. If you want to uninstall the MCR, you must locate uninstall.exe

within the directory where you installed the MCR. For example, if you selected C:\Program

Files\MATLAB\MATLAB Compiler Runtime\v717 as your installation directory, go to

\v717\uninstall\bin\win64\uninstall.exe

You can also uninstall the MCR by selecting Uninstall a program in the control panel

of your Windows operating system.

3 Folder Structure and Distributed Files

The folder structure and distributed ﬁles are described in this section.

airfoildatabase\

In this folder are text ﬁles (*.txt) that contain the aerodynamic data as well as the

x-y coordinates for a set of airfoil proﬁles. The aerodynamic data consists of lift and drag

coeﬃcients and the range of Reynolds numbers the coeﬃcients pertain. This folder also

holds AirfoilPrep developed by the NWTC, which will allow you to extend the lift and drag

coeﬃcients to the −180◦and 180◦range of angle of attack.

bl dstar\

This folder is used to store the boundary layer displacement thickness data (*.txt) for

diﬀerent angles of attack and Reynolds numbers for the airfoil under consideration. It is

used for noise calculation purposes in SWRDC. To analyse in detail the data produced by

XFOIL, you may refer to the ﬁles stored in this folder.

code\

This folder contains the MATLAB source code ﬁles (*.m) for SWRDC. You may open

these ﬁles and make adjustments or changes by using the MATLAB editor, but is not

recommended. If you have the compiled version of the code, you will not have access to this

folder.

commandwindow\

The text displayed in the command window for each optimization run is stored as a text

ﬁle in this folder.

documentation\

This folder contains this user guide and the ﬁles used to generate it.

exportedcoords\

The X-Y-Z coordinates (*.txt) for the blade design produced by the optimization is

stored in this folder. In addition, this folder holds the final blade shape.txt ﬁle that

contains the radius (m), chord (m) and twist (degrees) of the blade. This information can

be imported into a CAD program such as SolidWorks, which can then be used for fabrication

purposes.

GUI settings\

This folder holds MATLAB ﬁgure ﬁles (*.ﬁg) that allow the saving and loading of presets

for the SWRDC graphical user interface (GUI). In addition a screenshot of the GUI is stored

in this folder as GUI Input.bmp for each optimization run.

imagesGUI\

This folder holds JPG (*.jpg) images incorporated in the GUI. Do not delete or modify

any of these ﬁles. If you have the compiled version of the code, you will not have access to

this folder.

noisedatabase\

This folder holds the boundary layer displacement thickness data (*.dat) for a set of

airfoils required for noise analysis.

output\

This folder contains the Excel (*.xls) ﬁles summarizing the optimization results. Do not

delete the TEMPLATE Do Not Delete.xls ﬁle. This is a template used for outputting the

results. You can edit the formatting such as font size, graph colour, etc. of the output Excel

ﬁle by modifying this template.

turbinedatabase\

This folder holds blade data (*.txt) containing the radius (m), chord (m) and twist

(degrees) distributions for existing turbines. The blade design and performance determined

from SWRDC can be compared with this data.

wind data\

This folder holds windspeed probability distribution data (*.dat) for speciﬁc sites. You

may store and load windspeed probability data by using this folder.

xfoil.exe

This is the standalone executable for XFOIL developed by Mark Drela and is used for

noise analyses. Do not delete or modify this ﬁle.

SWRDC.m

The MATLAB script (*.m) used to start the SWRDC program. If you have the compiled

version of the code, you will have a ﬁle named SWRDC.exe instead.

README FIRST LICENSE.txt

The read me and license text ﬁle that must be read and fully understood prior to in-

stalling and using the SWRDC software.

4 Starting SWRDC

4.1 Source Code

After opening MATLAB and selecting the SWRDC directory, right click on the SWRDC.m ﬁle

and click Run. Alternatively, type SWRDC in the command window. A GUI should appear

as shown in Figure 4. Do not click Run Optimization on the GUI while in a directory other

than the one that holds the SWRDC.m ﬁle.

Figure 4: SWRDC graphical user interface (GUI).

4.2 Compiled Code

Locate the SWRDC directory and open SWRDC.exe. The program may take 5 minutes or

longer to initialize. Please be patient and wait for the GUI to appear.

5 Using the GUI

This section will explain all components of the SWRDC GUI and how to apply the appro-

priate settings. If you are searching for information of a particular component, you may

refer to the relevant subsection.

5.1 BEM Code Setup

The BEM Code Setup panel is used to adjust the BEM algorithm parameters in SWRDC.

The panel consists of three text boxes for the Max.Iterations,Num.Blade Elements, and

Relaxation Factor parameters as well as a drop-down menu for the ---Blade Element

Spacing---. The BEM analysis in SWRDC involves an iterative technique, which requires a

small (1-20) or large (200+) number of iterations to estimate the aerodynamic performance

of a rotor design. The appropriate number of iterations required depends on the wind

turbine under consideration and the value chosen for the relaxation factor.

A small number for the relaxation factor will ensure that the BEM algorithm will con-

verge to the ﬁnal solution. However, reducing this factor will at the expense require a greater

number of iterations. To guarantee accurate aerodynamic calculations, set the maximum

number of iterations to a large value (200+) and the relaxation factor to a small number

(<0.2). For quick and rough calculations, apply the opposite settings.

The number of blade elements parameter controls the resolution of the aerodynamic

results. Set this value to a large number for a slow and accurate calculation. For quick and

rough calculations, set this value to a small number.

The blade element spacing allows the resolution of the aerodynamic computations to

be concentrated on speciﬁc regions of the blade. For example, if half-cosine (finer

towards tip) is selected, the resolution at the blade tip will be high but the resolution at

the root will be low. The full-cosine option produces equal resolution at the tip and hub,

but a low resolution in the middle.

Figure 5: BEM code setup panel.

5.2 Turbine Data

Basic turbine data is entered into the Turbine Data panel. This data includes the maximum

allowable generator RPM (revolutions per minute), number of blades, rotor and hub radii,

and maximum allowable generator or rotor power.

The radius is measured from the centre of rotation (i.e. radius = 0 at centre of rotation).

Therefore, the hub radius is the distance measured from the centre of rotation and the outer

radius of the hub. The rotor radius is the distance measured from the centre of rotation

and the tip of the blade. Note the blade precone is always set to zero, and thus the swept

radius is equal to the rotor radius.

