Design, Production and Testing of a Small Horizontal ...

Design, Production and Testing of a Small Horizontal Axis Wind Turbine (HAWT) Rotor Progress Report No. 01 TEAM EDDY

PROJECT GROUP MEMBERS:  M. Semih BAYIR 1560911  Çağla Ceren CEYHAN 1503099  Çağrı KÖKSAL 1631761  Oğuzhan KALMAZ 1561117  Misagh Haji AMİRİ 1527886

23.12.2014 Department of Aerospace Engineering Middle East Technical University

Fall 2014

Contents 1.

Introduction: .......................................................................................................................................................3 

General Information: .....................................................................................................................................4

2.

Project Planning: ................................................................................................................................................7

3.

Theory ..................................................................................................................................................................8

4.

Current Status: ................................................................................................................................................. 13 

For NASA/LANGLEY LS(1)-0413 (GA(W)-2) AIRFOIL (ls413-il) ........................................................ 13

For Re# 50000, α=6 , Cl/Cd=35.9 at which Cl= 0.9343 

Cd=0.02602 ............................................................. 13

For S1223 (s1223-il) ...................................................................................................................................... 15

For Re# 50000, α=3.25 , Cl/Cd=42.3 at which Cl= 1.4206 

For MA409 (smoothed) (ma409sm-il) ......................................................................................................... 16

For Re# 50000, α=5.25 , Cl/Cd=43.6 at which Cl= 0.9169 

Cd=0.02105 ........................................................ 16

For GM15 (smoothed) (gm15sm-il) ............................................................................................................ 18

For Re# 50000, α=5.75 , Cl/Cd=46.1 at which Cl= 1.1025 

Cd=0.03358 ........................................................ 15

Cd=0.02393 ......................................................... 18

For FX 60-100 AIRFOIL (fx60100-il) ........................................................................................................ 20

For Re# 50000, α=5.75 , Cl/Cd=42.6 at which Cl= 1.0219

Cd=0.0240 ........................................................... 20

5.

DECISION and RESULTS .............................................................................................................................. 22

6.

Appendix: .......................................................................................................................................................... 25

1.

References .......................................................................................................................................................... 29

1. Introduction: The aim of this project is to design, produce and test a small horizontal axis wind turbine (HAWT) blade. This project will be done by groups containing 5 members during an academic semester. During lectures without wake rotation idealized blades, wake rotation and tip loss idealized blade and actual blades are simply off-designed respectively. At the end of semester each group will construct and test their blade performance at the ''Open-jet Wind tunnel’’ facility in the aerospace engineering department at Middle East Technical University (METU). Figure 1.Open-jet wind tunnel at METU

At the end of project, rotor of all turbines will be attached to the same hub and nacelle, which has capability of torque, power and thrust measurement for different tip speed ratio (TSR) conditions. Maximum diameter of turbine should not exceed 100 cm and after construction, they will expose to wind with speed of 5 m/s on wind tunnel which is illustrated at Figure 1. At the

end of test, result related for Cp(TSP),Ct(TSP) and power- wind speed will be collected and can be compared. 

General Information: There are two categories for modern wind turbine, namely horizontal axis wind turbines

(HAWT) and vertical axis wind turbine (VAWT). As it was mentioned before, for this project we consider HAWT which is most common used wind turbine. HAWT also divide into two category; upwind and downwind. For upwind HAWT, wind blows to blades which are mounted ahead of tower, however for downwind HAWT blades are mounted behind the tower of wind turbine. For this project, upwind HAWT will be the case. Table 1.Horizontal Axis Wind Turbine VS Vertical Axis Wind Turbine

Basically HAWT consist of four main components; 1) Blades 2) Hub 3) Nacelle 4) Tower (Fig.2).

For this project we only try to design and construct blades which are the most important component of wind turbine. As mentioned before, Hub and Nacelle will be same for all turbine bales in this project and they have capability of adjusting torque/thrust for different tip twist. Figure 2.Main Wind Turbine Components

HAWTs come in different shapes and designs, their blades number is different, it range from 1 blade up 12 or more blades dependent on the design conditions and customer choice. They also range in weight, height and size. A short and simple definition for HAWT mechanism is as follow; wind turn in bales of wind turbine and bales turn a shaft which is connected to generator and finally generator produce electricity. Fig.3 shows inside a HAWT and helps to understand this mechanism.

Figure 3.Components and Parts inside HAWT

Figure 4.HAWT mechanism

2. Project Planning: Basically task to be done for this project is divided to four main topics including: Aerodynamics, Modeling and Calculations, Structure and Production. All parts of the project works togather and feedbacks of all steps must be done. Figure 5.Tasks and Person responsible for each task AERODYNAMICS & DESIGN ÇAĞLA CEREN CEYHAN ÇAĞRI KÖKSAL MİSAGH HAJİ AMİRİ

CAD DRAWİNG& PRODUCTİON

CODES & CALCULATİONS

ÇAĞLA CEREN CEYHAN

SEMİH BAYIR

SEMİH BAYIR

OĞUZHAN KALMAZ

ÇAĞRI KÖKSAL

There is also a time schedule which shows start date for each task and how long will it take to be done. Table 2.Gantt chart of Project

18.Eyl Determine Application literature research Select Topology Competitor Study Estimation of Primary loads Tentative Design Performance Prediction Evaluate Design Estimate Cost Refine Design Build Prototype Test Prototype

08.Eki

28.Eki

17.Kas

07.Ara

27.Ara

16.Oca

05.Şub

3. Theory Following theory is same for with and without wake rotation cases. An HAWT rotor includes one or more blades in off design the parameters; airfoil selection , chord length, twist along the blade are important to analyze off design performance. An ideal rotor analyse take into consideration of the given parameters as in follows. For momentum theory; In fluid dynamics, the momentum theory or disk actuator theory is a theory describing a mathematical model of an ideal actuator disk, such as a propeller or rotor. For an ideal rotor calculation also we get an extra assumption; actuator disk and frictions ignored then the final equations take into consideration of the figure 6. Figure 6.Analysis of blade geometry for HAWT

From axial momentum; 𝒅𝑻 = 𝝆𝑼𝟐 (𝟏 − 𝒂)𝟒𝒂𝝅𝒓𝒅𝒓

From angular momentum; 𝒅𝑸 = 𝟒𝒂′ (𝟏 − 𝒂)𝝆𝑼𝝅𝒓𝟑 𝜴𝒅𝒓 Blade element theory;

