Development of Vortex Filament Method for Wind Power ... · PDF fileProf. Spyros Voutsinas**,...

DEVELOPMENT OF VORTEX FILAMENT METHOD

FOR WIND POWER AERODYNAMICS

PhD Candidate

Hamidreza Abedi*, [email protected]

Supervisors

Prof. Lars Davidson*, [email protected]

Prof. Spyros Voutsinas**, [email protected]*Division of Fluid Dynamics, Department of Applied Mechanics, Chalmers

University of Technology, Goteborg Sweden**Fluid Section, School of Mechanical Engineering, National Technical

University of Athens, Athens, Greece

OUTLINE

1 Motivation

2 Difficulty

3 Goal

4 Theory & modeling

5 Aerodynamic load calculation

Results

6 Wake aerodynamics

Results

7 Turbulent & sheared inflow

Results

8 Conclusion & future work

9 Acknowledgments

PhD Disputation, Hamidreza Abedi 15-April-2016 2 / 28

MOTIVATION

Aerodynamic load as the largest loads acting on wind turbine blades.

Acquiring an accurate-fast method to predict aerodynamic loads.

Preparing input data for the aeroelastic and drive train system.

Decreasing the operating and maintenance costs.


MODELING OF ROTOR AERODYNAMICS (PROS & CONS)

1 Blade Element Momentum (BEM) Method

Based on 1D ideal rotor disc (drag device) extended for the rotating disk

with wake rotation.. Most common tool for rotor aerodynamics. (Computationally cheap) Including a number of empirical and semi-empirical correction factors such

as yaw misalignment, dynamic inflow, finite number of blades, etc. (Low

Accuracy)

2 Computational Fluid Dynamics (CFD)

Applying Navier-Stokes solver for rotor aerodynamics. (High Accuracy) Advanced tool for rotor aerodynamics. (Computationally expensive)


GOAL

Preparing an Accurate & Fast design tool to predict unsteady

aerodynamic loads.

Developing Vortex Method instead of BEM and CFD. Handling any type of steady and unsteady inflow condition (uniform,

sheared and turbulent flows). Handling the yaw misalignment. Predicting the viscous effects (separation and stall conditions) using

Dynamic Stall model. Handling different type of movements such as pitching, coning and tilting.


FLOW OVER THE WIND TURBINE BLADE

Lift & Drag forces as the source of generated Power and Thrust.


GOVERNING EQUATIONS

Euler’s equations (for incompressible and inviscid fluid)

∇ ·v = 0

∂v

∂t+v ·∇v =−

∇p

ρ

Inviscid vorticity transport equation

∂Ω

∂t+v ·∇Ω = (Ω ·∇)v

Inviscid transport of vorticity (Helmholtz’s theorem)

Strength of a vortex tube is constant along its length. Irrotational motion of an inviscid fluid started from rest remains irrotational. A vortex line cannot end in the fluid; it must form a closed path, end at a

solid boundary or go to infinity.

⋆ Vorticity can only be generated at solid boundaries.⋆ Replacing the solid surface in contact with fluid by a distribution of vorticity.


VECTOR ANALYSIS OF FLUID DYNAMICS

(HELMHOLTZ’S DECOMPOSITION)

v = (∇×Ψ)+∇Φ = vω +vp

vω: a velocity field due to the vorticity in the flow

vp: an irrotational velocity field

Ψ: a vector potential

Φ: a scalar potential

Ω: vorticity (∇×v = Ω)

v ind (x) =−1

4π

∫V

(x −x′)×Ω

| x −x′ |3

dx′ (Biot-Savart’s law)


VORTEX FILAMENT METHOD, BLADE MODELING

Lifting line, Replacing the blade with varying strength vortex filament

Lifting surface, Replacing the blade surface with vortex panel(s)

Lifting line Lifting surface


VORTEX FILAMENT METHOD, WAKE MODELING

Prescribed Vortex Wake (forced wake geometry)

Free Vortex Wake (self-development wake geometry)


VORTEX FILAMENT METHOD, FREE WAKE METHOD

Advantage

Self-development of wake geometry, suitable for unsteady conditions. Applicable for a broad range of operating conditions such as yaw condition,

atmospheric turbulence and etc.

Disadvantage

Computationally expensive than prescribed vortex wake.


