...

Zanne2010.pdf

by user

on
Category: Documents
9

views

Report

Comments

Transcript

Zanne2010.pdf
UNIVERSITÁ DEGLI STUDI DI UDINE
Dottorato in Tecnologie Chimiche ed Energetiche
FLUID DYNAMIC MODELLING OF
WIND TURBINES
sec. D
Vz
Vr
Vr
Vt
0
Vt
D
3
Relatori:
Prof.Ing. Lorenzo BATTISTI
Prof.Ing. Piero PINAMONTI
Dottorando:
Dott.Ing. Luca ZANNE
Udine 21 Maggio 2010
Summary
Introduction
PART I : HAWT analysis
HAWT Fluid dynamics
A turbomachinery approach
Inverse design
Summary
PART II : VAWT analysis
VAWT fluid dynamics
VAWT experimental analysis
VAWT free vortex wake
Results and conclusions
Introduction
Wind energy market (EWEA)
Installed capacity
Offshore WE market (EWEA)
Aim of the thesis & thesis outline
The aim of the thesis is to analyze the fluid dynamic
models of wind energy conversion systems, pointing
out the limitations of current engineering models and
proposing innovative solutions from the design point
of view
The research activities have been divided in two main
parts, following the different rotor – flow
interaction characteristics:
1. Horizontal axis wind turbines - HAWT;
2. Crossflow wind turbines, as vertical axis wind
turbines - VAWT.
Part I : HAWT analysis
HAWT fluid dynamics
HAWT fluid dynamics is mainly based on the actuator disk concept
HAWT fluid dynamics
Actuator disk concept
The turbine generates mechanical work from the kinetic energy of the
fluid flow
The work exchange between
the fluid and the shaft is done
by is done by the rotor, which
can be modelled as an
actuator disk
The bladed rotor can be
represented with equivalent
forces distribuited over a
permeable, immaterial disk
Infinite number of blades
Infinite rotational velocity
HAWT fluid dynamics
Actuator disk – momentum theory
Froude applied for the first time the actuator disk concept to a
rotor in open flow.
He applied it with the 1D momentum balance in axial direction
Momentum equation
T = ∆p ⋅ Am = ρVz ,3 A3 (Vz ,0 − Vz ,3 )
Energy conservation
Weul =
∆p
ρ
=
Mass conservation
Vz2,0 − Vz2,3
Vz ,m Am = Vz ,3 A3
2
Vz ,1 ≅ Vz ,2 ≅ Vz ,m
Froude result!
Vz ,m =
Vz ,0 + Vz ,3
2
Actuator disk
Blade element – momentum theory
Drzewiecki first applied Froude result
dividing the rotor in different annular
streamtubes :
Non uniform loading
Vz ,m =
FN
Lift
φflow
FT
z
θpitch+βtwist
φflow
V0
αattack
Vrel.
chord line
Drag
-ωr
y
2
With the blade element airfoil theory
rotor performances can be easily
calculated
Raero
Wind.=[ -a·V0; -a’·ωr ]
Vz ,0 + Vz ,3
rotor plane
The annuli interaction is neglected
No swirl flow, (wake expansion?)
Ok lightly loaded rotors
HAWT fluid dynamics
General momentum theory
The general momentum theory should overcome the issues of
the swirl flow modelling
Momentum equation : axial
T = ∫ ( p1 − p2 ) dA = ∫  ρVz ,3 (Vz ,0 − Vz ,3 ) + ( p0 − p3 )  dA
Am
A3
tangential
M = ∫ ρVθ ,3Vz ,3 r3 dA
A3
1 + 1 2Vθ ,3 Ωr3 1 + 1 2Vθ ,2 Ωr 
2
1
ρ ∫A3 (Vz ,0 − Vz ,3 ) dA = ρΩ ∫A3Vz ,3Vθ ,3r3 
−
 dA
2
Vz ,3
Vz ,m


• GM theory is an
integral formulation
• It needs the wake
solution
radial
p3 − p0
ρ
=
(
p3 ( r3 ) − p3 rtip ,3
ρ
Solutions:
• De Vries
• Differential
8 V2
Weul = ⋅ 0
9 2
)=−
2
rtip ,3 Vθ ,3
∫r3
r3
dr3
Actuator disk – momentum theory
limitations
Actuator strip
Wake states
Conway exact
solution
HAWT fluid dynamics
Vortex theory
Vortex theory calculates the flow
field of the rotor wake by using the
fluid dynamic laws of vorticity (BiotSavart law, Kelvin’s theorem,
Helmholtz’s laws)
Introduced by Joukowski – Betz –
Prandtl
Most widespread for propeller analysis
and design (both for aerodynamic and
marine propellers) and for helicopter
rotor performance prediction
• Prescribed vortex wake
• Free vortex wake
Vortex theory
Prescribed vortex wake
Vz ,m =
Axial velocity
d Γ = 2π ⋅ d ( rVθ ,2 )
gθ ,m =
gθ ,3 =
d Γ r Ω + Vθ ,2 2
Vz , m
2π r
d Γ r3Ω + Vθ ,3
2π r3 Vz ,3
vz ,m = gθ 2
vz ,3 = gθ
Radial velocity
Vr ( r ,0 ) = −
1 r ∂Vz
r
( r,0 ) dr
r ∫0 ∂z
∂Vz ∂z ( r,0 ) =
gθ
gθ
+
r
2r 2π ( r − r )
∂Vz ∂z ( r,0 ) =
 1 1  gθ ( r − r )
−
 −