This theory involves that breaking a blade down into several small parts then determining the forces on each of these small blade elements. These forces are then integrated along the entire blade and over one rotor revolution in order to obtain the forces and moments produced by the entire propeller or rotor. One of the key difficulties lies in modeling the induced velocity on the rotor disk. Because of this the blade element theory is often combined with the momentum theory to provide additional relationships necessary to describe the induced velocity on the rotor. From BET; 𝟏 𝒅𝑭𝑵 = 𝑩 𝝆𝑼𝟐𝒓𝒆𝒍 (𝑪𝒍 𝒄𝒐𝒔𝝋 + 𝑪𝒅 𝒔𝒊𝒏𝝋)𝒄𝒅𝒓 𝟐 𝟏 𝒅𝑸 = 𝑩 𝝆𝑼𝟐𝒓𝒆𝒍 (𝑪𝒍 𝒔𝒊𝒏𝝋 − 𝑪𝒅 𝒄𝒐𝒔𝝋)𝒄𝒅𝒓 𝟐 Then combining the momentum theory and blade element theory where the thrust dT is the same force as the normal of d𝑭𝑵 . And the relative velocity is the free stream wind. Also Betz's law calculates the maximum power that can be extracted from the wind, independent of the design of a wind turbine in open flow. No wake rotation so a′=0, the axial induction factor a =1/3 take into consideration of Betz limit. With these assumptions momentum theory; 𝒅𝑻 = 𝝆𝑼𝟐 𝟒(𝒂)(𝟏 − 𝒂)𝝅𝒓𝒅𝒓 Then blade element theory with the assumption Cd=0 𝟏 𝒅𝑭𝑵 = 𝑩 ( ) 𝝆𝑼𝟐𝒓𝒆𝒍 (𝑪𝒍 )𝒄𝒐𝒔𝝋𝒄𝒅𝒓 𝟐 Where; 𝑼𝒓𝒆𝒍 = 𝑼(𝟏 − 𝒂)/𝒔𝒊𝒏𝝋 Based on the geometrical shape the 4th equation is; 𝑪𝒍 𝑩𝒄 = 𝒕𝒂𝒏𝝋𝒔𝒊𝒏𝝋 𝟒𝝅𝒓 To get the chord distribution define 𝝀𝒓 ; 𝝀𝒓 =λ(r/R) Then the chord with respect to r; 𝒄=

𝟖𝝅𝒓𝒔𝒊𝒏𝝋 𝟑𝑩𝑪𝒍 𝝀𝒓

Where; 𝝋 = 𝐭𝐚𝐧−𝟏 (𝟏 − 𝒂)/𝝀𝒓 Then we considered for a case with tip lose and wake rotation. BEM theory is used to solve a same problem but with wake rotation. Definition and details are as follow:

BEM theory is a compilation of both momentum theory and blade element theory. Momentum theory, which is useful in predicted ideal efficiency and flow velocity, is the determination of forces acting on the rotor to produce the motion of the fluid. This theory has no connection to the geometry of the blade, thus is not able to provide optimal blade parameters. Blade element theory determines the forces on the blade as a result of the motion of the fluid in terms of the blade geometry. By combining the two theories, BEM theory, also known as strip theory, relates rotor performance to rotor geometry. For momentum theory; The assumptions made in BEM theory is the aggregate of the assumptions made for momentum theory and blade element theory. The following assumption is made for momentum theory: Blades operate without frictional drag.

For an ideal rotor includes wake rotation but ignores drag (Cd=0) and tip losses (F=1) can be determined via the analysis developed for a general rotor. One can perform the optimization by taking the partial derivative of that part of the integral for CP which is a function of 𝟖 𝝀 𝑪𝑫 𝑪𝒑 = 𝟐 ∫ 𝑭 𝒔𝒊𝒏𝟐 𝝋(𝒄𝒐𝒔𝝋 − 𝝀𝒓 𝒔𝒊𝒏𝝋)(𝒔𝒊𝒏𝝋 + 𝝀𝒓 𝒄𝒐𝒔𝝋) [𝟏 − 𝒄𝒐𝒕𝝋] 𝝀𝒓 𝟐 𝒅𝝀𝒓 𝝀 𝝀𝒉 𝑪𝑳 the angle of the relative wind, j, and setting it equal to zero,

𝟎=

𝝏 [𝒔𝒊𝒏𝟐 𝝋(𝒄𝒐𝒔𝝋 − 𝝀𝒓 𝒔𝒊𝒏𝝋)(𝒔𝒊𝒏𝝋 + 𝝀𝒓 𝒄𝒐𝒔𝝋)] 𝝏𝝋

Then respectively; 𝝀𝒓 = 𝒔𝒊𝒏𝝋(𝟐𝒄𝒐𝒔𝝋 − 𝟏)/[(𝟏 − 𝒄𝒐𝒔𝝋)(𝟐𝒄𝒐𝒔𝝋 + 𝟏)]

𝝋= 𝒄=

𝟐 𝟏 𝐭𝐚𝐧−𝟏 𝟑 𝝀𝒓

𝟖𝝅𝒓 (𝟏 − 𝒄𝒐𝒔𝝋) 𝑩𝑪𝒍

Induction factor can be calculated 𝒂=

𝟏 𝟒𝒔𝒊𝒏𝟐 𝝋 𝟏+ ′ 𝝈 𝑪𝒍𝒄𝒐𝒔𝝋

𝒂′ =

𝟏 − 𝟑𝒂 𝟒𝒂 − 𝟏

These results can be compared with the result for an ideal blade without wake rotation for which has; 𝟐 𝝋 = 𝐭𝐚𝐧−𝟏 𝟑𝝀𝒓 𝒄=

𝟖𝝅𝒓 𝒔𝒊𝒏𝝋 ( ) 𝑩𝑪𝒍 𝟑𝝀𝒓

Do not regarding that the optimized value of j and c includes wake rotation, therefore could be significantly different from without wake rotation. But selecting a value as before at Cd/Cl minimum or vice versa Cl/Cd maximum. Solidity is the ratio of the planform area of the blades to the swept area, thus: 𝑹

𝟏 𝝈= ∫ 𝒄𝒅𝒓 𝝅𝑹𝟐 𝒓𝒉

When the modeling has a set of N number of blade sections of equal span, the solidity can be calculated from: 𝑵

𝑩 𝒄𝒊 𝝈≅ (∑ ) 𝑵𝝅 𝑹 𝒊=𝟏

The blade shapes for three sample optimum rotors, assuming wake rotation, are given in table. Table 2 .Non-dimensionalized chord distribution for different tip speed ratio

For an ideal rotor design with wake rotation 2 methods are conserning to calculate rotor performance which leads to blade design. Method 1 is solving for cl and α. The second one is more 𝟐

𝟏

𝝋𝒊,𝟏 = 𝟑 𝐭𝐚𝐧−𝟏 𝝀

𝒂𝒊,𝟏 =

Equation (*)

