Investigation of the effect of inflow turbulence on vertical axis wind turbine wakes

1

P Chatelain1, M Duponcheel1, S Zeoli2, S Buffin1, D-G Caprace1, G Winckelmans1 and L Bricteux2

1: Institute of Mechanics, Materials and Civil Engineering (iMMC) Université catholique de Louvain (UCL)

1348 Louvain-la-Neuve, Belgium

2: Mechanical Engineering Department Université de Mons (UMons)

7000 Mons, Belgium

Wake Conference 2017, May 30th - June 1st, 2017

Motivation and outline

• Methodology – The Vortex-Particle Mesh (VPM) method – Turbulent inlet for the VPM method

• Wake physics of a straight-bladed VAWT with turbulent inlet – Wake description – Sensitivity of wake statistics to turbulence properties

• Conclusions2

• VAWT wake physics: inherently unsteady aerodynamics • VAWT aerodynamic challenges

➡Use of an efficient Vortex Particle-Mesh (VPM) method to capture the large scale development of VAWT wakes

➡ From blade aerodynamics to far wake ➡ Influence of inflow turbulence on wake development and decay

Motivation

Outline

Airfoil Blade Rotor FarmWake

Vortex …

… Particle - Mesh method

➡ Efficiency, low dispersion, low dissipation + Immersed lifting lines with Dynamic stall model

Long time - large scale simulations of wake flows

3

�p =�

Vp

⇥ dV � ⇥p Vpxp

� = ⇥� u

�ijuij

��ij

Advection Differential operators Elliptic problems Remeshing of particles

Winckelmans, Encycl. Comp. Mech. 2004

Koumoutsakos, ARFM 2005

Chatelain et al., Flow Turb. Comb. 2013

interpolation

D!

Dt= r · (u!) + ⌫r2! +r ·

�⌫sgs

�r!s + (r!s)T

��

• 3-D synthetic turbulent velocity fields pre-computed using the Mann algorithm (WindSimu)

• Translated into vorticity field

• … then vortex particles fed into domain ( Lagrangian treatment = no time-step constraint )

• Inflow resolution < computational domain resolution allows long turbulent wind boxes (requires interpolation)

Turbulent inflow from pre-simulation

4

uz = U1

k!k

uturb box

! !turb box

Turbulent inflow from time-correlated planes

• Generate MANN 2D velocity planes • Perform the time correlation

• Compute vorticity planes • Map vorticity on particles

5

Hybrid Particle-Mesh Vortex Method

• Hybrid

• Efficient– Compact support of vorticity

– “Eulerian” CFL condition waived -> Lagrangian CFL

• Accurate– Low dispersion, high-order interpolation, finite-differences– Lagrangian distortion handled by particle reinitialization

3

dxp

dt= u(xp)

d↵p

dt=

�(! ·r)u(xp) + ⌫r2!(xp)

�vp

r2 = �!u = r⇥

Particles: Advection Mesh: RHS evaluations

uij

!ij

Particle-Mesh

Mesh-Particle interpolation

+

Hybrid Particle-Mesh Vortex Method

• Hybrid

• Efficient– Compact support of vorticity

– “Eulerian” CFL condition waived -> Lagrangian CFL

• Accurate– Low dispersion, high-order interpolation, finite-differences– Lagrangian distortion handled by particle reinitialization

3

dxp

dt= u(xp)

d↵p

dt=

�(! · r)u(xp) + ⌫r2!(xp)

�vp

r2 = �!u = r ⇥

Particles: Advection Mesh: RHS evaluations

uij

!ij

Particle-Mesh

Mesh-Particle interpolation

+

VPM DOMAIN

! = r⇥ (u+ u0)

(U 0)m = a (U 0)m�1 +p

1� a2 (u0)m

a = exp

✓��t

⌧t

◆

H-type VAWT configuration

• 3 straight-bladed VAWT

6

D = 3 m

h = 4.5 mc = 0.1725 m

U = 11 m/s

D/Δx Ldomain/D Ngrid

96 20 > 237M

Airfoil NACA 0015 + Dynamic stall

� =nc

D= 0.1725

AR =h

D= 1.5

� =!R

U= 3.21

Re =�Uc

⌫= 4.0⇥ 105

NCPUS Time to Sol.

