Small horizontal axis wind turbines (HAWTs) are increasingly used as source of energy production. Based on this observation, the blade element momentum theory (BEMT) is applied all along the blade span to calculate the optimal turbine aerodynamic performances. The main objective is to optimize the HAWT blade profile for specific initial conditions. The effects of three geometric parameters (the blade tip radius, the number of blades, and curvature) and one dynamic parameter (the tip speed ratio (TSR)) are determined for an upstream air speed of 7 m/s. A new empirical relation for the chord distribution over the blade span is presented here; c(r)/R=c0+A[1+r/R]exp(Br/R), where c0 = 0.04 is the chord offset, A = 1/Z is an amplitude, and B = [(Z/5) + 2] is the decay constant. It takes into account both the effect of blade tip radius and the number of the blades.

References

References
1.
Guney
,
M. S.
,
2011
, “
Evaluation and Measures to Increase Performance Coefficient of Hydrokinetic Turbines
,”
Renewable Sustainable Energy Rev.
,
15
(
8
), pp.
3669
3675
.
2.
Singh
,
P. M.
, and
Choi
,
Y. D.
,
2014
, “
Shape Design and Numerical Analysis on a 1MW Tidal Current Turbine for the South-Western Coast of Korea
,”
Renewable Energy
,
68
, pp.
485
493
.
3.
Khan
,
M. J.
,
Bhuyan
,
G.
,
Iqbal
,
M. T.
, and
Quaicoe
,
J. E.
,
2009
, “
Hydrokinetic Energy Conversion Systems and Assessment of Horizontal and Vertical Axis Turbines for River and Tidal Applications: A Technology Status Review
,”
Appl. Energy
,
86
(
10
), pp.
1823
1835
.
4.
Lee
,
M. H.
,
Shiah
,
Y. C.
, and
Bai
,
C. J.
,
2016
, “
Experiments and Numerical Simulations of the Rotor-Blade Performance for a Small-Scale Horizontal Axis Wind Turbine
,”
J. Wind Eng. Ind. Aerodyn.
,
149
, pp.
17
29
.
5.
Liu
,
S.
, and
Janajreh
,
I.
,
2012
, “
Development and Application of an Improved Blade Element Momentum Method Model on Horizontal Axis Wind Turbines
,”
Int. J. Energy Environ. Eng.
,
3
(
1
), p.
30
.
6.
Velázquez
,
M. T.
,
Carmen
,
M. V. D.
,
Francis
,
J. A.
,
Pacheco
,
L. A. M.
, and
Eslava
,
G. T.
,
2014
, “
Design and Experimentation of a 1MW Horizontal Axis Wind Turbine
,”
J. Power Energy Eng.
,
2
(
01
), pp.
9
16
.
7.
Liu
,
X.
,
Wang
,
L.
, and
Tang
,
X.
,
2013
, “
Optimized Linearization of Chord and Twist Angle Profiles for Fixed-Pitch Fixed-Speed Wind Turbine Blades
,”
Renewable Energy
,
57
, pp.
111
119
.
8.
Freitas Silva
,
P. A. S.
,
Shinomiya
,
L. D.
,
De Oliveira
,
T. F.
,
Pinheiro Vaz Jn
,
R.
,
Amarante Mesquita
,
A. L.
, and
Pinho Brasil
,
A. C.
, Jr.
,
2017
, “
Analysis of Cavitation for the Optimized Design of Hydrokinetic Turbines Using BEM
,”
Appl. Energy
,
185
(
Pt. 2
), pp.
1281
1291
.
9.
Al-Abadi
,
A.
,
Ertunç
,
E.
,
Weber
,
H.
, and
Delgado
,
A.
,
2014
, “
A Torque Matched Aerodynamic Performance Analysis Method for the Horizontal Axis Wind Turbines
,”
Wind Energy
,
17
(
11
), pp.
1727
1736
.
10.
Griffiths
,
R. T.
, and
Woollard
,
M. G.
,
1978
, “
Performance of the Optimal Wind Turbine
,”
Appl. Energy
,
4
(
4
), pp.