𝒓,𝒊

𝟏 𝟒𝒔𝒊𝒏𝟐 𝝋𝒊,𝟏 𝟏 + 𝝈′ 𝒊,𝒅𝒆𝒔𝒊𝒈𝒏 𝑪𝒍,𝒅𝒆𝒔𝒊𝒈𝒏 𝒄𝒐𝒔𝝋𝒊,𝟏

𝒂′ 𝒊,𝟏 =

𝟏 − 𝟑𝒂𝒊,𝟏 𝟒𝒂𝒊,𝟏 − 𝟏

To separate the number of iteration j number is used. 𝒕𝒂𝒏𝝋𝒊,𝒋 =

𝑼(𝟏−𝒂𝒊,𝒋 ) Ω𝒓(𝟏+𝒂′

𝒊,𝒋

= )

𝟏−𝒂𝒊,𝒋 (𝟏+𝒂′𝒊,𝒋 )𝝀𝒓,𝒊

Equation (**)

Then rearrange the equation (**) and equate the equation (*); 𝟐 𝟑

𝟏

𝐭𝐚𝐧−𝟏 𝝀

𝒓,𝒊

= 𝐭𝐚𝐧−𝟏

𝟏−𝒂𝒊,𝒋 𝟏−𝟑𝒂𝒊,𝟏 (𝟏+ )𝝀 𝟒𝒂𝒊,𝟏 −𝟏 𝒓,𝒊

=𝝋𝒊,𝟏

For each iteration of a and a’ the 𝒊𝒕𝒉 segment of blade are calculated.

𝑭𝒊,𝒋

𝑩 𝒓 ( 𝟐 ) [𝟏 − ( 𝑹𝒊 )] 𝟐 = 𝒄𝒐𝒔−𝟏 [ 𝒆𝒙𝒑 (− { 𝒓 }) ] 𝝅 ( 𝑹𝒊 ) 𝒔𝒊𝒏𝝋𝒊,𝒋 𝟖𝝅𝒓𝒊 𝒄𝒊 = (𝟏 − 𝒄𝒐𝒔𝝋𝒊 ) 𝑩𝑪𝒍

Because the cl values for each segment is depending the chord distrubution assumption is applicable. Other equations taking into consideration of these method as follows; ∝𝒊,𝒋 = 𝝋𝒊,𝒋 − 𝜽𝒑,𝒊

𝒂𝒊,𝒋+𝟏 =

𝒂𝒊,𝒋 = (

𝟏 𝟒𝑭𝒊,𝒋 𝒔𝒊𝒏𝟐 (𝝋𝒊,𝒋 ) [𝟏 + ] 𝝈′𝒊 𝑪𝒍,𝒊,𝒋 𝒄𝒐𝒔𝝋𝒊,𝒋

𝟏 ) [𝟎. 𝟏𝟒𝟑 + √𝟎. 𝟎𝟐𝟎𝟑 − 𝟎. 𝟔𝟒𝟐𝟕(𝟎. 𝟖𝟖𝟗 − 𝑪𝑻𝒓,𝒊,𝒋 )] 𝑭𝒊,𝒋

𝒂′𝒊,𝒋+𝟏 =

𝟏 𝟒𝑭𝒊,𝒋 𝒄𝒐𝒔𝝋𝒊,𝒋 −𝟏 𝝈′𝑪𝒍,𝒊,𝒋

∆𝝀𝒓 = 𝝀𝒓𝒊 − 𝝀𝒓(𝒊−𝟏) = 𝝀/𝑵 Corresponding power coefficient 𝟖

𝟐 𝑪𝒑 = 𝝀𝑵 ∑𝑵 𝒊=𝒌 𝑭𝒊. 𝒔𝒊𝒏 𝝋𝒊(𝐜𝐨𝐬 𝝋𝒊 − 𝝀𝒓𝒊 . 𝐬𝐢𝐧 𝝋𝒊)(𝐬𝐢𝐧 𝝋, − 𝝀𝒓𝒊 . 𝒄𝒐𝒔𝝋𝒊)(𝟏 −

𝑪𝒅 𝑪𝒍

𝐜𝐨𝐭 𝝋𝒊)𝝀𝟐𝒓𝒊 (eqn

****)

4. Current Status: Based on low Reynolds number and higher maximum Cl/Cd value datas corresponding airfoil type selection was completed. Then relatively a fortan code compiled. This code calculates for different tip speed ratios, non dimensionalized chord and twist distrubitons. These airfoils are selected dependingly the competitor research. For each case twist and chord distributions are in tables as follows:  For NASA/LANGLEY LS(1)-0413 (GA(W)-2) AIRFOIL (ls413-il) For Re# 50000, α=6 , Cl/Cd=35.9 at which Cl= 0.9343 Cd=0.02602 tip speed ratio 4 CHORD ϴ 0,175158 0,81088 0,305041 0,582198 0,300327 0,418879 0,264499 0,30878 0,22839 0,233346 0,19813 0,179699 0,173743 0,140063 0,154118 0,109781 0,138169 8,60E-02

tip speed ratio 4.5 CHORD ϴ 0,169524 0,794935 0,27538 0,546645 0,257924 0,379709 0,220551 0,272415 0,187196 0,201078 0,160708 0,15127 0,139989 0,114896 0,123623 8,73E-02 0,110483 6,58E-02

tip speed ratio 5 CHORD ϴ 0,16402 0,779159 0,248927 0,513477 0,222997 0,345108 0,186092 0,241378 0,155824 0,174096 0,132711 0,127794 0,115023 9,43E-02 0,101238 6,90E-02 9,03E-02 4,93E-02

tip speed ratio 5.5 CHORD ϴ 0,15865 0,763567 0,225392 0,482611 0,194093 0,314478 0,158732 0,214687 0,131488 0,15127 0,11129 0,108126 9,61E-02 7,71E-02 8,44E-02 5,38E-02 7,51E-02 3,58E-02

tip speed ratio 6 CHORD ϴ 0,148324 0,73299 0,185913 0,427317 0,149897 0,26305 0,118855 0,171373 9,69E-02 0,114896 8,13E-02 7,71E-02 6,98E-02 5,02E-02 6,11E-02 3,02E-02 5,42E-02 1,47E-02

0,125037 6,68E-02 tip speed ratio 6.5 CHORD ϴ 0,143373 0,718028 0,169418 0,402622 0,132923 0,241378 0,104152 0,153629 8,44E-02 0,100212 7,06E-02 6,47E-02 6,05E-02 3,95E-02 5,29E-02 2,08E-02 4,69E-02 6,29E-03 4,21E-02 -5,21E-03