The maximum power is enabled only if the Optimize AEP instead of Cp option is

selected in the Annual Energy Production (AEP) panel. Otherwise, it is not necessary to

input this value. The eﬃciency of conversion from mechanical to electrical power is assumed

to be 100% always.

Figure 6: Turbine data panel.

5.3 Starting Data

This panel contains the data required for the starting model described in Wood [1]. If

Perform starting analysis is selected, the optimization will minimize the time required

for the turbine to start. The input Windspeed at Starting is the windspeed the turbine

should start. Increasing the starting windspeed will allow the turbine to start more easily,

since a higher windspeed will increase the starting torque. A turbine with good starting

performance will be able to start at a low windspeed for this input ﬁeld. The moment of

inertia and the resistive torque of the generator and drivetrain (G&D) will increase the wind-

turbine starting time. Unless this information is available for the generator and drivetrain

you have selected for the wind turbine design, input zero for these ﬁelds.

Note that blades may produce a starting time of 701, 901, or 1101. These numbers

are not the result of starting calculations, but a penalty placed for blades that are unable

to start. If the blade optimization produces any of these three numbers several times, the

inputs in the starting data panel should be changed in a way to promote starting. This can

be achieved by increasing the starting windspeed or decreasing the G&D inputs. It is also

important to be aware that the starting time should be interpreted as a relative quantity. As

explained in Wood [1], the model cannot be used to calculate the actual “time” for starting.

In order to compute starting time realistically, the model requires the issues discussed in [1]

to be addressed.

Figure 7: Starting data panel.

5.4 Wind Data

The wind data panel allows the density and kinematic viscosity of air in the wind to be

speciﬁed.

Figure 8: Wind data panel.

5.5 Design Parameters

SWRDC is designed for variable-speed turbines that can operate at a single tip-speed ratio

(TSR) between the windspeed at starting and the windspeed at which the maximum gen-

erator RPM is reached. This TSR is called the design TSR, and must be speciﬁed by the

user. If the turbine is to be modelled as a ﬁxed-speed, the design TSR is equal to ωR

Vowhere

ωis the generator’s RPM converted to rad/s,Ris the rotor radius, and Vois the design

windspeed. Note that for the ﬁxed-speed case, the Display Cp-TSR curve in the Plotting

panel and the Optimize AEP instead of Cp in the Annual Energy Production (AEP)

panel should be disabled, since these have been programmed for variable-speed operation

only. Careful consideration should be given for the design TSR and windspeed, since the

rotor design will be signiﬁcantly inﬂuenced by these two inputs.

The pitch angle is the angle between the tip chord and the rotorplane. SWRDC allows

for ﬁxed-pitch turbines only. If a baseline blade is provided in the Baseline Blade panel

that has a pitch angle of 0◦and a negative or positive value of twist for the blade tip,

SWRDC will automatically recalculate the twist distribution such that the twist at the tip

becomes zero. The pitch angle will then be set to the previous value of twist at the blade

tip. The recalculated twist distribution and pitch produces an identical local pitch (local

pitch = twist + pitch) as the original conﬁguration. During the optimization, the tip twist is

assumed to be zero always. If the user desires a negative or positive value for twist towards

the blade tip, he or she must specify the appropriate pitch angle to take this into account.

Figure 9: Design parameters panel.

5.6 Structural Data

If the Perform structural optimization option is enabled, SWRDC will minimize the

blade mass while satisfying a maximum allowable strain. During the structural analysis,

the blade is modeled as a simple beam with isotropic material properties. The blade cross-

section can be modelled as solid or as a thin shell. The strain is calculated at points on the

cross-section where its magnitude is the largest. Maximum strain typically occurs on the

highest and lowest points of the upper and lower surfaces of the cross-section respectively.

To select whether the blade should be modelled as solid or hollow, use the Cross-Section

drop-down menu. If solid is selected, SWRDC will use the structural analysis to determine

whether a candidate blade is structurally feasible or infeasible. If hollow is selected, the

shell thickness along the length of the blade will be calculated such that each blade element

does not exceed the maximum allowable strain. You must also specify the minimum shell

thickness as a fraction of the chord length using the Min.Cap Thickness ﬁeld to avoid the

possibility of an inﬁnitely thin blade element.

When modelling the blade using isotropic material properties, the Elastic Modulus,

Ultimate Tensile Strain and Material Density of the material used for the blade fab-

rication is required. The ultimate tensile strain is the strain at the point on the stress-strain

curve where stress is a maximum. The stress-strain curve is obtained from a tensile test.

If desired, a Material Safety Factor can be applied on the ultimate tensile strain. The

structural analysis in SWRDC does not take fatigue eﬀects into account.)

The minimum and maximum ﬂapwise natural frequency ﬁelds (i.e. Min.Flap.Nat.Freq.

and Max.Flap.Nat.Freq.) are used for the analysis of blade natural frequencies. As a gen-

eral rule of thumb, the ﬁrst ﬂapwise natural frequency of the blade should be between 4p

and 5p, with p being the rotational frequency of the rotor, while the ﬁrst edgewise natu-

ral frequency of the blade should be close to 6.5-7p, to comply with good ﬁrst-frequency

separation requirements. Separating the blade natural frequencies from the harmonic vi-

bration associated with rotor rotation will prevent the occurrence of resonance. To exclude

frequency analysis in the optimization, enter 0 and 9999 for the Min.Flap.Nat.Freq. and

Max.Flap.Nat.Freq. ﬁelds respectively.

If the Perform structural optimization option is disabled, the optimization will not

attempt to minimize the mass but will still perform structural computations. The opti-

mization will determine if a candidate blade is structurally feasible or infeasible unless an

inﬁnite maximum strain is speciﬁed in the Ultimate Tensile Strain ﬁeld. The structural

computations are required for the estimation of starting time, since starting depends on the

inertia of the blade. To compute the inertia, the blade will be assumed solid and will use

the elastic modulus and material density speciﬁed in the Structural Data panel.

Figure 10: Structural data panel.

5.7 Load Case Data

The load case data is solely used for the structural component of SWRDC. Only two load

cases are available: Parked Condition (default) and Rotor Overspeed. The parked con-

dition simulates a hurricane whereby the rotor is stationary and is subjected to an extreme

windspeed in all directions (i.e. 0◦-360◦around the blade axis). The Rotor Overspeed case

simulates an incoming wind normal to the rotor plane that will cause the rotor to rotate

beyond the maximum allowable RPM of the generator.