2560 ~24h to 40h(depending on TI)

Inlet turbulence

• 4 cases : no turbulence and 3 different inflow turbulences

7

x/D

y/D

x/D

x/D

y/D

y/D

ux

/U1

ux

/U1

ux

/U1

TI = 2%, L = D/3, isotropic

TI = 7.5%, L = D/3, isotropic

TI = 7.5%, L = D, anisotropic, Γ = 3.9

Power curve and investigated operating point

8

CP =P

12⇢AU3

� =!R

U

Low resolution runs for whole curve (512 CPUS, 2h)

High resolution runs for present study

TI = 2%, iso, Cp = 0.346

TI = 7.5%, iso, Cp = 0.342

TI = 7.5%, aniso, Cp = 0.357

TI = 0% Cp = 0.339

Coalescing tip vortices

sheetsd�

dt

Recirculation

Volume rendering of k!k

TI = 0%

Volume rendering of k!k

TI = 2% iso

Volume rendering of k!k

TI = 7.5% iso

Volume rendering of k!k

TI = 7.5% aniso

Vorticity magnitude (side view)

TI = 0

TI = 7.5% aniso

TI = 7.5% iso

TI = 2% iso

Vorticity magnitude (top view)

TI = 0

TI = 7.5% aniso

TI = 2% iso

TI = 7.5% iso

Forces and Angle of attack

15

Uwind✓

Angle of attackTypical asymmetry between upstream and downstream parts of a revolution. Oscillations in the downstream part due to the wakes shed upstream

Tangential forceNormal force

TI = 0%

Forces and Angle of attack

16

Uwind✓

With low turbulent, almost no effect on the mean quantities and only small variations around the mean

TI = 2% iso

Angle of attack

Tangential forceNormal force

TI = 0%

Forces and Angle of attack

17

Uwind✓

As the turbulence increases, the envelopes increases but the mean profiles are only slightly affected

TI = 2% iso

TI = 7.5% iso

Angle of attack

Tangential forceNormal force

TI = 0%

Forces and Angle of attack

18

Uwind✓

The envelopes are significantly larger and, in the downstream part of a revolution, the wake signature is no longer present