9,98E-02 4,85E-02 tip speed ratio 7 CHORD ϴ 0,138565 0,703297 0,154754 0,379709 0,118525 0,221918 9,19E-02 0,137933 7,42E-02 8,73E-02 6,19E-02 5,38E-02 5,29E-02 3,02E-02 4,62E-02 1,26E-02 4,10E-02 -9,90E-04 3,68E-02 -1,18E-02

8,14E-02 3,36E-02 tip speed ratio 7.5 CHORD ϴ 0,138565 0,703297 0,154754 0,379709 0,118525 0,221918 9,19E-02 0,137933 7,42E-02 8,73E-02 6,19E-02 5,38E-02 5,29E-02 3,02E-02 4,62E-02 1,26E-02 4,10E-02 -9,90E-04 3,68E-02 -1,18E-02

6,76E-02 2,13E-02 4,87E-02 2,31E-03 tip speed ratio 8 tip speed ratio 8.5 CHORD ϴ CHORD ϴ 0,133902 0,688807 0,129382 0,674564 0,141702 0,358439 0,130065 0,338682 0,106237 0,204379 9,57E-02 0,188509 8,17E-02 0,123963 7,30E-02 0,11146 6,56E-02 7,59E-02 5,85E-02 6,58E-02 5,46E-02 4,43E-02 4,86E-02 3,58E-02 4,67E-02 2,19E-02 4,15E-02 1,47E-02 4,07E-02 5,38E-03 3,61E-02 -9,90E-04 3,61E-02 -7,38E-03 3,20E-02 -1,30E-02 3,24E-02 -1,75E-02 2,87E-02 -2,26E-02

tip speed ratio 9 tip speed ratio 9.5 tip speed ratio 10 CHORD ϴ CHORD ϴ CHORD ϴ 0,125005 0,660575 0,120772 0,646846 0,11668 0,633379 0,119671 0,320313 0,110368 0,303215 0,102024 0,287282 8,66E-02 0,174096 7,87E-02 0,160962 7,17E-02 0,148951 6,57E-02 0,100212 5,93E-02 9,00E-02 5,39E-02 8,08E-02 5,24E-02 5,67E-02 4,73E-02 4,85E-02 4,28E-02 4,11E-02 4,35E-02 2,82E-02 3,91E-02 2,13E-02 3,54E-02 1,52E-02 3,71E-02 8,15E-03 3,34E-02 2,31E-03 3,02E-02 -2,95E-03 3,23E-02 -6,67E-03 2,90E-02 -1,18E-02 2,62E-02 -1,64E-02 2,86E-02 -1,81E-02 2,57E-02 -2,26E-02 2,32E-02 -2,66E-02 2,56E-02 -2,71E-02 2,30E-02 -3,12E-02 2,08E-02 -3,48E-02

0,9

Segment vs Twist angle

0,8

ts 4

0,7

ts 4.5

0,6

ts 5

r/R

0,5

ts 5.5

0,4

ts 6

0,3

ts 7

0,2

ts 8

0,1 0 0E+00 -0,1

ts 9 2E-01

4E-01 6E-01 Twist angle

8E-01

1E+00

ts 10

0,35

Segment vs Chord lenght

0,3

ts 4 ts 4.5

r/R

0,25

ts 5

0,2

ts 5.5 0,15

ts 6

0,1

ts 7

0,05

ts 8

0 0E+00

ts 9

2E-01

4E-01

6E-01

8E-01

1E+00

ts 10

Chord lenght

 For S1223 (s1223-il)

For Re# 50000, α=3.25 , Cl/Cd=42.3 at which Cl= 1.4206 Cd=0.03358 tip speed ratio 4 CHORD ϴ 0,115198 0,858877 0,200619 0,630195 0,197519 0,466876 0,173956 0,356776 0,150207 0,281343 0,130306 0,227695 0,114267 0,188059 0,10136 0,157777 9,09E-02 0,133978 8,22E-02 0,114826

tip speed ratio 4.5 CHORD ϴ 0,111493 0,842931 0,181112 0,594641 0,169631 0,427705 0,145052 0,320411 0,123115 0,249075 0,105694 0,199267 9,21E-02 0,162892 8,13E-02 0,135314 7,27E-02 0,113753 6,56E-02 9,65E-02

tip speed ratio 5 CHORD ϴ 0,107873 0,827155 0,163714 0,561474 0,14666 0,393104 0,122389 0,289374 0,102483 0,222093 8,73E-02 0,175791 7,56E-02 0,142276 6,66E-02 0,117012 5,94E-02 9,73E-02 5,35E-02 8,16E-02

tip speed ratio 5.5 CHORD ϴ 0,104341 0,811563 0,148236 0,530608 0,127651 0,362474 0,104395 0,262684 8,65E-02 0,199267 7,32E-02 0,156123 6,32E-02 0,12511 5,55E-02 0,101834 4,94E-02 8,38E-02 4,45E-02 6,93E-02

tip speed ratio 6 CHORD ϴ 0,100899 0,79617 0,134484 0,501931 0,111832 0,335279 8,99E-02 0,239556 7,39E-02 0,179747 6,22E-02 0,139433 5,35E-02 0,110612 4,69E-02 8,91E-02 4,17E-02 7,24E-02 3,75E-02 5,91E-02

tip speed ratio 6.5 CHORD ϴ 9,75E-02 0,780986 0,122271 0,475314 9,86E-02 0,311047 7,82E-02 0,219369 6,37E-02 0,162892 5,35E-02 0,12511 4,59E-02 9,82E-02 4,02E-02 7,82E-02 3,57E-02 6,26E-02 3,21E-02 5,03E-02

tip speed ratio 7 CHORD ϴ 9,43E-02 0,766024 0,111423 0,450619 8,74E-02 0,289374 6,85E-02 0,201626 5,55E-02 0,148208 4,64E-02 0,112693 3,98E-02 8,75E-02 3,48E-02 6,88E-02 3,09E-02 5,43E-02 2,77E-02 4,28E-02

tip speed ratio 7.5 CHORD ϴ 9,11E-02 0,751294 0,101779 0,427705 7,80E-02 0,269915 6,05E-02 0,185929 4,88E-02 0,135314 4,07E-02 0,101834 3,48E-02 7,82E-02 3,04E-02 6,06E-02 2,69E-02 4,70E-02 2,42E-02 3,62E-02

tip speed ratio 8 CHORD ϴ 8,81E-02 0,736804 9,32E-02 0,406436 6,99E-02 0,252375 5,37E-02 0,171959 4,32E-02 0,123908 3,59E-02 9,23E-02 3,07E-02 6,99E-02 2,68E-02 5,34E-02 2,37E-02 4,06E-02 2,13E-02 3,05E-02