261
272
.
11.
Molenaar
,
D. P.
,
2003
, “
Cost Effective Design and Operation of Variable Speed Wind Turbines
,”
Ph.D. thesis
, Delft University, Delft, The Netherlands.
12.
Pinto
,
R. L. U. d. F.
, and
Gonçalves
,
B. P. F.
,
2017
, “
A Revised Theoretical Analysis of Aerodynamic Optimization of Horizontal-Axis Wind Turbines Based on BEM Theory
,”
Renewable Energy
,
105
, pp.
625
636
.
13.
Vandenberghe
,
D.
, and
Dick
,
E.
,
1987
, “
A Free Vortex Simulation Method for the Straight Bladed Vertical Axis Wind Turbine
,”
J. Wind Eng. Ind. Aerodyn.
,
26
(
3
), pp.
307
324
.
14.
Afungchui
,
D.
,
Kamoun
,
B.
, and
Helali
,
A.
,
2014
, “
Vortical Structures in the Wake of the Savonius Wind Turbine by the Discrete Vortex Method
,”
Renewable Energy
,
69
, pp.
174
179
.
15.
Sessarego
,
M.
,
Ramos-Garcia
,
N.
,
Hua
,
Y.
, and
Shen
,
W. Z.
,
2016
, “
Aerodynamic Wind-Turbine Rotor Design Using Surrogate Modeling and Three-Dimensional Viscous-Inviscid Interaction Technique
,”
Renewable Energy
,
93
, pp.
620
635
.
16.
Hansen
,
M. O. L.
, and
Johansen
,
J.
,
2004
, “
Tip Studies Using CFD and Comparison With Tip Loss Models
,”
Wind Energy
,
7
(
4
), pp.
343
356
.
17.
Mycek
,
P.
,
Gaurier
,
B.
,
Germain
,
G.
,
Pinon
,
G.
, and
Rivoalen
,
E.
,
2013
, “
Numerical and Experimental Study of the Interaction Between Two Marine Current Turbines
,”
Int. J. Mar. Energy
,
1
, pp.
70
83
.
18.
Moshfeghi
,
M.
,
Song
,
Y. J.
, and
Xie
,
Y. H.
,
2012
, “
Effects of Near-Wall Grid Spacing on SST-k–ω Model Using NREL Phase VI Horizontal Axis Wind Turbine
,”
J. Wind Eng. Ind. Aerodyn.
,
107–108
, pp.
94
105
.
19.
Costa Rocha
,
P. A.
,
Barbosa Rocha
,
H. H.
,
MouraCarneiro
,
F. O.
,
Vieira da Silva
,
M. E.
, and
Valente Bueno
,
A.
,
2014
, “
k–ω SST (Shear Stress Transport) Turbulence Model Calibration: A Case Study on a Small Scale Horizontal Axis Wind Turbine
,”
Energy
,
65
, pp.
412
418
.
20.
Xudong
,
W.
,
Shen
,
W. Z.
,
Zhu
,
W. J.
,
Sørensen
,
J. N.
, and
Jin
,
C.
,
2009
, “
Shape Optimization of Wind Turbine Blades
,”
Wind Energy
,
12
(
8
), pp.
781
803
.
21.
Xiong
,
L.
,
Xianmin
,
Z.
,
Gangqiang
,
L.
,
Yan
,
C.
, and
Zhiquan
,
Y.
,
2010
, “
Dynamic Response Analysis of the Rotating Blade of Horizontal Axis Wind Turbine
,”
Wind Eng.
,
34
(
5
), pp.
543
560
.
22.
Jourieh
,
M.
,
Kuszla
,
P.
,
Dobrev
,
I.
, and
Massouh
,
F.
,
2006
, “
Hybrid Rotor Models for the Numerical Optimisation of Wind Turbine Farms
,”
First International Symposium on Environment Identities and Mediterranean Area
(
ISEIMA
), Corte-Ajaccio, France, July 9–12, pp.