DIFFERENT APPROACHES

Lifting Line Prescribed Wake (LLPW)

Vortex Lattice Prescribed Wake (VLPW)

Vortex Lattice Free Wake (VLFW)

LLPW VLPW VLFW


Aerodynamic Load Calculation


VLFW METHOD, LOAD CALCULATION

Standard Potential Method.

2D Static Airfoil Data Method (Coupling the potential solution to the

tabulated airfoil data).

Dynamic Stall Method (Modification of the aerodynamic coefficients for

unsteady operating conditions).


MEASUREMENT, MEXICO TURBINE

Number of blades 3

Diameter [m] 4.5

Rotational speed [rad/s] 44.45

Hub height [m] 5.49

Cone angle [deg] 0

Pitch angle [deg] -2.3

MEXICO wind turbine specifications & radial distribution of blade elements


RESULTS (MEXICO TURBINE, NON-YAWED INFLOW)

0.2 0.4 0.6 0.8 150

100

150

200

250

300

350

r/R [−]

Fn[N

/m]

0.2 0.4 0.6 0.8 1

100

200

300

400

500

ag replacements

r/R [−]

Fn[N

/m]

0.2 0.4 0.6 0.8 1100

200

300

400

500

600

700

800

900

r/R [−]

Fn[N

/m]

Distribution of normal forces along the blade at left: V∞ = 10.01 m/s, middle: V∞ = 14.93 m/s, right:

V∞ = 23.96 m/s, and Ω = 44.45 rad/s, : Potential, : Viscous, : Experiment

0.2 0.4 0.6 0.8 10

5

10

15

r/R [−]

Ft[N

/m]

0.2 0.4 0.6 0.8 1

10

20

30

40

50

60

r/R [−]

Ft[N

/m]

0.2 0.4 0.6 0.8 10

50

100

150

200

r/R [−]

Ft[N

/m]

Distribution of tangential forces along the blade at left: V∞ = 10.01 m/s, middle: V∞ = 14.93 m/s, right:

V∞ = 23.96 m/s, and Ω = 44.45 rad/s, : Potential, : Viscous, : Experiment


Wake Aerodynamics


MEASUREMENT, MEXICO TURBINE, YAWED INFLOW,

RADIAL TRAVERSES

Radial traverses & Positions of blade 1 at different azimuthal angles


RESULTS (MEXICO TURBINE, YAWED INFLOW)

-3 -2 -1 0 1 2 310

11

12

13

14

15

ExpSim

x [m]

w[m

/s]

-3 -2 -1 0 1 2 3

0

2

4

6

8

10

12

14

16

18

ExpSim

x [m]w[m

/s]

-3 -2 -1 0 1 2 3-6

-4

-2

0

2

ExpSim

x [m]

u[m

/s]

-3 -2 -1 0 1 2 3-5

-3

-1

1

3

5

7

9

11

ExpSim

x [m]

u[m

/s]

-3 -2 -1 0 1 2 3-0.75

-0.25

0.25

0.75

1.25ExpSim

x [m]

v[m

/s]

-3 -2 -1 0 1 2 3-2

-1

0

1

2

3

4ExpSim

x [m]

v[m

/s]

Velocity components, Left:upstream (-0.15m) and Right: downstream

(+0.15m) of the rotor, position of blade 1 at 0 , Exp: Experiment, Sim:

Simulation

-3 -2 -1 0 1 2 310

11

12

13

14

15

ExpSim

x [m]

w[m

/s]

-3 -2 -1 0 1 2 34

6

8

10

12

14

16

18

ExpSim

x [m]

w[m

/s]

-3 -2 -1 0 1 2 3-4.5

-2.5

-0.5

1.5

3.5

ExpSim

x [m]

u[m

/s]

-3 -2 -1 0 1 2 3-8

-6

-4

-2

0

2

4

6

8

10

ExpSim

x [m]

u[m

/s]

-3 -2 -1 0 1 2 3-0.75

-0.25

0.25

0.75

1.25ExpSim

x [m]

v[m

/s]

-3 -2 -1 0 1 2 3-2.5

-1.5

-0.5

0.5

1.5

2.5

ExpSim

x [m]

v[m

/s]

Velocity components, Left:upstream (-0.15m) and Right: downstream

(+0.15m) of the rotor, position of blade 1 at 60 , Exp: Experiment,

Sim: Simulation


MEASUREMENT, MEXICO TURBINE, YAWED INFLOW,

AXIAL TRAVERSES

-2

0

2

4

6

8

-6-4-2024

x [m]

z[m

]