tip speed ratio 8.5 CHORD ϴ 8,51E-02 0,72256 8,55E-02 0,386679 6,29E-02 0,236505 4,80E-02 0,159456 3,85E-02 0,113753 3,20E-02 8,38E-02 2,73E-02 6,26E-02 2,38E-02 4,70E-02 2,11E-02 3,50E-02 1,89E-02 2,54E-02

tip speed ratio 9 CHORD ϴ 8,22E-02 0,708572 7,87E-02 0,368309 5,69E-02 0,222093 4,32E-02 0,148208 3,45E-02 0,104658 2,86E-02 7,62E-02 2,44E-02 5,61E-02 2,12E-02 4,13E-02 1,88E-02 2,99E-02 1,69E-02 2,09E-02 1

tip speed ratio 10 CHORD ϴ 7,67E-02 0,681376 6,71E-02 0,335279 4,72E-02 0,196948 3,54E-02 0,12881 2,81E-02 8,91E-02 2,33E-02 6,32E-02 1,98E-02 4,50E-02 1,73E-02 3,16E-02 1,53E-02 2,13E-02 1,37E-02 1,32E-02

Segment vs Twist angle

0,8 r/R

tip speed ratio 9.5 CHORD ϴ 7,94E-02 0,694842 7,26E-02 0,351212 5,17E-02 0,208958 3,90E-02 0,138041 3,11E-02 9,65E-02 2,57E-02 6,93E-02 2,19E-02 5,03E-02 1,91E-02 3,62E-02 1,69E-02 2,54E-02 1,52E-02 1,68E-02

ts 4 ts 4.5

0,6

ts 5

0,4

ts 5.5 ts 6

0,2 0 0E+00

ts 7 2E-01

4E-01

6E-01

8E-01

1E+00

ts 9

Twist angle

0,25

ts 8

Segment vs Chord lenght

ts 4

0,2

ts 4.5 ts 5

r/R

0,15

ts 5.5 0,1

ts 6 ts 7

0,05 0 0E+00

ts 8 2E-01

4E-01

6E-01

8E-01

Chord lenght

 For MA409 (smoothed) (ma409sm-il) For Re# 50000, α=5.25 , Cl/Cd=43.6 at which Cl= 0.9169 Cd=0.02105

1E+00

ts 9 ts 10

tip speed ratio 4 CHORD ϴ 0,178482 0,82397 0,31083 0,595288 0,306027 0,431969 0,269518 0,32187 0,232724 0,246436 0,20189 0,192789 0,17704 0,153153 0,157043 0,122871 0,140791 9,91E-02 0,12741 7,99E-02

tip speed ratio 6.5 CHORD ϴ 0,151139 0,74608 0,189441 0,440407 0,152742 0,27614 0,121111 0,184463 9,88E-02 0,127986 8,28E-02 9,02E-02 7,11E-02 6,33E-02 6,22E-02 4,33E-02 5,53E-02 2,77E-02 4,97E-02 1,54E-02

tip speed ratio 4.5 CHORD ϴ 0,172741 0,808025 0,280605 0,559735 0,262818 0,392798 0,224736 0,285505 0,190749 0,214168 0,163758 0,16436 0,142646 0,127986 0,125969 0,100407 0,11258 7,88E-02 0,10165 6,16E-02

tip speed ratio 5 CHORD ϴ 0,167133 0,792249 0,253651 0,526567 0,227228 0,358197 0,189623 0,254468 0,158781 0,187186 0,135229 0,140884 0,117206 0,10737 0,10316 8,21E-02 9,20E-02 6,24E-02 8,29E-02 4,67E-02

tip speed ratio 5.5 CHORD ϴ 0,16166 0,776657 0,229669 0,495701 0,197777 0,327568 0,161744 0,227777 0,133984 0,16436 0,113402 0,121216 9,79E-02 9,02E-02 8,60E-02 6,69E-02 7,65E-02 4,89E-02 6,89E-02 3,44E-02

tip speed ratio 7 CHORD ϴ 0,146094 0,731118 0,172633 0,415712 0,135445 0,254468 0,106128 0,166719 8,60E-02 0,113302 7,19E-02 7,78E-02 6,17E-02 5,26E-02 5,39E-02 3,39E-02 4,78E-02 1,94E-02 4,29E-02 7,88E-03

tip speed ratio 7.5 CHORD ϴ 0,141195 0,716387 0,157691 0,392798 0,120775 0,235008 9,37E-02 0,151023 7,56E-02 0,100407 6,30E-02 6,69E-02 5,39E-02 4,33E-02 4,71E-02 2,57E-02 4,17E-02 1,21E-02 3,75E-02 1,33E-03

tip speed ratio 8 CHORD ϴ 0,136443 0,701897 0,144391 0,371529 0,108253 0,217469 8,33E-02 0,137053 6,69E-02 8,90E-02 5,57E-02 5,74E-02 4,76E-02 3,50E-02 4,15E-02 1,85E-02 3,68E-02 5,71E-03 3,30E-02 -4,41E-03

tip speed ratio 9 CHORD ϴ 0,127378 0,673665 0,121942 0,333403 8,82E-02 0,187186 6,69E-02 0,113302 5,34E-02 6,98E-02 4,43E-02 4,13E-02 3,78E-02 2,12E-02 3,29E-02 6,42E-03 2,91E-02 -4,98E-03 2,61E-02 -1,40E-02

tip speed ratio 6 CHORD ϴ 0,156328 0,761263 0,208362 0,467024 0,173266 0,300372 0,139334 0,20465 0,114422 0,144841 9,64E-02 0,104527 8,30E-02 7,57E-02 7,27E-02 5,41E-02 6,46E-02 3,75E-02 5,81E-02 2,42E-02

tip speed ratio 9.5 tip speed ratio 10 CHORD ϴ CHORD ϴ 0,123064 0,659936 0,118894 0,646469 0,112463 0,316305 0,10396 0,300372 8,01E-02 0,174052 7,31E-02 0,162041 6,05E-02 0,103135 5,49E-02 9,39E-02 4,81E-02 6,16E-02 4,36E-02 5,41E-02 3,99E-02 3,44E-02 3,61E-02 2,83E-02 3,40E-02 1,54E-02 3,07E-02 1,01E-02 2,96E-02 1,33E-03 2,67E-02 -3,26E-03 2,62E-02 -9,49E-03 2,37E-02 -1,36E-02 2,35E-02 -1,81E-02 2,12E-02 -2,17E-02

tip speed ratio 8.5 CHORD ϴ 0,131837 0,687654 0,132533 0,351772 9,75E-02 0,201599 7,44E-02 0,12455 5,96E-02 7,88E-02 4,95E-02 4,89E-02 4,23E-02 2,77E-02 3,68E-02 1,21E-02 3,26E-02 5,99E-05 2,93E-02 -9,49E-03

r/R

0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 -0,10E+00

0,35 0,3

Segment vs Twist angle

ts 4 ts 4.5 ts 5 ts 4.5 ts 6 ts 7 ts 8

2E-01

4E-01 6E-01 Twist angle

8E-01

1E+00

Segment vs Chord lenght

ts 10

ts 4 ts 4.5

0,25

r/R

ts 9

ts 5

0,2

ts 5.5

0,15

ts 6

0,1

ts 7

0,05

ts 8

0 0E+00

ts 9 2E-01

4E-01

6E-01

8E-01

1E+00

ts 10

Chord lenght

 For GM15 (smoothed) (gm15sm-il)