173
177
.
23.
Yang
,
Y.
,
Li
,
C.
,
Zhang
,
W.
,
Yang
,
J.
,
Ye
,
Z.
,
Miao
,
W.
, and
Ye
,
K.
,
2016
, “
A Multi-Objective Optimization for HAWT Blades Design by Considering Structural Strength
,”
J. Mech. Sci. Technol.
,
30
(
8
), pp.
3693
3703
.
24.
Bottasso
,
C.
,
Campagnolo
,
F.
, and
Croce
,
A.
,
2012
, “
Multi-Disciplinary Constrained Optimization of Wind Turbines
,”
Multibody Syst. Dyn.
,
27
(
1
), pp.
21
53
.
25.
Jureczko
,
M.
,
Pawlak
,
M.
, and
Mezyk
,
A.
,
2005
, “
Optimisation of Wind Turbine Blades
,”
J. Mater. Process. Technol.
,
167
(
2–3
), pp.
463
471
.
26.
Chehouri
,
A.
,
Younes
,
R.
,
Ilinca
,
A.
, and
Perron
,
J.
,
2015
, “
Review of Performance Optimization Techniques Applied to Wind Turbines
,”
Appl. Energy
,
142
, pp.
361
388
.
27.
ElQatary
,
I.
, and
Elhadidi
,
B.
,
2014
, “
Comparison Between OpenFOAM CFD & BEM Theory for Variable Speed—Variable Pitch HAWT
,”
ITM Web Conf.
,
2
, p.
05001
.
28.
Batten
,
W.
,
Bahaj
,
A.
,
Molland
,
A.
, and
Chaplin
,
J.
,
2007
, “
Experimentally Validated Numerical Method for the Hydrodynamic Design of Horizontal Axis Tidal Turbines
,”
Ocean Eng.
,
34
(
7
), pp.
1013
1020
.
29.
Batten
,
W.
,
Bahaj
,
A.
,
Molland
,
A.
, and
Chaplin
,
J.
,
2008
, “
The Prediction of the Hydrodynamic Performance of Marine Current Turbines
,”
Renewable Energy
,
33
(
5
), pp.
1085
1096
.
30.
Lee
,
J. H.
,
Park
,
S.
,
Kim
,
D. H.
,
Rhee
,
S. H.
, and
Kim
,
M.
,
2012
, “
Computational Methods for Performance Analysis of Horizontal Axis Tidal Stream Turbinesm
,”
Appl. Energy
,
98
, pp.
512
523
.
31.
Rajakumar
,
S.
, and
Ravindran
,
D.
,
2012
, “
Iterative Approach for Optimizing Coefficient of Power, Coefficient of Lift and Drag of Wind Turbine Rotor
,”
Renewable Energy
,
38
(
1
), pp.
83
93
.
32.
Zhu
,
W. J.
,
Shen
,
W. Z.
, and
Sørensen
,
J. N.
,
2014
, “
Integrated Airfoil and Blade Design Method for Large Wind Turbines
,”
Renewable Energy
,
70
, pp.
172
183
.
33.
Tachos
,
N. S.
,
Filios
,
A. E.
,
Margaris
,
D. P.
, and
Kaldellis
,
J. K.
,
2009
, “
A Computational Aerodynamics Simulation of the NREL Phase II Rotor
,”
The Open Mech. Eng. J.
,
3
(
1
), pp.
9
16
.
34.
I. F. S. A.
Kabir
, and
E. Y. K.
Ng
,
2017
, “
Insight Into Stall Delay and Computation of 3D Sectional Aerofoil Characteristics of NREL Phase VI Wind Turbine Using Inverse BEM and Improvement in BEM Analysis Accounting for Stall Delay Effect
,”
Energy
,
120
, pp.
518
536
.
35.
Rahimi
,
H.
,
Dose
,
B.
,
Stoevesandt
,
B.
, and
Peinke
,
J.
,
2016
, “
Investigation of the Validity of BEM for Simulation of Wind Turbines in Complex Load Cases and Comparison With Experiment and CFD
,”
J. Phys.: Conf. Ser.
,
749
(
1
), p.