The 50-year windspeed ﬁeld is used to specify the extreme windspeed for both the

parked and rotor overspeed cases. The loads associated with the extreme windspeed will be

multiplied by the Load Safety Factor value. The Rotor Overspeed Factor is enabled

for the rotor overspeed load case only. If a load case associated with normal operation

is desired, select the Rotor Overspeed load case, a Rotor Overspeed Factor of 1, and a

windspeed considered as normal in the 50-year windspeed ﬁeld.

Figure 11: Load case data panel.

5.8 Blade Parameterization

B´ezier curves that are manipulated by control points (CPs) deﬁne the blade twist and chord

distributions. The twist and chord are both required to be monotonically decreasing. The

dimensional thickness is the product of the relative thickness and the chord. The relative

thickness is deﬁned in the Airfoil Thickness (frac.chord) ﬁeld in the Airfoil Data

panel (see section 5.10). Figure 12 illustrates the blade parameterization.

0 0.5 1

r/R(dimensionless)

Twist (degrees)

Twist vs. r/R

0 0.5 1

0.1

0.2

0.3

0.4

r/R(dimensionless)

Chord (m)

Chord vs. r/R

0 0.5 1

−1

r/R(dimensionless)

Thickness/Chord (%)

% Thickness vs. r/R

0 0.5 1

0.01

0.02

0.03

r/R(dimensionless)

Thickness (m)

Dimensional Thickness vs. r/R

Twist

Chord

Thickness

CP Thickness

Figure 12: Control points (CPs) determine the blade element (BE) values for twist and

chord. The dimensional thickness is the product of the relative thickness and the chord.

The number of CPs that determine the twist and chord can be adjusted using the

Num.Control Points (N) ﬁeld. Increasing the number of CPs increases the complexity of

the B´ezier curve making it bend more.

The radial location of the CPs are ﬁxed and distributed according to the spacing chosen

in the ---Control Point Spacing--- drop-down menu. There are four options available:

uniform (default),half-cosine (finer towards hub),half-cosine (finer towards

tip) and full-cosine. In the half-cosine (finer towards hub) option, CPs are spaced

with higher density towards the hub and lower density towards the tip. The half-cosine

(finer towards tip) is the opposite of half-cosine (finer towards hub). In the

full-cosine option, CPs are spaced with higher density near the hub and tip, but lower

density in the middle. The ---Control Point Spacing--- option allows the blade to be

designed with greater maneuverability in speciﬁc regions.

The Twist Upper Bound,Twist Lower Bound,Chord Upper Bound, and Chord Lower

Bound ﬁelds determine the upper and lower bounds for the CPs controlling the twist and

chord. Note when entering the Twist Lower Bound that there is an additional CP for twist

at the blade tip which is set to zero (hard-coded in). To apply a twist other than zero at

the blade tip, you must make the appropriate adjustment using the Pitch angle (deg.)

ﬁeld in the Design Parameters panel (see section 5.5).

Figure 13: Blade parameterization panel.

5.9 Genetic Algorithm Parameters

SWRDC uses a genetic algorithm (GA) as the optimization algorithm, which can be con-

trolled using the Genetic Algorithm Parameters panel. The ﬁrst parameter is Population

Size, which determines the number of individuals for each generation. Increasing the pop-

ulation size allows the GA to search more thoroughly the design space and hence obtain a

better result. However, increasing the population size will also increase the time to compute

each generation. The overall computing time scales linearly with Population Size. The

size of the population must also be a number that will produce an integer when divided by

four. The GA within SWRDC will not function otherwise. A population size larger than

100 is recommended.

The Num.Generations parameter is the maximum number of generations that the GA

will run before it terminates. The GA may, however, terminate sooner if the population

converges to a single optimum solution. Increasing Num.Generations will ensure the GA

converges to the optimal blade design. A number larger than 50 for Num.Generations is

recommended.

To create children and potentially superior individuals, the GA utilizes the crossover and

mutation operators. Each operator contains settings which can be controlled by the user.

These settings can signiﬁcantly inﬂuence the performance of the GA. For Crossover Type,

either SBX or Uniform can be selected. For the SBX, the crossover is performed between

two parents according to a scheme described in Deb [3] and requires a SBX index. The

SBX index controls the probability of creating near parent solutions or distant solutions as

children. When Uniform is selected, a random binary vector is created and selects the genes

where the vector is 1 from the ﬁrst parent and the genes where the vector is a 0 from the

second parent, and combines the genes to form the child. The Crossover Probability

controls whether two parents will be subjected to crossover or not, and is a parameter for

both the SBX and Uniform crossover types.

Mutation speciﬁes how the GA makes small random changes to create mutated chil-

dren, promoting the diversity of the population. Only polynomial mutation as described in

Deb [3] is available, which depends on the Mutation Index and Mutation Probability pa-

rameters. The Mutation Index controls the intensity of the mutation (or the randomness)

when altering the genes of a child. The Mutation Probability is the probability that each

gene from a child will be mutated. A commonly used heuristic for Mutation Probability

is 1/number of variables, where the number of variables in SWRDC is 2N+ 1. Nis the

number of control points as speciﬁed in the Num.Control Points (N) ﬁeld on the Blade

Parameterization panel.

The last option, Load initial population “endPop.mat”, allows the user to input a

population from a previous optimization as the initial population. For each optimization run

and for each generation, a ﬁle named endPop.mat will be stored in the SWRDC directory. By

loading endPop.mat from a previous optimization, the GA begins the blade design process

using an already improved population instead of one generated at random.

Figure 14: Genetic algorithm parameters panel.

5.10 Airfoil Data

The Airfoil Data panel is where all the airfoil data for the aerodynamic and structural

analyses is entered. The Re.Array ﬁeld is where the range of Reynolds numbers for the

airfoil lift and drag data is loaded. The length of Re.Array must match the number of lift

and drag data entered in the Lift/Drag Data ﬁeld. To enter Re.Array, you can either type

the Reynolds numbers in the text box or load it from a ﬁle using the Browse button. If

typing Reynolds numbers in the text box, remember to enclose them with square brackets

(i.e. [ ]).

Figure 15: Airfoil data panel.