For Re# 50000, α=5.75 , Cl/Cd=46.1 at which Cl= 1.1025 Cd=0.02393 tip speed ratio 4 CHORD ϴ 0,148435 0,815244 0,258503 0,586561 0,254509 0,423242 0,224146 0,313143 0,193546 0,237709 0,167903 0,184062 0,147236 0,144426 0,130605 0,114144 0,11709 9,03E-02 0,105961 7,12E-02

tip speed ratio 4.5 CHORD ϴ 0,143661 0,799298 0,233367 0,551008 0,218574 0,384072 0,186903 0,276778 0,158637 0,205442 0,13619 0,155633 0,118632 0,119259 0,104762 9,17E-02 9,36E-02 7,01E-02 8,45E-02 5,28E-02

tip speed ratio 5 CHORD ϴ 0,138997 0,783522 0,21095 0,51784 0,188976 0,349471 0,157701 0,245741 0,132051 0,17846 0,112464 0,132158 9,75E-02 9,86E-02 8,58E-02 7,34E-02 7,65E-02 5,37E-02 6,90E-02 3,80E-02

tip speed ratio 5.5 CHORD ϴ 0,134446 0,76793 0,191006 0,486974 0,164482 0,318841 0,134515 0,21905 0,111428 0,155633 9,43E-02 0,11249 8,14E-02 8,15E-02 7,15E-02 5,82E-02 6,36E-02 4,01E-02 5,73E-02 2,57E-02

tip speed ratio 6 CHORD ϴ 0,130011 0,752537 0,173286 0,458298 0,144098 0,291645 0,115878 0,195923 9,52E-02 0,136114 8,01E-02 9,58E-02 6,90E-02 6,70E-02 6,04E-02 4,54E-02 5,37E-02 2,87E-02 4,83E-02 1,54E-02

tip speed ratio 6.5 CHORD ϴ 0,125695 0,737353 0,157549 0,431681 0,127029 0,267414 0,100722 0,175736 8,21E-02 0,119259 6,89E-02 8,15E-02 5,92E-02 5,46E-02 5,18E-02 3,45E-02 4,60E-02 1,90E-02 4,13E-02 6,68E-03

tip speed ratio 7 CHORD ϴ 0,1215 0,722391 0,143571 0,406985 0,112644 0,245741 8,83E-02 0,157993 7,16E-02 0,104575 5,98E-02 6,91E-02 5,13E-02 4,39E-02 4,48E-02 2,51E-02 3,98E-02 1,07E-02 3,57E-02 -8,51E-04

r/R

tip speed ratio 9 CHORD ϴ 0,105934 0,101414 7,34E-02 5,57E-02 4,44E-02 3,68E-02 3,14E-02 2,74E-02 2,42E-02 2,17E-02

0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 0,0E+00 -0,1

0,664939 0,324676 0,17846 0,104575 6,10E-02 3,25E-02 1,25E-02 -2,30E-03 -1,37E-02 -2,27E-02

tip speed ratio 7.5 CHORD ϴ 0,117425 0,707661 0,131145 0,384072 0,100443 0,226282 7,79E-02 0,142296 6,29E-02 9,17E-02 5,24E-02 5,82E-02 4,49E-02 3,45E-02 3,92E-02 1,69E-02 3,47E-02 3,37E-03 3,12E-02 -7,40E-03

tip speed ratio 9.5 CHORD ϴ 0,102347 9,35E-02 6,67E-02 5,03E-02 4,00E-02 3,32E-02 2,83E-02 2,46E-02 2,18E-02 1,95E-02

tip speed ratio 8 CHORD ϴ 0,113473 0,69317 0,120084 0,362802 9,00E-02 0,208742 6,92E-02 0,128326 5,56E-02 8,03E-02 4,63E-02 4,86E-02 3,96E-02 2,63E-02 3,45E-02 9,74E-03 3,06E-02 -3,01E-03 2,74E-02 -1,31E-02

0,651209 0,307579 0,165325 9,44E-02 5,28E-02 2,57E-02 6,68E-03 -7,40E-03 -1,82E-02 -2,68E-02

tip speed ratio 8.5 CHORD ϴ 0,109643 0,678927 0,110222 0,343045 8,11E-02 0,192872 6,19E-02 0,115823 4,96E-02 7,01E-02 4,12E-02 4,01E-02 3,51E-02 1,90E-02 3,06E-02 3,37E-03 2,71E-02 -8,67E-03 2,43E-02 -1,82E-02

tip speed ratio 10 CHORD ϴ 9,89E-02 8,65E-02 6,08E-02 4,56E-02 3,63E-02 3,00E-02 2,56E-02 2,22E-02 1,97E-02 1,76E-02

Segment vs Twist angle

0,637743 0,291645 0,153314 8,52E-02 4,54E-02 1,95E-02 1,41E-03 -1,20E-02 -2,23E-02 -3,04E-02

ts 4 ts 4.5 ts 5 ts 5.5 ts 6 ts 7 ts 8

2,0E-01

4,0E-01 6,0E-01 Twist angle

8,0E-01

1,0E+00

ts 9 ts 10

0,3

Segment vs Chord lenght

ts 4

0,25

ts 4.5

r/R

0,2

ts 5

ts 5.5

0,15

ts 6

0,1

ts 7 0,05

ts 8 ts 9

0 0,0E+00

2,0E-01

4,0E-01

6,0E-01

8,0E-01

1,0E+00

ts 10

Chord lenght

 For FX 60-100 AIRFOIL (fx60100-il)