TI = 2% iso

TI = 7.5% iso

TI = 7.5% aniso

Angle of attack

Tangential forceNormal force

TI = 0%

-1

0

1

y/D

0

0.5

1

u/U

-1

0

1

y/D

-2 0 2 4 6 8 10 12 14 16x/D

0

0.02

0.04

TKE/U

2

Mean wake : horizontal planes

19x/D

Recirculation region where the wake transitions to turbulence

x

y

-2

0

2

y/D

0

0.5

1

u/U

-2

0

2

y/D

-2 0 2 4 6 8 10 12 14 16x/D0

0.01

0.02

0.03

0.04

TKE/U

2

TI = 2% iso

TI = 0%

Faster transition and higher TKE

Recirculation topology modified

-2

0

2

y/D

0

0.5

1

u/U

-2

0

2

y/D

-2 0 2 4 6 8 10 12 14 16x/D0

0.01

0.02

0.03

0.04

TKE/U

2

20x/D

x

y

-2

0

2

y/D

0

0.5

1

u/U

-2

0

2

y/D

-2 0 2 4 6 8 10 12 14 16x/D0

0.01

0.02

0.03

0.04

TKE/U

2

TI = 7.5% iso

TI = 7.5% aniso

No recirculation region, very high TKE and large wake spreading

Faster transition and higer TKE

Mean wake : horizontal planes

u/U

∞

0

0.5

1

y/D-2 -1 0 1 2

z/D

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

TKE/U

2 ∞

0

0.01

0.02

0.03

0.04

Mean wake : vertical planes

21

x/D = 1

x/D = 7x/D = 10

x/D = 15

z

y

Uwind

0

0.5

1

u/U

∞

-1 0 1y/D

-1.5

-1

-0.5

0

0.5

1

1.5

z/D

0

0.01

0.02

0.03

0.04

TKE/U

2 ∞

u/U

∞

0

0.5

1

y/D-2 -1 0 1 2

z/D

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

TKE/U

2 ∞

0

0.01

0.02

0.03

0.04

u/U

∞

0

0.5

1

y/D-2 -1 0 1 2

z/D

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

TKE/U

2 ∞

0

0.01

0.02

0.03

0.04

TI = 2% iso

TI = 7.5% iso

TI = 7.5% aniso

TI = 0%

Asymmetric wake, most TKE is due to tip vortices

u/U

∞

0

0.5

1

y/D-2 -1 0 1 2

z/D

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

TKE/U

2 ∞

0

0.01

0.02

0.03

0.04

Mean wake : vertical planes

22

x/D = 5

x/D = 15

z

y

Uwind

0

0.5

1

u/U

∞

-1 0 1y/D

-1.5

-1

-0.5

0

0.5

1

1.5

z/D

0

0.01

0.02

0.03

0.04

TKE/U

2 ∞

u/U

∞

0

0.5

1

y/D-2 -1 0 1 2

z/D

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

TKE/U

2 ∞

0

0.01

0.02

0.03

0.04

u/U

∞

0

0.5

1

y/D-2 -1 0 1 2

z/D

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

TKE/U

2 ∞

0

0.01

0.02

0.03

0.04

TI = 2% iso

TI = 7.5% iso

TI = 7.5% aniso

TI = 0%

Faster decay of the wake due to the turbulence. In the last case, the wake has already much decayed

u/U

∞

0

0.5

1

y/D-2 -1 0 1 2

z/D

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

TKE/U

2 ∞

0

0.01

0.02

0.03

0.04

Mean wake : vertical planes

23

x/D = 10

x/D = 15

z

y

Uwind

0

0.5

1

u/U

∞

-1 0 1y/D

-1.5

-1

-0.5

0

0.5

1

1.5

z/D

0

0.01

0.02

0.03

0.04

TKE/U

2 ∞

u/U

∞

0

0.5

1

y/D-2 -1 0 1 2

z/D

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

TKE/U

2 ∞

0

0.01

0.02

0.03

0.04

u/U

∞

0

0.5

1

y/D-2 -1 0 1 2

z/D

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

TKE/U

2 ∞

0

0.01

0.02

0.03

0.04

TI = 2% iso

TI = 7.5% iso

TI = 7.5% aniso

TI = 0%

The asymmetry persists for long distances but is reduced with increased turbulence levels

0 50 100 150 200 250 300 350x

-20

-15

-10

-5

0

5

10

15

20

y

Comparison of the two turbulent inflow methods

24

3-D Mann Precursor

Time-correlated 2-D planesThe methods give similar results even though the 3-D precursor gives higher TKE in the wake but a smaller variation of AoA

✓

↵

-2

0

2

x2

0 5 10 15y2

0.02

0.04

z2

-2

0

2

x2

0 5 10 15y2

0.02

0.04

z2

3-D Mann Precursor

Time-correlated 2-D planes✓

x/D

y/D

TKE/U21

y/D

Conclusions

• Application of Vortex Particle-Mesh method to the investigation of VAWT wakes with various inflow turbulence (different intensities and structures)

• Complex wake topology and dynamics due to unsteady loading of the blades - Asymmetric wake, presence of streamwise corner vortices

and a recirculation region

• Inflow turbulence accelerates the development of the instabilities of tip vortex interactions, leading to an accelerated wake decay

• The strong anisotropic case shows large scale wake meandering and the recirculation region is no longer present

• Comparison with HAWT wakes25

Wakes: upcoming projects

• Learning and collective intelligence for optimized operations in wake flows

• Reproduction of bird flying gaits and self-organization into formations

26

ERC Consolidator GrantWake Op Collhttps://sites.uclouvain.be/wakeopcoll2017-2022

Concerted Research Action RevealFlighthttps://sites.uclouvain.be/revealflight2017-2022

27

Acknowledgments

The PPM (Parallel Particle Mesh) library

Simulations performed on the Cenaero - CECI Tier-1 Infrastructure funded by the Walloon Region, Grant No. 1117545

UCL CISM - Institut de Calcul Intensif et de Stockage de Masse CECI - Consortium des Equipements de Calcul Intensif

Lifting lines, immersed in VPM

28

Lift

Circulation

↵

Bound vorticity

Aerodynamic performance

Dynamic Stall

Shed vorticity Added to bulk vorticity

↵

Flow relative to lifting line

Line configuration (chord)

↵ urel