2π ( r − r ) r 2  4 2π 
r 5
gθ
2
Vz ,0 + Vz ,3
2
Part I : HAWT analysis
A turbomachinery approach
V ∂rVθ
1 ∂p 0
 ∂V ∂V 
= Fr + θ
− Vz  r − z 
ρ ∂r
r ∂r
∂r 
 ∂z
Vz
∂Vθ Vr ∂rVθ
+
= Fθ
∂z
r ∂r
1 ∂p 0
 ∂V ∂V
= Fz + Vr  r − z
ρ ∂z
∂r
 ∂z
∂rVr ∂rVz
+
=0
∂r
∂z
∂Vθ

 + Vθ
∂z

A turbomachinery approach
Stoke’s stream function
ωθ =
∂ 2ψ
∂r 2
∂Vr ∂Vz
−
∂z
∂r
−
1 ∂ψ ∂ 2ψ
+
= −rωθ
r ∂r ∂z 2
ωθ = Vθ
∂ 2ψ
∂r 2
∂ 2ψ
∂r 2
−
−
d ( rVθ )
dψ
−
r dp 0
ρ dψ
1 ∂ψ ∂ 2ψ
+
=0
r ∂r ∂z 2
d ( rVθ ) r 2 dp 0
1 ∂ψ ∂ 2ψ
+ 2 = −rωθ = −rVθ
+
r ∂r ∂z
dψ
ρ dψ
Linearized solution : Horlock actuator disk solution
∂ 2ψ
1 ∂ψ ∂ 2ψ
−
+
= − F (r )
∂r 2 r ∂r ∂z 2
 Vz ,3 − Vz ,0  kz
Vz ( r , z ) = Vz ,0 + 
e
2


Vr ( r , z ) = −
1 r  Vz ,3 ( r ) − Vz ,0  kz
kr 
 e dr
r ∫0 
2

Froude result
A turbomachinery approach
Motion in region II
The flow is determined by
rVθ
p0
Euler equation
1
ρ
(p
0
2
)
− p10 = ΩrVθ = Weul
Wu equation
(
0
0

1 ∂ψ ∂ 2ψ  p2 − p1
−
+
= −
∂r 2 r ∂r ∂z 2 
Ω2

∂ 2ψ
The angular momentum
distribution can be assigned
Vθ = k1r n +
k2
r
rVθ = k1r n +1 + k 2
)
ρ

+r
d ( rVθ )
1 dp20
= Ωr 2 − rVθ
 ρ dψ
dψ

2
Free vortex distribution
rVθ = const
(
)
The radial equilibrium theory applied
to wind turbines
Radial momentum equilibrium
V ∂rVθ
1 ∂p 0
 ∂V ∂V 
= Fr + θ
− Vz  r − z 
ρ ∂r
r ∂r
∂r 
 ∂z
dV
1 dp 0 Vθ d ( rVθ )
=
+ Vz z
ρ dr
r
dr
dr
ISRE
Sections 1 - 2
Vz2 − Vz2,hub =
2
(p
ρ
0
)
− pr0,hub − 2 ∫
r
r , hub
Wu hypothesis
∂Vr ,1
∂z
=−
∂Vr ,2
∂z
dVz ,m
1 dp20 Vθ ,2 d ( rVθ ,2 )
=
+ 2Vz ,m
ρ dr
r
dr
dr
Vθ ∂rVθ
r
 ∂V 
dr + 2 ∫
Vz  r  dr − Vr2 − Vr2,hub
r
,
hub
r ∂r
 ∂z ψ
(
)
Wu hypothesis on a streamline
 ∂Vr ,1 
 ∂Vr ,2 

 = −

 ∂z ψ
 ∂z ψ
dVz ,m
dVr ,m
1 dp20 Vθ ,2 d ( rVθ ,2 )
=
+ 2Vz ,m
+ 2Vr ,m
ρ dr
r
dr
dr
dr
The radial equilibrium theory
results and comments
Radial equilibrium solution for a uniformly loaded disk
λ=8
8 V2
Weul = ⋅ 0
9 2
λ=2
8 V2
Weul = ⋅ 0
9 2
The radial equilibrium theory
results and comments
Mikkelsen actuator disk – CFD
solution for a uniformly highly
loaded disk (wind turbine state)
8 V2
Weul = ⋅ 0
9 2
Conway actuator disk – vortex
theory exact solution for a (almost)
parabolic highly loaded disk
(propeller state) CT = 3.147
The radial equilibrium theory
results and comments
Power and thrust coefficients for
the different flow field solution
models with a constant work
extraction
Conway velocity at the centre of
the disk for a propeller
The radial equilibrium theory
on a streamline
Radial equilibrium with meridional velocity
dVs ,m
1 dp20 Vθ ,2 d ( rVθ ,2 )
=
+ 2Vs ,m
ρ dr
r
dr
dr
Vs2,m = Vz2,m + Vr2,m
Denton / Cumpsty approach
∂V
V2
1 ∂ 2 1 ∂p 0
1 ∂ 2 2 Vs ∂
Vs =
+ Vs s sin ( ε + δ ) + s cos ( ε + δ ) − 2
r Vθ +
( rVθ ) tan γ + Fd
2 ∂q
∂s
rs
r ∂s
ρ ∂q
2r ∂q
(
∂V
V2
1 ∂Vs2 1 ∂p 0
1 ∂ 2 2
=
+ Vs s sin ε − s cos ε − 2
r Vθ
ρ ∂r
∂s
2 ∂r
rs
2r ∂q
(
∂Vs2,m
∂r
=
)
Coning / yaw effects
Turbulence wake state / stall
)
 1
∂Vs ,m
1 ∂p20
1  1 ∂ 2 2
+ 2Vr ,m
− Vs2,m cos ε 
+
r Vθ
 − 2