For Re# 50000, α=5.75 , Cl/Cd=42.6 at which Cl= 1.0219 Cd=0.0240 tip speed ratio 4 CHORD ϴ 0,160143 0,815244 0,278892 0,586561 0,274582 0,423242 0,241825 0,313143 0,208812 0,237709 0,181146 0,184062 0,158849 0,144426 0,140907 0,114144 0,126325 9,03E-02 0,114318 7,12E-02

tip speed ratio 4.5 CHORD ϴ 0,154992 0,799298 0,251773 0,551008 0,235814 0,384072 0,201645 0,276778 0,171149 0,205442 0,146932 0,155633 0,127989 0,119259 0,113025 9,17E-02 0,101012 7,01E-02 9,12E-02 5,28E-02

tip speed ratio 6.5 CHORD ϴ 0.13560931 0.73735327 0.16997564 0.43168080 0.13704778 0.26741356 0.10866668 0.17573594 8,86E+06 0.11925893 7,43E+06 8,15E+06 6,38E+06 5,46E+06 5,58E+06 3,45E+06 4,96E+06 1,90E+06 4,46E+06 6,68E+05

tip speed ratio 5 CHORD ϴ 0,14996 0,783522 0,227588 0,51784 0,203881 0,349471 0,17014 0,245741 0,142467 0,17846 0,121334 0,132158 0,105163 9,86E-02 9,26E-02 7,34E-02 8,25E-02 5,37E-02 7,44E-02 3,80E-02

tip speed ratio 7 CHORD ϴ 0,131083 0,722391 0,154895 0,406985 0,121528 0,245741 9,52E-02 0,157993 7,72E-02 0,104575 6,46E-02 6,91E-02 5,53E-02 4,39E-02 4,83E-02 2,51E-02 4,29E-02 1,07E-02 3,85E-02 -8,51E-04

tip speed ratio 5.5 CHORD ϴ 0,14505 0,76793 0,206071 0,486974 0,177455 0,318841 0,145125 0,21905 0,120217 0,155633 0,10175 0,11249 8,78E-02 8,15E-02 7,71E-02 5,82E-02 6,87E-02 4,01E-02 6,18E-02 2,57E-02

tip speed ratio 7.5 CHORD ϴ 0,126687 0,707661 0,141488 0,384072 0,108365 0,226282 8,41E-02 0,142296 6,78E-02 9,17E-02 5,66E-02 5,82E-02 4,84E-02 3,45E-02 4,22E-02 1,69E-02 3,75E-02 3,37E-03 3,36E-02 -7,40E-03

tip speed ratio 6 CHORD ϴ 0.14026567 0.75253671 0.18695314 0.45829773 0.15546319 0.29164532 0.12501787 0.19592308 0.10266483 0.13611405 8,65E+06 9,58E+06 7,44E+06 6,70E+06 6,52E+06 4,54E+06 5,80E+06 2,87E+06 5,21E+06 1,54E+06

tip speed ratio 8 CHORD ϴ 0,122423 0,69317 0,129555 0,362802 9,71E-02 0,208742 7,47E-02 0,128326 6,00E-02 8,03E-02 4,99E-02 4,86E-02 4,27E-02 2,63E-02 3,72E-02 9,74E-03 3,30E-02 -3,01E-03 2,96E-02 -1,31E-02

tip speed ratio 8.5 CHORD ϴ 0,118291 0,678927 0,118916 0,343045 8,75E-02 0,192872 6,68E-02 0,115823 5,35E-02 7,01E-02 4,44E-02 4,01E-02 3,79E-02 1,90E-02 3,30E-02 3,37E-03 2,93E-02 -8,67E-03 2,63E-02 -1,82E-02

tip speed ratio 9 CHORD ϴ 0,11429 0,109413 7,91E-02 6,00E-02 4,79E-02 3,98E-02 3,39E-02 2,95E-02 2,61E-02 2,34E-02

0,664939 0,324676 0,17846 0,104575 6,10E-02 3,25E-02 1,25E-02 -2,30E-03 -1,37E-02 -2,27E-02

1

tip speed ratio 9.5 CHORD ϴ 0,110419 0,100907 7,19E-02 5,42E-02 4,32E-02 3,58E-02 3,05E-02 2,65E-02 2,35E-02 2,11E-02

0,651209 0,307579 0,165325 9,44E-02 5,28E-02 2,57E-02 6,68E-03 -7,40E-03 -1,82E-02 -2,68E-02

tip speed ratio 10 CHORD ϴ 0,106677 9,33E-02 6,56E-02 4,92E-02 3,91E-02 3,24E-02 2,76E-02 2,40E-02 2,12E-02 1,90E-02

Segment vs Twist angle

0,637743 0,291645 0,153314 8,52E-02 4,54E-02 1,95E-02 1,41E-03 -1,20E-02 -2,23E-02 -3,04E-02 ts 4

0,8

r/R

ts 4.5 0,6

ts 5

0,4

ts 7 ts 8

0,2

ts 9

0 0,0E+00 -0,2

ts 10 2,0E-01

4,0E-01 6,0E-01 Twist angle

8,0E-01

1,0E+00

Segment vs Chord lenght

r/R

0,4

ts4

0,3

ts 4.5

0,2

ts 5

0,1

ts 5.5

0 0,0E+00

ts 6

2,0E-01

4,0E-01

6,0E-01

Chord lenght

8,0E-01

1,0E+00

ts 7 ts 8

5. DECISION and RESULTS The decision for the small HAWT blade off design airfoil selection is GM(15) smoothed. Because ın the experiment the Re# is about 10000-15000 so for lower Reynolds number maximum Cl/Cd value is observed for this airfoil. And then we started to analize all details. Via using same fortran code different tip speed ratios Cp values are calculated by using eq. **** are as follows TS RATIO 4 4,0999999 4,1999998 4,2999997 4,3999996 4,4999995 4,5999994 4,6999993 4,7999992 4,8999991 4,999999 5,099999 5,1999989 5,2999988 5,3999987 5,4999986 5,5999985 5,6999984 5,7999983 5,8999982 5,9999981

Cp 0,41817912 0,42002365 0,42175043 0,42336556 0,42487454 0,42628264 0,42759487 0,42881575 0,42994964 0,43100068 0,43197274 0,43286943 0,43369427 0,43445036 0,43514091 0,43576863 0,43633646 0,43684685 0,43730229 0,4377051 0,43805745

AR 5,7210398 5,9232855 6,1285086 6,3366857 6,5477939 6,7618146 6,978725 7,1985035 7,4211335 7,646594 7,8748655 8,1059313 8,3397713 8,5763712 8,815711 9,0577726 9,3025455 9,5500088 9,8001451 10,052946 10,308388

TS RATIO 6,099998 6,199998 6,299998 6,399998 6,499998 6,599998 6,699997 6,799997 6,899997 6,999997 7,099997 7,199997 7,299997 7,399997 7,499997 7,599997 7,699997 7,799996 7,899996 7,999996 8,099997

Cp 0,438361 0,438619 0,438832 0,439003 0,439132 0,439222 0,439274 0,43929 0,43927 0,439217 0,439131 0,439014 0,438867 0,438691 0,438486 0,438255 0,437998 0,437715 0,437408 0,437078 0,436724