Airfoil Thickness (frac.chord) is the relative thickness (dimensional thickness/chord)

of the airfoil being used in the blade design. This value is for plotting purposes only and does

not need to be exact. In the structural analysis, the relative thickness is calculated using

the proﬁle coordinates entered in the Profile Coord. ﬁeld. To load the lift and drag data,

and the proﬁle coordinates, use the Browse button. Note the lift and drag data, and proﬁle

coordinates must be located in the \airfoildatabase folder in the SWRDC directory.

You can check if all your data has been entered correctly by clicking on the Check

Inputs button. A ﬁgure displaying all of your data should appear as shown in Figure 16. If

the data was not properly entered, the message “—-!!!!!PLEASE CHECK YOUR AIRFOIL

DATA!!!!—-” will appear on the MS-DOS window if you are using the compiled version, or

the MATLAB command window if you are using the source code.

0 0.25 0.5 0.75 1

−0.3

−0.2

−0.1

0.1

0.2

0.3

0.4

Profile Coordinates

x/c

y/c

−180 −90 0 90 180

−1

−0.5

0.5

1.5

2Lift Data

Angle of Attack (°)−180 −90 0 90 180

0.2

0.4

0.6

0.8

1.2

1.4 Drag Data

Angle of Attack (°)

100000

150000

200000

300000

500000

Reynolds Number

Figure 16: Airfoil data checking.

5.11 XFOIL Airfoil Noise Database Calculation

SWRDC includes an automated noise database calculation algorithm using the XFOIL code

developed by Mark Drela [5]. The noise database pertaining to the airfoil used in the blade

design is necessary to perform noise analyses. The database consists of boundary layer

displacement thickness values for diﬀerent Reynolds numbers and angles of attack.

The database can be computed before an optimization begins by selecting the Compute

airfoil noise database before optimization? option. If selected, you do not need to

load a ﬁle for the Load airfoil noise database ﬁeld in the Noise Data panel, but do

need to specify the range of Reynolds numbers and angles of attack in the Load reference

alfa and Load reference Reynolds ﬁelds. Default values are included in the GUI for your

convenience. The noise database calculation is performed soon after the Run Optimization

button is pressed and before the optimization begins. The alternative is to compute the

database and store it as a ﬁle by clicking on the Compute button. You must then load this

ﬁle on the Load airfoil noise database ﬁeld.

The Viscous-solution iteration limit controls the maximum number of iterations

for XFOIL to converge to a solution. Increasing the number of iterations will increase the

chances of obtaining an accurate noise database, but will also increase the computing time

for the database calculation. XFOIL will often not converge to a solution and the accuracy

of the database will be adversely aﬀected. A default value of 200 is included in the GUI as

reference.

The drop-down menu labelled ---Transition trigger (N crit)--- provides two op-

tions: untriggered:N crit=9 (default) and triggered:N crit=4. For details concern-

ing this option, refer to section 7.4, the thesis of Zhu [2], or the XFOIL user guide on the

XFOIL website: http://web.mit.edu/drela/Public/web/xfoil/. Whether the untrig-

gered or triggered option is selected will be reﬂected in the Noise Data panel on the right

of the “Flow is:” text as shown in Figure 18.

Figure 17: XFOIL airfoil noise database calculation panel.

5.12 Noise Data

If the Perform noise analysis option is enabled, SWRDC will minimize the noise emission

by altering the blade’s shape. Several parameters are necessary in order to estimate noise

involving the location of the rotor relative to the observer’s position, wind characteristics,

and parameters that inﬂuence the aero-acoustics near the blade sections and tip. Fields are

accompanied with a short text and a few have help buttons to assist the user in selecting

the appropriate settings. Here are a few additional notes:

•For Power law factor, you may refer to the notes in section 7.3.1.

•The Turbulence length scale and Turbulence intensity ﬁelds should be set to

zero unless for speciﬁc research purposes.

•The Tip shape can either be Squared or Rounded. The default is Squared since

SWRDC does not take the rounded tip into account in the aerodynamic and structural

calculations. Futhermore, SWRDC will not round the tip when exporting the geometry

if the Print final coordinates option is selected, and will not display a rounded

tip when Final blade 3D option is selected, both options which can be found in the

Plotting panel.

•A ﬁgure illustrating the Bluntness thickness at trailing edge is available in sec-

tion 7.3.2. Make sure the trailing edge (TE) thickness is taken into consideration when

loading the airfoil proﬁle coordinates in the Airfoil Data panel. SWRDC will not

check whether the Bluntness thickness at trailing edge matches the TE thick-

ness in the airfoil proﬁle coordinates ﬁle. SWRDC will not crash if this aspect is

neglected.

•A value between 1 and 1.2 is recommended for the Tip factor. Please refer to

section 7.3.3 or for a more detailed description, see Brooks, Pope, and Marcolini [6].

For a detailed description of all parameters, refer to the thesis of Zhu [2].

Figure 18: Noise data panel.

As mentioned in section 5.11, a noise database pertaining to the airfoil speciﬁed in the

Airfoil Data panel is necessary to perform noise analyses. The database consists of bound-

ary layer displacement thickness values for diﬀerent angles of attack and Reynolds numbers

as shown in the Load reference alfa and Load reference Reynolds ﬁelds respectively.

The database is integrated into the noise analysis either by computing it before an opti-

mization begins using the Compute airfoil noise database before optimization? op-

tion, or by loading an already existing database ﬁle. To load an already existing database,

click Browse next to the Load airfoil noise database ﬁeld. Ensure that the Load

reference alfa and Load reference Reynolds ﬁelds matches accordingly with the database

ﬁle. This can be checked by clicking the Check Inputs button. A ﬁgure such as the one

shown in Figure 19 should appear and if not, the message “Input noise database ﬁle does not

match reference alfa and/or Reynolds number range(s)” will be displayed in either the MS-

DOS or MATLAB command windows. For the Load reference alfa and Load reference

Reynolds ﬁelds, you can type the numbers manually into the text boxes or load them from

a ﬁle using the Browse buttons. If you are typing the numbers manually, ensure to enclose

them with square brackets (i.e. [ ]).

−10

0.02

0.04

0.06

0.08

AoA (degrees)

δ* at TE − Pressure Side

Re (106)

δ* at TE (m)

−10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

AoA (degrees)

δ* at TE − Suction Side

Re (106)

δ* at TE (m)

Figure 19: Boundary layer displacement thickness as a function of Reynolds number (Re)

and angle of attack (AoA) for the pressure (left) and suction (right) sides of the SG6043

airfoil.