∂s
ρ ∂r
 rs ,1 rs ,2  2r ∂q
(
)
Tip effects
Unsteady dynamics
Considerations on the
turbomachinery approach
• The theory handles an expanding and rotating wake.
• Only the disk station has to be solved to obtain the information
needed to compute CP and CT.
• The method is simple and robust also for low tip speed ratios
• Arbitrary disk loading can be analyzed.
• The mathematics involved are comparable with those of the
usual actuator disk approaches.
• The actual velocities distribution are qualitatively assessed even
though more work has to be carried out to better understand the
fluid flow in the neighborhood of the disk and in the wake.
• The radial velocity gradients along the streamlines at the disk
have to be better described to reduce the axial velocity
overestimation at the disk inner portion.
Part I : HAWT analysis
Inverse Design
Inverse design and direct design methods
The turbine close field structure
The blade architecture
Blade forces
Fθ , Z = ρ ⋅ Vz ,m ⋅ s ⋅ (Vθ ,2 − Vθ ,1 ) = ρ ⋅ V 2 z ,m ⋅ s ⋅ ( tan α 2 − tan α1 )
Fz , Z = ( p10 − p20 ) ⋅ s +
1
ρ ⋅ Vθ2,2 ⋅ s
2
Weul = U ⋅ (Vθ ,2 − Vθ ,1 ) = U ⋅ Vz ,m ⋅ (tan α 2 − tan α1 ) = U ⋅ Vz ,m ⋅ (tan β 2 − tan β1 )
k 

Weul = rω ⋅  k1r n + 2 
r 

Flow angles
 U + Vθ ,1 
 Vz ,1 


β1 = tan −1 
 U + Vθ ,m 
 Vz ,m 


β m = tan −1 
 U + Vθ ,2 
 Vz ,2 


β 2 = tan −1 
Vz ,m Vz ,1 Vz ,2
The blade architecture
Cy =
Fy
Fy ,max
= 2⋅
C y = 0.8
Dloc =
Wmax − W2
Wmax
s
( tan β2 − tan β1 ) cos2 β2
cz
Zweifel
Lieblein
cz = c ⋅ cos β m
s
CL = 2 (tan β 2 − tan β1 ) cos β m
c
θ=
π
2
− β m − sen −1 (
CL, ID
2π
)
Inverse Design
Results and discussion
Gaia turbine
Inverse Design
Results and discussion
1
VDz / V0
0.5
0.2
0.4
0.6
0.8
0
1
0
0.2
0.4
40
20
0
0.2
0.4
0.8
The blade architecture and
loads
1
0.6
0.8
40
20
0
1
0
0.2
0.4
r/R
0.6
0.8
1
0.2
0.1
r/R
1.5
0
0.2
0.4
0.6
0.8
0
0
0.2
0.4
0.6
0.8
0.2
0.4
0.8
60
40
20
0
1
Fn / q0R
0
0.2
0.4
0.6
0.8
0.4
0.4
0.6
0.8
0
0.2
0.4
0.5
0.2
0.4
0.6
r/R
0.6
0.8
1
0.6
0.8
1
0.6
0.8
1
0.2
0
0.2
0.4
r/R
1
0
1
r/R
r/R
0
0.8
0.4
0
1
0.6
r/R
0.6
0.2
0.2
0.2
1
0
1
r/R
0
0
2
0.4
0
80
r/R
0.6
λ=6,Z=3
0.6
1
0
1
r/R
Mt / q0R3
r/R
1
0.5
dCp / d(r/R)
0
Ft / q0R
0.5
0
0
2
1
Psi
p1-p2 / q0
1
Mn / q0R3
0
0.6
r/R
beta1-beta2 [deg]
alpha2 [deg]
r/R
betam [deg]
0
0.5
P / 1/2rhoAV 30
0
Flow characteristics
C/R
W / 1/2V 20
1
0.8
1
0.6
0.4
0.2
0
0
0.2
0.4
r/R
Inverse Design
Results and discussion
λ=6,Z=3
Inverse Design
Results and discussion
λ = 1.5 , Z = 3
Part II : VAWT analysis
VAWT fluid dynamics
Darrieus eggbeater – Darrieus H/V
– Gorlov type
Building environment
Offshore multi Mega Watt
CL =
dL
1 ρ W 2 c dh
2 0
VAWT fluid dynamics
The double disk BEM for VAWT
Flow characteristics
β = tan −1
Vsenϑ cos δ
( V cosϑ + Ωr ) cos γ
C N = CL cos β + C D sin β
2
W 2 = ( Vcosϑ + Ωr ) cos γ  + ( Vsenϑ cos δ )
Re =
CL =
Blade element forces
2
CT = C L sin β − C D cos β
1
dh
dFN = ρ0 W2 c
CN
2
cos δ
cW
ν0
dL
1 ρ W 2 c dh
2 0
CD =
dD
1 ρ W 2 cdh
2 0
dFT =
1
dh
ρ0 W 2 c
CT
2
cos δ
Shaft torque/power
dM = dFT Ω
N BL
1 ϑ
dM Ω
Nϑ ∫ ∫ ∫
MΩ
CP =
=
1 ρ A V3
1 ρ A V3
0
sw
0
2
2 0 sw 0
VAWT fluid dynamics
The double disk BEM for VAWT
Blade element
dFx = dFT cos ϑ cos βc cos γ + dFN sin ϑ cos δ
dFx = B 2
CTH =
∆ϑ
π
dFx
dFx
1
ρ0 V02 dAs
2
dAs = dh r dϑ sinϑ
Momentum theory
α=
V
V0
dFx = 2ρ dA s V(V0 -V)
CTH =
dFx
1
ρ V02 dA s
2
=
2ρ dA s V(V0 -V)
= 4α (1 − α )
1
2
ρ V0 dA s
2
The double disk BEM for VAWT
Corrections
Glauert correction
CTH =
26
4
(1 − α ) +
15
15
Tip losses
Post stall airfoil performance
correction
Flow curvature
Dynamic stall
Streamtubes expansion
VAWT fluid dynamics
Validation and results
Sandia 5m
Darrieus
3blades
NACA0015
Four geometric characteristics
VAWT fluid dynamics
Validation and results
Blade tangential and normal
force coefficients
Shaft forces and torque
Mean value and fluctuations
VAWT fluid dynamics
Validation and results
Shaft torque and forces diagrams
2-bladed
3-bladed
3-bladed
2-bladed
presents the best power performance
presents lower forces fluctuations
Gorlov type presents the lowest fatigue loads (complex geometry)
a 90° reduces the loads fluctuations but needs rotor balancig
VAWT fluid dynamics
Limitations of VAWT BEM codes
• The circular path is simplified in two actuator disks
• The momentum equilibrium is applied only in axial direction
• The axial expansion is generally neglected or not
correctly/completely implemented
• The turbulent wake state correction is taken from HAWT
corrections
• No (or weak) interaction between streamtubes
• Tip losses correction is of doubtful application for VAWT
• Complex geometry not resolvable from a fluid dynamic point of
view
• Unsteady fluid dynamic effects are of difficult implementation
Part II : VAWT analysis
VAWT experimental analysis
VAWT experiments in controlled conditions
The Politecnico di Milano Large Wind
Tunnel
High speed test section: 4x3.84m
Wind speed up to 55m/s
Possibility to work in open/close test
section
2 different rotor prototypes designed by
Tozzi Nord Wind Turbines:
PDF1 – research purpose
PDF3 – commercial turbine
The turbines layout and the
instrumentations
PDF1
3 Blades
H = 1.46m
D = 1.03m
NACA0021
Solidity 0.25
Rotor position
Torque
Support loads
PDF3
3 Blades - Gorlov
H = 2.5m
D = 1.78m
P = 1.5kW
H(tower) = 3.5m
Rotor position
Torque (electric)
Support loads
Aerodynamics
Directional pneumatic
5 holes probe
Single sensor hot wire
anemometer
VAWT experimental analysis
PDF1 rotor - Performance
Blockage : 0.097 close test section
Blockage effects up to 20-30% for
CP and 10-20% for CT
Reynolds numbers very important
on power performance for
Re < 200000
VAWT experimental analysis
PDF1 rotor - Aerodynamics
λ = 1.6
λ = 2.6
Wake non symmetric and deformed
turnwise (in particular at low tip
speed ratios)
λ = 1.6
In closed wind tunnel there is an
higher velocity due to blockage
effects
VAWT experimental analysis
PDF1 rotor - Aerodynamics
Wind tunnel blockage