AR 10,56647 10,82716 11,09046 11,35634 11,62481 11,89584 12,16941 12,44553 12,72418 13,00533 13,289 13,57516 13,8638 14,15491 14,44849 14,74452 15,043 15,34391 15,64724 15,953 16,26116

TS RATIO 8,199997 8,299997 8,399998 8,499998 8,599999 8,699999 8,799999 8,9 9 9,1 9,200001 9,300001 9,400002 9,500002 9,600002 9,700003 9,800003 9,900003 10

Cp 0,436349 0,435953 0,435536 0,435099 0,434643 0,434168 0,433676 0,433165 0,432638 0,432094 0,431535 0,43096 0,43037 0,429765 0,429146 0,428514 0,427868 0,427209 0,426538

AR 16,57173 16,8847 17,20005 17,51778 17,83789 18,16036 18,48519 18,81239 19,14193 19,47381 19,80804 20,1446 20,4835 20,82472 21,16826 21,51412 21,8623 22,21279 22,56559

Then selecting of the tip speed ratio is completed λ=6.8. The corresponding chord and twist distribution as in follows;

SEGMENT 0,0500 0,1500 0,2500 0,3500 0,4500 0,5500 0,6500 0,7500 0,8500 0,9500

Distance from root(mm) 21,4750 64,4250 107,3750 150,3250 193,2750 236,2250 279,1750 322,1250 365,0750 408,0250

CHORD mm 52,8987404 63,9805147 50,7284039 39,9280672 32,4398182 27,1598676 23,2949614 20,363779 18,0728304 16,236898

TWIST(°) 41,7313376 23,8718337 14,5603784 9,44373471 6,31484591 4,22970651 2,74882151 1,64581916 0,79373704 0,11631832

Then relatively q blade design as in follows total length is 429.5 mm and the injunction part which is not inludes in this report is 20,5 mm then total rotor radius is 450 mm. Just review part is not completed.

6. Appendix: C=================================================== ==================== C----------------------------------------------------------------------C BLADE SHAPE FOR 3-BLADED IDEAL ROTOR WITH WAKE ROTATION C AND TIP LOSS C----------------------------------------------------------------------C------------------------M. SEMIH BAYIR--------------------------------C=================================================== ==================== CHARACTER*17,X1,X2,X3,X4,X5,X6,X7,X8,X9 CHARACTER*30,NAME,NAME2 DIMENSION CPI(61),CNUM(61),ARI(61) 100 PRINT*,'AIRFOIL NAME :>' READ*,NAME C PRINT*,'TIP SPEED RATIO :>' C READ(*,*) CLAM CLAM=4. J=1 PRINT*,'LIFT COEFFICIENT :>' READ(*,*) CL

PRINT*,'DRAG COEFFICIENT :>' READ(*,*) CD PRINT*,'ANGLE OF ATTACK :>' READ(*,*) ALPHA 110 WRITE(NAME2,11)'TS=',CLAM 11 FORMAT(A3,F4.1) OPEN(1,FILE='RESULTS-'//TRIM(NAME)//'_'//TRIM(NAME2)//'.txt') X1='SEGMENT' X2='PHI' X3='LAMDA_R' X4='PHI_REF' X5='A' X6='LOSS_FACTOR' X7='CHORD' X8='TWIST' X9='C_THRUST' WRITE(1,*)X1,X7,X8 RR=10 PI=3.141592 CP=0. AREA=0. DO I=1,10 C--------------INITIALS------------------------------------------------R=REAL(I) SEG=(R-0.5)/RR SEG2=R/RR CLAMR=SEG*CLAM B=1/CLAMR PHIREF=(2.0/3.0)*(ATAN(B)) AREF=1/(1+(4*(SIN(PHIREF))**2/(4*COS(PHIREF)*(1-COS(PHIREF))))) APREF=(1-3*AREF)/(4*AREF-1) C----------------------------------------------------------------------10

C1=(1.0-AREF)/((1+APREF)*CLAMR) PHI=ATAN(C1)

F=2/PI*ACOS(EXP((-3/2*(1-SEG))/(SEG*SIN(PHI)))) CH=(8*PI*SEG/(3*CL))*(1-COS(PHI)) SIGMA=3*CH/(2*PI*SEG) CT=(SIGMA*(1-AREF)**2*(CL*COS(PHI)+CD*SIN(PHI)))/(SIN(PHI)**2) IF(CT.GT.0.AND.CT.LT.0.96) THEN ANEW=1/(1+(4*F*(SIN(PHI)**2))/(SIGMA*CL*COS(PHI))) ELSEIF(CT.GE.0.96.AND.CT.LE.1) THEN ANEW=(1/F)*(0.143+SQRT(0.0203-0.6427*(0.889-CT))) ENDIF APNEW=1/((4*F*COS(PHI))/(SIGMA*CL)-1) ERR1=AREF-ANEW ERR2=APREF-APNEW AREF=ANEW APREF=APNEW IF(ERR1.GT.0.001.OR.ERR2.GT.0.001) GOTO 10 TWIST=PHI-ALPHA*(PI/180) SF=SIN(PHI) CF=COS(PHI) TF=TAN(PHI) AREA=AREA+CH/RR CP=CP+(8/(CLAM*RR))*(F*SF**2*(CF-CLAMR*SF)*(SF+CLAMR*CF)* * (1-(CD/CL)/TF)*CLAMR**2) WRITE(1,*) SEG,CH,TWIST ENDDO AR=1/AREA CPI(J)=CP CNUM(J)=CLAM ARI(J)=AR IF (CLAM.LT.10) THEN CLAM=CLAM+0.1 J=J+1 GOTO 110 ENDIF

OPEN(3,FILE='Cp-'//TRIM(NAME)//'.txt') WRITE(3,30)'TS RATIO','POWER COEFFICIENT','AR' 30 FORMAT(3X,A8,4X,A17,5X,A2) DO J=1,61 WRITE(3,*)CNUM(J),CPI(J),ARI(J) ENDDO CLOSE(3) PRINT*,'' PRINT*,' DONE' PRINT*,'' GOTO 100 STOP END

7. References  

 

Manwell, J., & McGowan, J. (2009). Wind energy explained theory, design and application(pp. 120-145). Chichester: Wiley. 495-Wind. (n.d.). Retrieved November 12, 2014, from http://www.metuclass.edu.tr Airfoil database list (D). (n.d.). Retrieved December 22, 2014, from http://airfoiltools.com/search/list?page=d&no=1 UIUC Airfoil Data Site. (n.d.). Retrieved December 10, 2014, from http://mselig.ae.illinois.edu/ads/coord_database.html