Axial traverses & Blades Tip vortices


RESULTS (MEXICO TURBINE, YAWED INFLOW)

-6 -4 -2 0 2 4 64

6

8

10

12

14

16

Exp

Sim

z [m]

w[m

/s]

-6 -4 -2 0 2 4 6-2

0

2

4

6

8

10

12

14

ExpSim

z [m]w[m

/s]

-6 -4 -2 0 2 4 6-4

-2

0

2

4

6ExpSim

z [m]

u[m

/s]

-6 -4 -2 0 2 4 6-5

-3

-1

1

ExpSim

z [m]

u[m

/s]

-6 -4 -2 0 2 4 6-2

-1

0

1

2

3

Exp

Sim

z [m]

v[m

/s]

-6 -4 -2 0 2 4 6-1.5

-0.5

0.5

1.5ExpSim

z [m]

v[m

/s]

Positive outboard (x=+1.84797m, AB) and midboard (x=+1.37697m,

CD) traverses velocity components at the rotor plane, Exp:

Experiment, Sim: Simulation

-6 -4 -2 0 2 4 66

8

10

12

14ExpSim

z [m]

w[m

/s]

-6 -4 -2 0 2 4 67

9

11

13

15ExpSim

z [m]

w[m

/s]

-6 -4 -2 0 2 4 6-7

-6

-5

-4

-3

-2

-1

0

ExpSim

z [m]

u[m

/s]

-6 -4 -2 0 2 4 6-4

-3

-2

-1

0

1

ExpSim

z [m]

u[m

/s]

-6 -4 -2 0 2 4 6-4

-3

-2

-1

0

1

2

ExpSim

z [m]

v[m

/s]

-6 -4 -2 0 2 4 6-2.5

-1.5

-0.5

0.5

1.5

2.5ExpSim

z [m]

v[m

/s]

Negative outboard (x=-1.84797m, GH) and midboard (x=-1.37697m,

EF) traverses velocity components at the rotor plane, Exp:

Experiment, Sim: Simulation


Turbulent & Sheared Inflow


WIND FIELDS


NREL TURBINE, TURBULENT INFLOW

Evolution of the wake under the turbulent velocity field generated by LES


RESULTS (NREL 5-MW TURBINE)

20 40 60 80 1002

2.1

2.2

2.3

2.4

2.5

2.6

t [s]

p[M

W]

20 40 60 80 1001.8

1.85

1.9

1.95

2

t [s]p[M

W]

Time history of power production at mean wind speed 8 m/s at hub height and Ω = 1.0032 rad/s, left:

wind field generated by LES (unsteady), right: wind field generated by power law (steady), : mean


CONCLUSION & FUTURE WORK

A vortex-based computational method for predicting unsteady aerodynamic loads on wind

turbine rotor blades was implemented.

It was found out that the VLFW method is the most accurate method.

Potential solution of VLFW method was coupled to tabulated airfoil data and a

semi-empirical model to take into account the viscosity and the dynamic stall effects.

The implemented VLFW method was validated against the BEM and CFD methods, the

GENUVP code by National Technical University of Athens (NTUA), Hono turbine

measurement data and MEXICO wind tunnel measurements with a quite good

agreement.

Geometrical parameters such as the blade discretization (both spanwise and chordwise

sections), the discretization of the wake elements, the wake truncation length and vortex

core size affects the accuracy of the VLFW model.

The VLFW method was successfully used to study the influence of turbulent and sheared

inflows.

Employing an iterative method the so-called decambering approach for the post-stall

prediction could provide better approximation for viscous effects than the 2D static airfoil

data method.

Including the nacelle and tower in the study of wake aerodynamics is crucial.

Coupling the VLFW code into an aeroelastic solver would be necessary.


ACKNOWLEDGMENTS

This work was financed through the Swedish Wind Power Technology Centre

(SWPTC).

The technical support of National Technical University of Athens (NTUA) is

greatfully acknowledged.

MEXICO data: The consortium which carried out the EU FP5 project Mexico,

’Model rotor EXperiments In COntrolled conditions’.

CFD data for NREL 5-MW turbine: Denmark Technical University (DTU), Danish

Energy Agency (EUDP project j.nr. 64011-0094) and the Ministry of Science

(DSF project Sagsnr. 12-130590).


Thanks for Your Attention


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