1
1
1
1
 

T = AD  p0 + ρV02 − ρVD2  −  p3 + ρV32 − ρVD2  
2
2
2
2
 


V0' VD
C
=
+ T
V
V0 V0
4 D
V0
1D momentum theory doesn’t seem
the best model for blockage effects
VAWT experimental analysis
PDF1 rotor - Aerodynamics
Unsteady flow field
λ = 2.5
VAWT experimental analysis
PDF3 rotor - Dynamics
Dynamic analysis and modelling
Part II : VAWT analysis
2D Free vortex wake
Bound and shed vorticity
L = Cl
1
ρW 2 c = ρW Γ B
2
1
Γ B = ClWc
2
δΓ S = −
d ΓB
δθ
dθ
Induced velocitites (Biot-Savart)
u=−
( y − y0 )
Γ
2π ( x − x0 )2 + ( y − y0 )2 + h 2
v=
( x − x0 )
Γ
2π ( x − x0 )2 + ( y − y0 )2 + h 2
Shed vortex position
Flow characteristics
2
W 2 = ΩR + (U 0 + uC ) cos (θ ) + vC sin (θ )  + (U 0 + uC ) sin (θ ) − vC cos (θ ) 
(U 0 + uC ) sin (θ ) − vC cos (θ )
φ = tan −1 −
ΩR + (U 0 + uC ) cos (θ ) + vC sin (θ )
α =φ − β
2
(
)
xS ,i = xS ,i −1 + U 0 + uS ( xS ,i −1 , yS ,i −1 ) ⋅ dt
y S ,i = yS ,i −1 + vS ( xS ,i −1 , yS ,i −1 ) ⋅ dt
(
)
xS ,i = xS ,i −1 + U 0 + 0.5 ⋅ uS ( x S ,i , y S ,i ) + uS ( xS ,i −1 , yS ,i −1 )  ⋅ dt