5.13 Objective Weight Factors

These weights allow the user to select which objectives are more important to him or her.

Given a two-objective problem of maximizing CPand minimizing starting time, if the user

believes that aerodynamic eﬃciency is more important than starting time for his or her

blade design, then the weight for CPshould be high and the weight for starting should

be low (e.g. w1= 0.9 and w2= 0.1). Note the sum of the weights should be equal to

one and each weight must be strictly positive. See equation (1) in section 1. Furthermore,

specifying a weight of zero for any one of the objectives is the equivalent of excluding the

objective from the optimization. For example, if w2 for starting time is zero, SWRDC will

not attempt to minimize starting time.

Figure 20: Objective weight factors panel.

5.14 Plotting

All the SWRDC plotting options are located in the Plotting panel. The user may se-

lect up to four plots to be displayed while the optimization is running: Blade geometry,

Structural performance,Final blade 3D and Optimization progress. When the Blade

geometry and Structural performance options are selected, the geometry and structural

performance for each candidate blade design will be displayed. The geometry and structural

performance plots will also be displayed for the baseline and ﬁnal blade designs. Note that

when both of these plotting options are activated, the overall run time for the optimization

may increase.

Figure 21: Plotting panel.

An example of a geometry plot is shown in Figure 22. The geometry plot contains all the

relevant information about a candidate blade’s geometry as described in section 5.8. Please

refer to section 5.8 for details.

Figure 22: Blade geometry plot.

A structural performance plot is shown in Figure 23, which includes ﬁve sub-plots: shell

thickness, stiﬀness, bending moment, deﬂection, and 1st ﬂapwise eigenmode, all versus the

non-dimensionalized radial position of the blade, r/R. The shell thickness plot contains

the dimensional and relative thickness of the shell. The dimensional shell thickness is in

metres (black line) while the relative thickness is the dimensional shell thickness divided by

the chord (green line). When the Cross-Section option in the Structural Data panel is

set to Solid, the relative shell thickness shown should be a straight horizontal line. This

corresponds with the case when the shell is at the maximum thickness, thus creating a

‘Solid’ blade. If the Structural Data panel is set to Hollow, the shell thickness represents

the thickness required to maintain structural integrity of the blade based on the load case

entered in the Load Case Data panel (see section 5.7).

The stiﬀness plot depicts the stiﬀness along the ﬁrst (EI1) and second (EI2) principal

axes and depends strongly on the shell thickness. Since the blade cross-section is modelled

as either hollow or solid, the stiﬀness in the edgewise direction will always be larger than

in the ﬂapwise direction. This is shown in Figure 23, where EI2is much larger than EI1.

The bending moments along the ﬁrst (M1) and second (M2) principal axes, the ﬂapwise

(un) and edgewise (ut) deﬂections, and the deﬂection shape of the ﬁrst ﬂapwise eigenmode,

Uy,flap1and Uz,f lap1, are included in the structural plot.

Figure 23: Structural performance plot.

If the Final blade 3D option is selected, a three-dimensional plot of the ﬁnal blade

design will appear when the optimization is ﬁnished. Figure 24 depicts such a ﬁgure.

Figure 24: Final blade 3D plot.

If the Optimization Progress option is selected, either a three- or two-dimensional

plot will appear following each generation, displaying the objective values of the population.

The best individual of the population as described in section 6.1 and the utopia point

will be displayed as well, and are labelled ‘Best” and “Utopia” respectively. The utopia

point holds the ideal objective value for each objective being considered, where CPis equal

to the Betz limit and Starting, Mass and Noise are equal to zero (i.e. CP=0.593 and

Starting=Mass=Noise=0). The utopia point represents the best possible result for any

blade design but is impossible to achieve. If the optimization is functioning properly, the

best individual should approach the utopia point in the Optimization progress plot. The

utopia point will only appear if the Optimize Cp instead of AEP option is deactivated.

The Optimization Progress plot is only available for three- or two-objective problems.

Figure 25: Optimization progress for a three-objective problem.

The last option, Display Cp-TSR curve, will write the CPand CTas a function of the

tip-speed ratio (TSR) in the Excel results ﬁle for the baseline and ﬁnal blade designs. Both

curves are computed assuming the turbine is a variable-speed machine and is operating at

the design windspeed for all TSRs. Figure 26 depicts the CP-TSR and CT-TSR curves in

the Excel results ﬁle.

Figure 26: CP-TSR and CT-TSR curves displayed on the Excel results output ﬁle.

5.15 Parallel Computing Toolbox - MATLAB - MathWorks

The Parallel Computing Toolbox panel allows SWRDC to run in parallel and signif-

icantly reduce the overall computing time. To run SWRDC in parallel, select the Run

optimization in parallel option and input an appropriate number of processors. The

maximum allowable number that can be entered into the Number of processors ﬁeld will

be the total number of processors in your computer system or 12. The number of processors

that your computer holds can be determined by viewing the Performance tab on the Win-

dows Task Manager or typing WMIC CPU Get NumberOfLogicalProcessors /Format:List

on the MS-DOS command prompt. The larger the number speciﬁed in the Number of

processors ﬁeld, the faster the optimization will become. If you are using MATLAB and

the original source code, you must have the Parallel Computing Toolbox installed.

Figure 27: Parallel computing toolbox - MATLAB - MathWorks panel.

5.16 Results File

The purpose of the Results File panel is to allow the user to select the ﬁle name and

location of the Excel results ﬁle. The Excel ﬁle will contain the results for the ﬁnal blade

design and also the baseline blade if the Run Baseline Blade option is selected on the

Baseline Blade panel.

Figure 28: Results ﬁle panel.

Click the Save as button to display the window shown in Figure 29. Type the ﬁle name

and click Save. The ﬁle name and location will then be displayed in the text box on the

Results File panel.

Figure 29: Saving the Excel results ﬁle.

5.17 Annual Energy Production (AEP)

If the Optimize AEP instead of Cp option on the Annual Energy Production (AEP)

panel is enabled, SWRDC will minimize the AEP instead of the power coeﬃcient, CP,

for the rotor/blade design. This feature can only be used if the turbine is a variable-speed

machine that can operate at a single tip-speed ratio between a range of ﬂow speeds, deﬁned

in the Annual Energy Production (AEP) panel as the cut-in and cut-out windspeeds.