012015
.
36.
Drela
,
M.
, and
Youngren
,
H.
,
2001
, “
XFOIL 6.9 User Primer, XFOIL Documentation
,” Massachusetts Institute of Technology, Cambridge, MA, accessed Oct. 6, 2017, http://web.mit.edu/drela/Public/web/xfoil/xfoil_doc.txt
37.
Snel
,
H.
,
1998
, “
Review of the Present Methods of Rotor Aerodynamics
,”
Wind Energy
,
1
, pp.
46
69
.
38.
Bai
,
C.-J.
, and
Wang
,
W.-C.
,
2016
, “
Review of Computational and Experimental Approaches to Analysis of Aerodynamic Performance in Horizontal-Axis Wind Turbines (HAWTs)
,”
Renewable Sustainable Energy Rev.
,
63
, pp.
506
519
.
39.
Chen
,
C.
,
Choi
,
Y.
, and
Yoon
,
H.
,
2013
, “
Blade Design and Performance Analysis on the Horizontal Axis Tidal Current Turbine for Low Water Level Channel
,”
IOP Conf. Ser.: Mater. Sci. Eng.
,
52
(
5
), p.
052020
.
40.
Mahri
,
Z. L.
,
Zid
,
S.
, and
Salah
,
R. M.
,
2013
, “
An Optimal Design of the Wind Turbine Blade Geometry Adapted to a Specific Site Using Algerian Wind Data
,”
ROMAI J.
,
9
(
2
), pp.
143
154
.
41.
Lee
,
J. H.
,
Kim
,
D. H.
,
Rhee
,
S. H.
,
Do
,
I. R.
,
Shin
,
B. C.
, and
Kim
,
M. C.
,
2011
, “
Computational and Experimental Analysis for Horizontal Axis Marine Current Turbine Design
,”
Second International Symposium on Marine Propulsors
(
SMP
), Hamburg, Germany, June 15–17, pp. 371–376.
42.
Johnson
,
D. A.
,
Gu
,
M.
, and
Gaunt
,
B.
,
2016
, “
Wind Turbine Performance in Controlled Conditions: BEM Modeling and Comparison With Experimental Results
,”
Int. J. Rotating Mach.
,
2016
, p.
5460823
.
43.
Mirghaed
,
M. R.
, and
Roshandel
,
R.
,
2013
, “
Site Specific Optimization of Wind Turbines Energy Cost: Iterative Approach
,”
Energy Convers. Manage.
,
73
, pp.
167
175
.
44.
Selig
,
M. S.
, and
McGranahan
,
B. D.
,
2004
, “
Wind Tunnel Aerodynamic Tests of Six Airfoils for Use on Small Wind Turbines
,”
ASME J. Sol. Energy Eng.
,
126
(
4
), pp.
986
1001
.
45.
Ahmed
,
M. R.
,
2012
, “
Blade Sections for Wind Turbine and Tidal Current Turbine Applications—Current Status and Future Challenges
,”
Int. J. Energy Res.
,
36
(
7
), pp.
829
844
.
46.
Drouen
,
L.
,
Charpentier
,
J. F.
,
Semail
,
E.
, and
Clenet
,
S.
,
2012
, “
A Global Approach for the Design of a Rim-Driven Marine Turbine Generator for Sail Boat
,”
IEEE—XX International Conference on Electrical Machines
(
ICEM
), Marseille, France, Sept. 2–5, pp.
549
555
.
47.
Tenguria
,
N.
,
Mittal
,
N. D.
, and
Ahmed
,
S.
,
2010
, “
Investigation of Blade Performance of Horizontal Axis Wind Turbine Based on Blade Element Momentum Theory (BEMT) Using NACA Airfoils
,”
Int. J. Eng., Sci. Technol.
,
2
(
12
), pp.
25
35
.
48.
Benini
,
E.
, and
Toffolo
,
A.