(
)
yS ,i = yS ,i −1 + 0.5 ⋅ vS ( xS ,i , y S ,i ) + vS ( xS ,i −1 , yS ,i −1 ) ⋅ dt
VAWT 2D Free vortex wake
Validation and results
Comparison with Shen et al. actuator
surface – CFD computations of a 2bladed rotor
• Flow characteristics are
qualitatively well assessed
• Viscosity is quite important
VAWT 2D Free vortex wake
Validation and results
• The angle of attack is well
reproduced
• Airfoil database are very
important
• Normal force coefficient peak not
well reproduced: dynamic stall
model to be improved
Validation and results
Ferreira panel model
The angle of attack is
reproduced sufficiently well
The efficiency seems
slightly lower than HAWT
Drag!
Conclusions - HAWT
• HAWT analysis : actuator disk – momentum theory
• Shortcomings : swirl flow, wake expansion, tip effects
• General momentum theory can’t overcome these issues
• Turbomachinery approach
• Radial equilibrium
• Radial equilibrium in meridional flow
• Turbomachinery approach + inverse design
• Innovative dsign should be found
Conclusions - VAWT
• VAWT complex 3D geometry, working in his own wake
• VAWT analysis : double moultiple streamtubes – BEM model
• DMS-BEM limitations
• 2D free vortex wake
• Airfoil database + DS + tip correction
• Slightly lower efficiency
• Blockage effects and Reynolds numbers
• 1D momentum theory is not suited for VAWT - unsteady
• Structural dynamics : aeroelastic codes + free wake codes
References - HAWT
1. Glauert H. Airplane Propellers (Div L) in Aerodynamic Theory (Vol 4). Durand WF ed. Springer: Berlin, 1935.
2. Horlok JH. Axial Flow Turbines. Butterworths: London, England, 1966.
3. Wilson RE, Lissaman PBS. Applied Aerodynamics of Wind-power Machines. Corvallis: Oregon State University, 1974.
4. Horlock JH. Actuator Disk Theory – Discontinuities in thermo-fluid dynamics. McGraw-Hill: New York, 1978.
5. Acton O. Turbomacchine Macchine a Fluido (vol 4). UTET: Torino, 1986.
6. Eppler R. Airfoil Design and Data Springer Verlag: Berlin/New York, 1990
7. Johnson W. Helicopter Theory. Dover Publications: New York, 1994.
8. Lewis RI. Turbomachinery Performance Analysis. Arnold: London, 1996.
9. Cebeci T. An Engineering Approach to the Calculation of Aerodynamic Flows. Horizons Publishing, 1999.
10. Burton T, Sharpe D, Jenkins N, Bossanyi E. Wind Energy Handbook. John Wiley & Sons: Chichester, 2001.
11. Osnaghi C. Teoria delle turbomacchine. Società Editrice Esculapio, 2002.
12. Cumpsty NA. Compressor Aerodynamics. 2nd ed. Krieger scientific: New York, 2004.
13. Leishman JG. Principles of Helicopter Aerodynamics. 2nd ed. Cambridge University Press: Cambridge, 2006.
14. Hansen MOL. Aerodynamics of Wind Turbines 2nd ed. Earthscan: London, 2008.
15. Rankine WJM. On the mechanical principles of the action of propellers. Transaction of the Institute of Naval Architects 1865; 6 :13-30.
16. Froude W. On the elementary relation between pitch, slip and propulsive efficiency. Transaction of the Institute of Naval Architects 1878; 19 : 47.
17. Froude RE. On the part played in propulsion by difference in pressure. Transaction of the Institute of Naval Architects 1889; 30 : 390-423.
18. Drzewiecki S. Méthode pour la détermination des eléments mécaniques des propulseurs hélicoidaux. Bullet. de l’Ass. Technique Maritime 1892.
19. Betz A. with Appendix by Prandtl L. Schraubenpropellermit Geringstem Energieverlust. Göttinger Nachrichten 1919; 193–217.
20. De Bothezat G. The general theory of blade screws. NACA-TR-29, 1920.
21. Goldstein S. On the vortex theory of screw propellers. Proc. Royal Soc. 1929; 123 : 440-465.
22. Theodorsen T. The theory of propellers. NACA-TR-775-776-777-778, 1944.
References - HAWT
23. Zweifel O. The spacing of turbomachine blading, especially with large angular deflections Brown Boweri Rev. 1945 Dec. 436-44
24. Wu C, Wolfenstein L. Application of radial equilibrium condition to axial-flow compressor and turbine design. NACA-TR-955, 1950.
25. Wu C. A general theory of three-dimensional flow in subsonic and supersonic turbomachines of axial-, radial-, and mixed-flow types. NACA-TN2604, 1952.
26. Marble FE, Michelson I. Analytical investigation of some three-dimensional flow problems in turbomachines. NACA-TN-2614, 1952.
27. Hawthorne WR, Horlock JH. Actuator disc theory of the incompressible flow in axial compressors. Proc. Instn. Mech. Engrs. 1962; 176 : 789-814.
28. Wu TY. Flow through a heavily loaded actuator disc. Schifftechnik 1962; 9 : 134 138.
29. Creveling HF, Carmody RH. Axial flow compressor design computer programs incorporating full radial equilibrium. NASA-CR-54532, 1968.
30. Greenberg MD, Powers SR. Nonlinear actuator disk theory and flow field calculations, including nonuniform loading. NASA-CR-1672, 1970.
31. Stoddard FS. Momentum theory and flow states for windmills. Wind Tech. J. 1977; 1 : 3-9.
32. Hütter U. Optimum wind-energy conversion system. Ann. Rev. Fluid Mech. 1977; 9 : 399-419.
33. Denton JD. Throughflow calculations for axial flow turbines. Trans. ASME, J. Eng.Power. 1978; 100.
34. De Vries O. Fluid dynamic aspects of wind energy conversion. AGARDograph AG-243, 1979.