To calculate the AEP, a probability density function to describe the ﬂow distribution

of a wind site is required. There are three probability distributions to choose from using

the ---Probability type--- drop-down menu: Rayleigh,Weibull, and User-defined.

The default is the Rayleigh distribution, which requires the cut-in, cut-out and mean

windspeeds. If the Weibull distribution is selected, the user must specify the form factor,

k, and the scale factor, A (m/s), instead of the mean windspeed. The last option is the

User-defined distribution, which allows any arbitrary ﬂow probability distribution to be

used for calculating the AEP. To open a user-deﬁned distribution, click Browse. The ﬁle

name and location will then be displayed in the text box on the Annual Energy Production

(AEP) panel. Note the ﬁrst and last windspeed entries in the user-deﬁned distribution must

represent the cut-in and cut-out windspeeds. To visualize the input data on the Annual

Energy Production (AEP) panel, click the Check Inputs button.

If the Optimize AEP instead of Cp option disabled, SWRDC will maximize the CP.

Note that optimizing a rotor/blade for maximum CPdoes not necessarily create a turbine

with the highest AEP.

Figure 30: Annual energy production.

5.18 Baseline Blade

If Run Baseline Blade is selected, SWRDC will calculate the baseline blade design with the

ﬁle name and location speciﬁed in the text box on the Baseline Blade panel. The results

for the baseline design will be shown on the MS-DOS (compiled) or command window

(MATLAB) as described in section 6.1 as well as in the Excel results ﬁle described in

section 6.3. To locate and open the desired baseline design, click the Browse button. The

ﬁle name and location will then be displayed in the text box on the Baseline Blade panel.

To run a test on the baseline blade using the models in SWRDC, click the Test button. If

it fails, please review the data on the baseline blade ﬁle.

The ﬁrst line on the baseline blade ﬁle must have the following three headers: radius (m),

chord (m), and twist (degrees). The data below the headers must match the dimensions

given in the headers (i.e. meters, meters, and degrees respectively). Any number of rows is

allowed for the blade data, but it must include the radius, chord and twist at the root and

tip of the blade. An example is shown in Figure 32, where the hub and rotor radii are equal

to 0.1333 and 1.5 meters respectively.

Figure 31: Baseline blade.

Figure 32: Example of blade data used as a baseline.

5.19 Saving and Loading GUI Settings

GUI settings for SWRDC can be saved or loaded using this panel. To save the data stored

in the GUI, click Save GUI settings. The GUI settings must be stored as a MATLAB

ﬁgure ﬁle (*.ﬁg). To load GUI settings from a previous session, click Load GUI settings.

When loading, the GUI will close (and all data on it will be lost) and a new one will appear

with the settings you have loaded.

Figure 33: Saving and loading GUI settings.

6 Running an Optimization

6.1 Clicking the Run Optimization button

Once all settings on the GUI have been applied, the optimization can be executed by clicking

on the Run Optimization button shown in Figure 33. If you are running SWRDC on the

compiled version, information relating to the optimization and its progress will be displayed

on the MS-DOS window as shown in Figure 34. If you are using MATLAB and the original

source code, the information will be displayed on the command window.

Figure 34: Running the optimization.

The program begins by displaying basic information about SWRDC and a disclaimer

that README FIRST LICENSE.txt must be read before installing or using SWRDC.

If the Run Baseline Blade option in the Baseline Blade panel is selected, SWRDC will

calculate the baseline blade design and display the results as shown below:

For explanations of each heading, for example Cp / AEP, please refer to section 6.2. A ran-

dom initial population of candidate blade designs will then start to generate. The size of the

initial population will be equal to the number speciﬁed in the Population Size ﬁeld in the

Genetic Algorithm Parameters panel. If the Load initial population “endPop.mat”

option in the Genetic Algorithm Parameters panel is selected, the population stored in

the “endPop.mat” ﬁle will be generated instead.

Once the initial population is ﬁnished calculating, “Initial population calculation com-

plete” will appear followed by “Generation = 0”. The zero value indicates that the ﬁrst

iteration has begun and will not ﬁnish until “Generation = 1” appears. Each iteration repre-

sents a generation of children, which will be half the Population Size. Consequently, each

iteration involves only half the computing cost required for generating the initial population.

The last step for each iteration is to determine the best individual of the current population.

The best individual is determined by selecting the individual with the smallest value for

equation (1) and that does not violate the constraints. The value for equation (1) of the

best individual is displayed in the Best Value ﬁeld. The overall constraint violation is

calculated following a scheme described in Deb [3] and takes priority over the value obtained

for equation (1) when selecting the best individual. The overall constraint violation of

the best individual is displayed in the Best Constraint ﬁeld. A value of zero for Best

Constraint indicates that the blade does not violate any constraint. Once “Generation =

1” appears, the ﬁrst iteration is complete and the subsequent iteration will begin.

During the optimization, a wait bar will display the optimization’s progress by ﬁlling a

bar with red from left to right. To abort the optimization, click “Cancel” on the wait

bar. The optimization will be aborted once the current iteration (or generation) is ﬁnished

calculating. Depending on the Population Size chosen and the point where the cancel

button was pressed, it may take several minutes or hours before the iteration is complete.

Figure 6.1 illustrates what occurs after the cancel button on the wait bar is pressed or when

the maximum number of generations speciﬁed in the Num. Generations ﬁeld in the Genetic

Algorithm Parameters panel is reached. For the example optimization shown below, the

maximum number of generations is ﬁve. After Generation = 5 is displayed, the last best in-

dividual recorded becomes the ﬁnal blade design. The ﬁnal blade design is re-evaluated in or-

der to display its optimum performance with respect to the objectives and constraints: Cp /

AEP, starting, mass, strain, etc. For this particular example, the ﬁnal design has the follow-

ing: Cp=0.321, Starting=0.091, Mass=0.178, C.1: Strain=0,...,1stFlapEigenFreq=353.580.

SWRDC will then record the results of the ﬁnal blade design into an Excel ﬁle. The

recording takes a few minutes to complete; please be patient and wait until “FINISHED”

appears before opening or manipulating the Excel results ﬁle. For details regarding the

Excel ﬁle and the outputs from SWRDC, refer to section 6.3.