,
2002
, “
Optimal Design of Horizontal Axis Wind Turbines Using Blade Element Theory and Evolutionary Computation
,”
ASME J. Sol. Energy Eng.
,
124
(
4
), pp.
357
363
.
49.
Burton
,
T.
,
Jenkins
,
N.
,
Sharpe
,
D.
, and
Bossanyi
,
E.
,
2011
,
Wind Energy Handbook
,
2nd ed.
,
Wiley
, Chichester, UK.
50.
Johnson
,
W.
,
1980
,
Helicopter Theory
, Princeton University Press, Princeton, NJ.
51.
Le Gouriérès
,
D.
,
2014
,
Wind Power Plants: Theory and Design
, Pergamon Press, Oxford, UK.
52.
Manwell
,
J. F.
,
McGowan
,
J. G.
, and
Rogers
,
A. L.
,
2009
,
Wind Energy Explained: Theory, Design and Application
,
2nd ed.
,
Wiley
, Chichester, UK.
53.
Glauert
,
H.
,
1963
, “
Airplane Propellers
,”
Aerodynamic Theory
,
W. F.
Durand
, ed.,
Dover
Publications,
Mineola, NY
, pp.
169
360
.
54.
Wilson
,
R. E.
, and
Lissaman
,
P. B. S.
,
1974
, “
Applied Aerodynamics of Wind Power Machines
,” Oregon State University, Corvallis, OR, Report No. NSF/RA/N-74113.
55.
Anderson
,
M. B.
,
1980
, “
A Vortex-Wake Analysis of a Horizontal Axis Wind Turbine and a Comparison With Modified Blade Element Theory
,”
Third International Symposium on Wind Energy Systems
(
WES
), Lyngby, Denmark, Aug. 26–29, pp. 357–374.
56.
Branlard
,
E.
,
2011
, “
Wind Turbine Tip-Loss Corrections – Review, Implementation and Investigation of New Models
,”
Master's thesis
, RisøDUT (Technical University of Denmark), Lyngby, Denmark.
57.
Shen
,
Z. W.
,
Mikkelsen
,
R.
, and
Sørensen
,
J. N.
,
2005
, “
Tip Loss Corrections for Wind Turbine Computations
,”
Wind Energy
,
8
(
4
), pp.
457
475
.
58.
Clifton Smith
,
M. J.
,
2009
, “
Wind Turbine Blade Optimisation With Tip Loss Corrections
,”
Wind Eng.
,
33
(
5
), pp.
477
496
.
59.
Herráez
,
I.
,
Stoevesandt
,
B.
, and
Peinke
,
J.
,
2014
, “
Insight Into Rotational Effects on a Wind Turbine Blade Using Navier–Stokes Computations
,”
Energies
,
7
(
10
), pp.
6798
6822
.
60.
Guntur
,
S.
,
Bak
,
C.
, and
Sørensen
,
N.
,
2011
, “
Analysis of 3D Stall Models for Wind Turbine Blades Using Data From the MEXICO Experiment
,”
13th International Conference on Wind Engineering
(
ICWE
), Amsterdam, The Netherlands, July 10–15.
61.
Breton
,
S. P.
,
Coton
,
F. N.
, and
Moe
,
G.
,
2008
, “
A Study on Rotational Effects and Different Stall Delay Models Using a Prescribed Wake Vortex Scheme and NREL Phase VI Experiment Data
,”
Wind Energy
,
11
(
5
), pp.
459
482
.
62.
Sarraf
,
C.
,
Djeridi
,
H.
,
Prothin
,
S.
, and
Billard
,
J. Y.
,
2010
, “
Thickness Effect of NACA Foils on Hydrodynamic Global Parameters, Boundary Layer States and Stall Establishment
,”
J. Fluids Struct.
,
26
(
4
), pp.
559
578
.
63.
Xu
,
G.
, and
Sankar
,
L. N.
,
2002
, “
Application of a Viscous Flow Methodology to the NREL Phase VI Rotor
,”
ASME
Paper No. WIND2002-30.
You do not currently have access to this content.