35. Milborrow DJ. 1982 Performance, blade loads and size limits for horizontal axis wind turbines 4th BWEA Wind Energy Conversion(Cranfield: BHRA)
36. De Vries o. On the theory of the horizontal-axis wind turbines. Ann. Rev. Fluid Mech. 1983; 15 : 77-96.
36. Lee JHW, Greenberg MD. Line momentum source in shallow inviscid fluid. J. Fluid Mech. 1984; 145 : 287-304.
37. Kerwin JE. Marine propellers. Ann. Rev. Fluid Mech. 1986; 18 : 367-403.
38. Øye S. A simple vortex model. Proc. of the Third IEA Symposium on the Aerodynamics of Wind Turbines, ETSU, Harwell 1990, 4.1-5.15.
39. Van Kuik GAM. On the limitations of Froude’s actuator disc concept. PhD Thesis dissertation 1991, Technical University of Eindhoven.
40. Hansen C, Butterfield CP. Aerodynamics of horizontal axis wind turbines Ann. Rev. Fluid Mech. 1993; 25 : 115-149.
41. Sørensen JN. A survey of CFD methods in rotor aerodynamics. 7th IEA Symp. On Aerodynamics of Wind Turbines, Lyngby, November 1993.
42. Conway JT. Analytical solutions for the actuator disk with variable radial distribution of load. J. Fluid Mech. 1995; 297 : 327-355.
43. Sørensen JN, Kock CW. A model for unsteady rotor aerodynamics. J. Wind Eng. Ind. Aerodyn. 1995; 58 : 259-275.
References - HAWT
44. Snel H, van Holten Th. Review of recent aerodynamical research on wind turbines with relevance to rotorcraft. Aerodynamics and Aerocoustics of
Rotorcraft 1995; AGARD CP 552 : 7-11.
45. Sijtsma P, Sparenberg JA. On the equivalence of a dipole layer of constant strength and a concentrated vortex along its edge. ZAMM Z. angew.
Math. Mech. 1996; 76 : 480-482.
46. Colinsk AT. Modern helicopter aerodynamics. Ann. Rev. Fluid Mech. 1997; 29 : 515-567.
47. Conway JT. Exact actuator disk solutions for non-uniform heavy loading and slipstream contraction. J. Fluid Mech. 1998; 365 : 235-267.
48. Snel H. Review of the present status of rotor aerodynamics. Wind Energy 1998; 1 : 46-69.
49. Sørensen JN, Shen WZ, Munduate X. Analysis of wake states by a full-field actuator disc model. Wind Energy 1998; 1 : 73-88.
50. Magnusson M. Near-wake behaviour of wind turbines aerodynamics. J. Wind Eng. Ind. Aerodyn. 1999; 80 : 147-167.
51. Sparenberg JA, de Jager EM. Concentrated force acting in an inviscid and incompressible parallel flow. Math. Meth. Appl. Sci. 2000, 23 : 16371654.
52. Corten GP. Flow separation on wind turbine blades. PhD Thesis dissertation 2001, University of Utrecht.
53. Chaney K, Eggers Jr AJ. Expanding wake induction effects on thrust distribution on a rotor disc. Wind Energy 2002; 5 : 213-226.
54. Leishman JG. Challenges in modeling the unsteady aerodynamics of wind turbines. Wind Energy 2002; 5 : 85-132.
55. Mikkelsen R. Actuator disc methods applied to wind turbines. PhD Thesis dissertation 2003, Technical University of Denmark.
56. Van Kuik GAM. An inconsistency in the actuator disc momentum theory. Wind Energy 2003; 7 : 9-19.
57. Veermer LJ, Sørensen JN, Crespo A. Wind turbine wake aerodynamics. Progr. in Aerospace Sci. 2003; 39 : 467-510.
58. Spalart PR. On the simple actuator disk. J. Fluid Mech. 2003; 494 : 399-405.
59. Sharpe DJ. A general momentum theory applied to an energy extracting actuator disc. Wind Energy 2004; 7 : 177-188.
60. Medici D. Wind turbine wakes - control and vortex shedding. TR KTH Mechanics Royal 2004, Institute of Technology of Stockholm.
61. Shen WZ, Mikkelsen R, Sørensen JN and Bak C. Tip loss corrections for wind turbine computations Wind Energy 2005; 8: 457-475
62. Wald QR. The aerodynamics of propellers. Progr. in Aerospace Sci. 2006; 42 : 85-128.
63. Bak C. Research in aeroelasticity EFP-2005 Risø National Laboratory Wind Energy Department 2006; Risø-R-1559(EN).
References - HAWT
64. Hansen MOL, Sørensen JN, Voutsinas S, Sørensen N, Madsen HAa. State of the art in wind turbine aerodynamics and aeroelasticity. Progr. in
Aerospace Sci. 2006; 42 : 285-330.
65. Crawford C. Re-examining the precepts of the blade element momentum theory for coning rotors disc. Wind Energy 2006; 9 : 457-478.
66. Sant T. Improving BEM based aerodynamic models in wind turbine design codes. PhD Thesis dissertation 2007, Delft University of Tecnology.
67. Okulov VL, Sørensen JN. Stability of helical tip vortices in a rotor far wake. J. Fluid Mech. 2007; 576 : 1-25.
68. Wood DH. Including swirl in the actuator disk analysis of wind turbines. Wind Eng. 2007; 31 : 317-323.
69. Battisti L, Soraperra G. Analysis and application of pre-design methods for HAWT rotors. Proc. of EWEC (Milan, 7-10 May 2007).
70. Simon JF. Contribution to throughflow modelling for axial flow turbomachines. PhD Thesis dissertation 2007, Université de Liège.
71. L Battisti, G Soraperra, R Fedrizzi and L Zanne. Inverse design-momentum, a method for the preliminary design of horizontal axis wind turbines.
Proc. The Science of making Torque from Wind (Lyngby, Denmark, 28-31 August 2007) (J. of Physics: Conference Series Vol 75) IOP Publishing Ltd
72. Okulov VL, Sørensen JN. Refined Betz limit for rotors with a finite number of blades. Wind Energy 2008; 11 : 415-426.
73. Casey M, Robinson C. A new streamline curvature throughflow method for radial turbomachinery. Proc. ASME Turbo Expo (Berlin, 9-13 June