6.2 Optimization Headings

The headings are as follows: Cp / AEP, Starting, Mass (kg), C.1: Strain, C.2: Freq.L,

C.3: Freq.U, Noise (dB), and 1stFlapEigenFreq (rad/s). Each quantity is calculated for all

candidate blade designs, the baseline design if provided, and the ﬁnal optimum design. The

example shown in Figure 6.2 will be used to explain some of the headings.

1. Cp / AEP

The power coeﬃcient is displayed here and must be between 0 and 0.59. If zero is

displayed, this signiﬁes that the BEM algorithm was unable to converge to a feasible so-

lution. If the Optimize AEP instead of Cp option is selected in the Annual Energy

Production (AEP) panel, the number shown will represent the AEP in kWh/year.

2. Starting

Starting time is displayed here and should be treated as a relative quantity. If a

starting time of 701, 901, or 1101 is shown, this signiﬁes that the candidate blade

is unable to start. If Perform starting analysis in the Starting Data panel is

not selected, starting time will be displayed as “NaN” for all blades to indicate that

starting is excluded from the optimization.

3. Mass (kg)

Blade mass is displayed here in kilograms regardless of whether or not the Perform

structural optimization option in the Structural Data panel is selected.

4. C.1: Strain

The ﬁrst constraint (C.1) represents the maximum value of strain along the blade’s

length that must be below the maximum allowable strain as determined by the Ultimate

Tensile Strain and Material Safety Factor ﬁelds in the Structural Data panel.

A number equal to zero or below signiﬁes that the strain constraint is satisﬁed. A

positive value under this heading signiﬁes that the candidate blade is structurally in-

feasible and is accompanied by the message “Max Strain at Max Thickness Exceeded”

as shown in Figure 6.2, where the value of C.1: Strain is 0.049374.

5. C.2: Freq.L

The second constraint (C.2) represents the amount which the 1st ﬂapwise eigenfre-

quency of the blade diﬀers from the acceptable lower bound. A negative quantity or

a value of zero indicates that the lower bound is met. Otherwise, the lower bound is

violated. In Figure 6.2, the lower bound is violated since a value of 0.1072 appears

under the C.2: Freq.L heading.

6. C.3: Freq.U

The third constraint (C.3) represents the amount which the 1st ﬂapwise eigenfrequency

of the blade diﬀers from the acceptable upper bound. A negative quantity or a value

of zero indicates that the upper bound is met. Otherwise, the upper bound is violated.

In Figure 6.2, the upper bound is met since a value of -0.9997 appears under the C.3:

Freq.U heading.

7. Noise (dB)

Noise emitted by the blade is displayed here in decibels (dB). If Perform noise

analysis in the Noise Data panel is not selected, noise will be displayed as “NaN”

for all blades to indicate that noise is excluded from the optimization.

8. 1stFlapEigenFreq (rad/s)

The 1st ﬂapwise eigenfrequency of the blade is displayed here in radians per second

(rad/s).

6.3 Optimization Finished: Analysing the Outputs

When the optimization is ﬁnished, the word “FINISHED” should appear on the bottom of

the MS-DOS window (compiled) or on the bottom of the command window (MATLAB) as

shown in Figure 35.

Figure 35: Optimization ﬁnished.

The Excel ﬁle containing the results of the ﬁnal blade design should be located in the

directory speciﬁed in the GUI prior to running the optimization. There are three sheets in

the Excel ﬁle, namely: Performance Results, Optimized Blade Shape, and Baseline Blade

Shape.

In the Performance Results sheet, the performance of the optimized and baseline (if

selected) blades will displayed, speciﬁcally: power coeﬃcient / AEP, power, torque, thrust,

ﬂapwise root-bending moment, starting time, blade mass, strain violation, frequency viola-

tion 1 and 2, 1st ﬂapwise eigenfrequency, and noise. In addition, a summary of the turbine

input data will be shown. If a baseline blade was provided and the optimization was per-

formed correctly, then the overall results for the optimized blade shown on the Performance

Results sheet should be better than the baseline design. If this is not the case, it may be

necessary to adjust the parameters in the Genetic Algorithm Parameters panel such as

increasing the number of generations or the population size, in order to achieve a better

result.

In the optimized and baseline blade shape sheets are the chord and twist distributions,

pitch angle, and the CP-TSR curves if the Display Cp-TSR curve option is selected. Note

the CP-TSR curves are computed assuming the turbine is a variable-speed machine and is

operating at the design windspeed for all TSRs.

Figure 36: Excel results ﬁle showing the Performance Results sheet.

7 Notes on GUI Inputs

The GUI includes push buttons with question or exclamation marks to assist the user in

selecting the appropriate settings. These push buttons generate messages or images, which

are summarized in this section.

7.1 Objective Weight Factors

Note: w1 + w2 + ... = 1

7.2 Genetic Algorithm Data: Population Size

Population size must be even when divided by 2.

7.3 Noise Data

7.3.1 Power Law Factor

The mean wind speed varies with height and it’s often described with power law relationship:

Vz=Vref Z

Zref γ

where γis the power law factor which gives the amount of shear, typically between 0.1

and 0.25. Instead of specifying the value of the power law factor, you can use the built-in

estimate using the expression by Counihan (1975):

γ= 0.24 + 0.096 log10 zo+ 0.016(log10 zo)2

where zois the surface roughness.

7.3.2 Bluntness Thickness at Trailing Edge

7.3.3 Tip Factor

The tip vortex formation noise spectrum in a 1/3-octave presentation is predicted by:

SPLTIP = 10 log M2M3

maxl2¯

e−30.5(log St00 + 0.3)2+ 126.

The spanwise extent at the trailing-edge of the separation due to the tip vortex, l, depends

on the angle of attack of the tip, αTIP .αTIP must be redeﬁned according to computed

sectional loading if the blade has a small aspect ratio, is twisted, or encounters non-uniform

ﬂow over its span. Since a wind-turbine blade normally possesses some these characteristics,

αTIP should be corrected. The redeﬁned α0

TIP is:

α0

TIP ="∂L0/∂y

(∂L0/∂y)refy→TIP #αTIP

where the term within the square brackets is referred to as the tip factor and is typically

between 1 and 1.2.

7.3.4 Sound Pressure Level at Diﬀerent Observer Positions

7.4 XFOIL Airfoil Noise Database Calculation: Transition Crite-

rion

Transition in an XFOIL solution is triggered by one of two ways:

1. free transition: eNcriterion is met;

2. forced transition: a trip or the trailing edge is encountered.