2008).
74. Ramakrishna PV, Govardhan M. Study of sweep and induced dihedral effects in subsonic axial flow compressor passages – Part I: design
considerations – changes in incidence, deflection, and streamline curvature. I.J.Rotating Machinery 2009; 2009.
75. www.gaia-wind.com
References - VAWT
1. Glauert H. Airplane Propellers - Aerodynamic Theory, W. F. Durand ed, Chapter XI. Berlin:Springer Verlag, 1935.
2. Glauert H. The Elements of Aerofoil and Airscrew Theory. 2nd ed. Cambridge University Press: Cambridge, England, 1947.
3. Abbott IH, Von Doenhoff AE. Theory of Wing Sections. Dover Publications Inc.: New York, 1959.
4. Horlok JH. Axial Flow Turbines. Butterworths: London, England, 1966.
5. Wilson RE, Lissaman PBS. Applied Aerodynamics of Wind-power Machines. Corvallis: Oregon State University, 1974.
6. Clancy LJ. Aerodynamics, John Wiley & Sons: New York, 1975.
7. Barlow JB, Rae WH, Pope A. Low Speed Wind Tunnel Testing. 3rd ed. John Wiley & Sons Inc.: New York, 1999.
8. Katz J, Plotkin A. Low Speed Aerodynamics. 2nd ed. Cambridge University Press: Cambridge, 2000.
9. Paraschivoiu I. Wind Turbine Design - With Emphasis on Darrieus Concept. Polytechnic International Press, 2002.
10. Leishman JG. Principles of Helicopter Aerodynamics. 2nd ed. Cambridge University Press: Cambridge, 2006.
11. Hansen MOL. Aerodynamics of Wind Turbines 2nd ed. Earthscan: London, 2008.
12. Glauert H. A General Theory of the Autogyro, ARCR R&M, No. 1111, 1926.
13. Darrieus GJM. Turbine having its rotating shaft transverse to the flow of the current. US patent 1,835,018, 8-12-1931.
14. Jacobs E, Sherman A. Airfoil characteristics as affected by variations of the Reynolds number. NACA Report 586, 1937.
15. Riegels FW. Aerofoil sections: results from wind-tunnel investigations, Theoretical foundation, Ch.7, London, Butterworths Ed., 1961.
16. Maskell EC. A Theory of the blockage effects on bluff bodies and stalled wings in an enclosed wind tunnel. ARC/R&M-3400, 1963.
17. Strickland JH. The Darrieus turbine: A performance prediction model using multiple streamtubes, SAND75-0431, 1975.
18. Muraca RJ, Stephens MV, Dagenhart JR. Theoretical performance of cross-wind axis turbines with results for a catenary vertical axis configuration,
NASA TMX-72662, 1975.
19. Blackwell BF, Sheldal RE, Feltz LV. Wind tunnel performance data for the Darrieus wind turbine with NACA0012 blades, Sandia National
Laboratories, Albuquerque, New Mexico, SAND76-0130, 1976.
20. Sheldahl RE, Blackwell BF. Free-air performance tests of a 5-metre-diameter Darrieus turbine. Sandia National Laboratories, Albuquerque, New
Mexico, SAND77-1083, 1977.
21. De Vries O. Fluid dynamic aspects of wind energy conversion. AGARDograph AG-243, 1979.
References - VAWT
22. Strickland J, Webster B, Nguyen T. A vortex model of the Darrieus turbine: an analytical and experimental study. Sandia National Laboratories,
Albuquerque, New Mexico, SAND79-7058, 1979.
23. Read S, Sharpe DJ. An extended multiple streamtube theory for vertical axis wind turbines, 2nd BWEA Workshop (April 1980).
24. Sheldahl RE, Klimas PC. Aerodynamic characteristics of 7 symmetrical airfoil sections through 180-degree angle of attack for use in aerodynamics
analysis of vertical axis wind turbine. Sandia National Laboratories: SAND80-2114, 1980.
25. Sheldahl RE, Klimas PC, Feltz LV. Aerodynamic performance of a 5-metre-diameter Darrieus turbine with extruded NACA-0015 blades. SAND800179, 1980.
26. Strickland J, Webster B, Nguyen T. A vortex model of the Darrieus turbine: an analytical and experimental study. Sandia National Laboratories,
Albuquerque, New Mexico, SAND81-7071, 1981.
27. Viterna LA, Corrigan RD. Fixed pitch rotor performance of large horizontal axis wind turbines, NASA CP-2230, 1981.
28. Madsen HAa. The actuator cylinder. A flow model for vertical axis wind turbines. Aalborg University Centre: Aalborg, Denmark, 1982.
29. Carne TG, Nord AR. Modal testing of a rotating wind turbine. Sandia National Laboratories, Albuquerque, New Mexico, SAND82-0631, 1982.
30. Oler JW, Strickland JH et Al. Dynamic stall regulation of the Darrieus turbine. Sandia National Laboratories, Albuquerque, New Mexico, SAND837029, 1983.
31. Wilson RE, Walker SN. Performance analysis of horizontal axis wind turbines, Oregon State Univ., Corvallis, OR, 1984.
32. Loeffler AL Jr, Steinhoff JS. Computation of wind tunnel wall effects in ducted rotor experiments. AIAA Journal of Aircraft 1985; 22, n.3: 188-192
33. Marini M, Massardo A, Satta A, Zamparo G. Theoretical aerodynamic methods for VAWT analysis. Energy Conversion Engineering Conference,
1989.
34. Homicz GF. Numerical simulation of VAWT stochastic aerodynamic loads produced by atmospheric turbulence: VAWT-SAL code. Sandia National
Laboratories, Albuquerque, New Mexico, SAND91-1124, 1991.
35. Tangler LJ, Ostowari C. Horizontal axis wind turbine post stall airfoil characteristics synthetization. Solar Energy Research Institute. SERI/TP-2574400 - UC Cathegory 261 - DE91002198.
36. Mandal C, Burton JD. The effects of dynamic stall and flow curvature on the aerodynamics of darrieus turbines applying the Cascade model. Wind
Eng 1994; 18 (6): 267–282.
37. Allet A, Paraschivoiu I. Viscous flow and dynamic stall effects on vertical-axis wind turbines. International Journal of Rotating Machinery 1995; 2,
n.1: 1-14
References - VAWT
38. Abdel Azim El-Sayed AF, Hirsch C and Derdelinckx R. Dynamics of vertical axis wind turbines (Darrieus Type), International Journal of Rotating
Machinery 1995; 2, n.1: 33-41.
39. Fortunato B, Dadone A, Trifoni V. A two-dimensional methodology to predict vertical axis wind turbine performance. Journal of Solar Energy
Engineering 1995; 117:187-193.
40. Mercker E, Wiedemann J. On the correction of the interference effects in open jet wind tunnels. SAE - 960671, 1996.
41. Allet S, Halle I, Paraschivoiu I. Numerical simulation of dynamic stall around an airfoil in darrieus motion. Journal of Solar Energy Engineering,
1999; 121: 69-76.
42. Lindenburg C. Stall coefficients. Aerodynamic airfoil coefficients at large angles of attack. IEA symposium on the aerodynamics of wind turbines.
(NREL, CO, USA: December 4-5, 2000).
43. Corten GP. Flow separation on wind turbine blades. PhD Thesis dissertation 2001. Utrecht University, The Netherlands.
44. Fujisawa N, Shibuya S. Observations of dynamic stall on Darrieus wind turbine blades. Journal of Wind Engineering and Industrial Aerodynamics
2001; 89, n. 2: 201–214.
45. Mikkelsen R, Sørensen JN. Modelling of wind tunnel blockage. Proc. CD-ROM Global Windpower Conference and Exhibition (2002).
46. Mertens S, van Kuik G, van Bussel G. Performance of a H-Darrieus in the skewed flow on a roof. Journal of Solar Energy Engineering 2003; 125:
433–440.
47. Timmer WA, van Rooij RPJOM. Summary of the Delft University wind turbine dedicated airfoils. AIAA-2003-0352, 2003.
48. Grignoux T, Gibert R et Al. Eoliennes en milieu urbain – Etat de l’art. ARENE, Ile-de-France, 2004.
49. Van Bussel GJW, Mertens S et Al. TURBY®: concept and realisation of a small VAWT for the built environment. The Science of making Torque
from Wind (Delft : 19-21 April 2004).
50. Hansen MH, Gaunaa M, Madsen HA. A Beddoes-Leishman type dynamic stall model in state-space and indicial formulations. Risø National
Laboratory. Risø-R-1354, 2004.
51. Montgomerie B. Methods for root effects, tip effects and extending the angle of attack range to ±180°, with application to aerodynamics for
blades on wind turbines and propellers. FOI Swedish Defence Research Agency. FOI-R—1305—SE, 2004.
52. Mertens S. Wind energy in the build environment. PhD Thesis dissertation 2006. Delft University of Technology, The Netherlands.
53. Van Der Tempel J. Design of support structures for offshore wind turbines. PhD Thesis dissertation 2006. Delft University of Technology, The
Netherlands.
References - VAWT
54. Ferreira CS, van Kuik G, van Bussel G. Wind tunnel hotwire measurements, flow visualization and thrust measurement of a VAWT in skew.
AIAA/ASME Wind Energy Symposium (2006).
55. Sørensen JN, Shen WZ and Mikkelsen R. Wall correction model for wind tunnels with open test section, AIAA Journal 2006; 44, n.8.
56. Claessens MC. The design and testing of airfoils for application in small vertical axis wind turbines. MSc Thesis dissertation 2006. Delft University
of Technology, The Netherlands.
57. Sant T. Improving BEM based aerodynamic models in wind turbine design codes. PhD Thesis dissertation 2007, Delft University of Tecnology.
58. Ferreira CS, van Bussel GJW et Al. 2D PIV visualization of dynamic stall on a vertical axis wind turbine. AIAA/ASME Wind Energy Symposium,
(2007).
59. Fitzgerald RE. Wind tunnel blockage corrections for propellers. MS Thesis 2007. University of Maryland, Department of Aerospace Engineering,
College Park MD.
60. Islam M, Ting D, Fartaj A. Aerodynamic models for Darrieus-type straight-bladed vertical axis wind turbines. Renewable & sustainable energy
reviews 2008. 12: 1087-1109.
61. Dixon C, Ferreira CS et Al. A 3D unsteady panel method for vertical axis wind turbines. EWEC Brussels (31 March – 3 April 2008).
62. Hofemann C, Ferreira CS, et Al. 3D Stereo PIV study of tip vortex evolution on a VAWT. EWEC, Brussels, (2008).
63. Vita L, Paulsen US et Al. “A novel floating offshore wind turbine concept” EWEC (Marseille : 16 - 19 March 2009).
64. Battisti L, Brighenti A, Zanne L. Analisi dell’effetto della scelta dell’architettura palare sulle prestazioni di turbine eoliche ad asse verticale. 64°
Congresso Nazionale ATI. L'Aquila. (6 - 11 September 2009).
65. Shen WZ, Zhang JH, Sørensen JN. The actuator surface model: a new Navier–Stokes based model for rotor computations. Journal of Solar Energy
Engineering 2009; 131.
66. Battisti L, Zanne L et Al. Aerodynamic measurements on a vertical axis wind turbine in a large scale wind tunnel. Proc. of ASME Turbo Expo 2010.
Glasgow, UK (14-18 June 2010).
67. Ferreira CS. The near wake of the VAWT. PhD Thesis dissertation 2009, Delft University of Tecnology.
68. The Eurocode 1, Part 2-4: Wind actions (ENV 1991-2-4: 1994).
69. http://www.sandia.gov/wind/topical.htm#VAWTARCHIVE
70. http://www.tozzinord.it/
Fly UP