The eNmethod is always active, and free transition can occur upstream of the trip. The eN

method has the user-speciﬁed parameter Ncrit, which is the log of the ampliﬁcation factor of

the most-ampliﬁed frequency which triggers transition. A suitable value of this parameter

depends on the ambient disturbance level in which the airfoil operates, and mimics the eﬀect

of such disturbances on transition. Below are typical values of Ncrit for various situations.

situation Ncrit

sailplane 12-14

motorglider 11-13

clean wind tunnel 10-12

average wind tunnel 9

dirty wind tunnel 4-8

8 Building a CAD File using SolidWorks

This section will demonstrate how the coordinates from SWRDC are imported in a computer-

aided design (CAD) program such as SolidWorks. Once the blade is imported into Solid-

Works, you can use the CAD ﬁle to build the blade on a rapid-prototyping machine or a

computer numerical control (CNC) milling machine, for example. SolidWorks 2012 x64 Stu-

dent Edition on a Windows 7 operating system will be used to demonstrate the procedure.

1. The ﬁrst step is to open SolidWorks. An interface such as the one shown in Figure 37

should appear.

Figure 37: 1

2. Click on File →New, select Part: a 3D representation of a single design

component and click OK.

Figure 38: 1

3. On the Features tab, click Curves and select Curve Through XYZ Points.

Figure 39: 1

4. Click Browse and ﬁnd the exportedcoords folder where the coordinates from the opti-

mization are located. Make sure Text Files (*.txt) is selected on the drop-down menu

above the Open and Cancel buttons. Begin by opening the pro coords1.txt ﬁle,

which represents the X-Y-Z coordinates of the outer proﬁle for the ﬁrst blade element.

Figure 40: 1

5. The X-Y-Z coordinates will be displayed on a table. The X, Y, and Z coordinates

correspond to the horizontal, vertical and longitudinal directions of the blade element

respectively and are measured in metres (m). The X-direction is aligned with the

airfoil proﬁle’s chord line, while the Z-direction is aligned with the blade length. The

Y-direction points towards the airfoil proﬁle’s upper surface. Click OK to import the

coordinates.

Figure 41: 1

6. Place a reference plane by clicking Reference Geometry →Plane and select the airfoil

as the ﬁrst reference. Click on the green check mark to accept.

Figure 42: 1

7. The airfoil should be embedded on a reference plane as shown in Figure 43.

Figure 43: 1

8. On the Sketch tab, click Sketch and select the plane that coincides with the airfoil

proﬁle.

Figure 44: 1

9. The plane with the airfoil should be displayed in a frontal view as shown in Figure 45.

Figure 45: 1

10. Click on Convert Entities and select the airfoil proﬁle. A text that reads Edge<1>

should appear under the Entities to Convert ﬁeld. Click on the green check mark

to accept. The airfoil proﬁle should then appear as a thick black line as opposed to a

light blue colour. Exit the sketch.

Figure 46: 1

11. The outer proﬁle coordinates have been imported and converted as a sketch. Select

Curve Through XYZ Points after clicking the Curves button on the Features tab.

Open the inner coordinates for the ﬁrst blade element by selecting the cap coords1.txt

ﬁle. If the blade was modelled as a solid in the optimization, ignore steps 11 and 12.

Figure 47: 1

12. Click on the plane where the outer airfoil proﬁle is situated. Click Sketch on the

Sketch tab. Convert the inner proﬁle to a sketch by repeating step 10. The ﬁrst blade

element is complete.

Figure 48: 1

13. Place the second blade element by repeating steps 3-12 using the pro coords2.txt

and cap coords2.txt ﬁles. The interface should display two blade cross-sections as

shown in Figure 49.

Figure 49: 1

14. Create a guide curve by clicking Curves on the Features tab and selecting Curve

Through Reference Points. To create the guide curve, select the reference points

on the leading edges of each airfoil and click on the green check mark to accept. Click

Loft Boss/Base on the Features tab and select the outer proﬁles for the Profiles

ﬁeld and the guide curve for the Guide Curves ﬁeld. Click on the green check mark

to accept.

Figure 50: 1

15. A solid portion of the blade should appear as shown in Figure 51. If the blade was

modelled as solid in the optimization, repeat steps 3-15 for all blade elements and skip

steps 16 and 17. Once all blade elements are taken into account, the CAD ﬁle is ready

for fabrication.

Figure 51: 1

16. To model a hollow blade, click Lofted-Cut on the Features tab and select the inner

proﬁles by clicking on their reference points for the Profiles ﬁeld. If necessary, create

a guide curve using the reference points on the inner proﬁles. Click on the green check

mark to accept.

Figure 52: 1

17. A hollow portion of the blade should appear as shown in Figure 53. Repeat steps 3-17

for all blade elements. Once all blade elements are taken into account, the CAD ﬁle

is ready for fabrication.

Figure 53: 1

9 Final Remarks

Although a reasonable eﬀort was made to ensure the SWRDC code is as error-free and

accurate as possible, the developer does not guarantee that SWRDC is bug-free, will not

produce unrealistic or incorrect results, and will not crash. SWRDC has not been fully tested

and you may use SWRDC for evaluation purposes only. Please interpret the results carefully

and report back any conﬁrmed errors to the developer. You may send your comments and

questions to msessare@ucalgary.ca.

References

[1] Wood D. Small Wind Turbines: Analysis, Design, and Application. Green energy and

technology, Springer, 2011.

[2] Zhu WJ. Modelling of noise from wind turbines. Master’s Thesis, Technical University

of Denmark 2004.

[3] Deb K. Multi-Objective Optimization using Evolutionary Algorithms. Wiley: Chichester,

2001.

[4] Hansen MOL. Aerodynamics of wind turbines. 2 edn., Earthscan: London, 2008.

[5] Drela M. XFOIL: An analysis and design system for low Reynolds number airfoils.

Conference on Low Reynolds Number Airfoil Aerodynamics, University of Notre Dame,

1989.

[6] Brooks TF, Pope DS, Marcolini MA, (US) PM. Airfoil self-noise and prediction. Wash-

ington, D.C. : National Aeronautics and Space Administration, Oﬃce of Management,

Scientiﬁc and Technical Information Division, 1989.

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