methods and challenges in cfd modelling of tidal...
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Methods and Challenges in CFD Modelling of Tidal-Stream Turbines
David Apsley
With acknowledgements to:
Umair Ahmed, Imran Afgan,
Tim Stallard, Peter Stansby
Contents 1. Fully-resolved turbine geometry
The ReDAPT project
Inflow turbulence
Time-dependent loads
2. Actuator representations of turbines Simple actuator disk
Blade-element momentum theory
Rotating actuator lines
3. Waves Free-surface methods
Wave types (regular, solitary, spectral, focused)
4. Some computational tools
5. Future work
The ReDAPT Project • Reliable Data Acquisition Platform for Tidal
– full-scale field measurements (Edinburgh)
– CFD simulations (Manchester)
• Our aim: use CFD to investigate how realistic flow features influence turbine loading:
– shear flow
– turbulence
– (waves)
– finite depth
– support tower
The TGL/Alstom/GE Turbine
CFD Code and Modelling
• Code_Saturne
• RANS and LES for turbulence.
• Sliding-mesh interface
• Synthetic turbulence at inflow
Synthetic Eddy Method (SEM)
N
eddy
eddyL
eddy
jiji faN
u1
)(ε1
)( xxx
)()()()(3
zyx
BL
L
zf
L
yf
L
xf
L
Vf x
Lx, Ly, Lz = integral length scales for component i
aij = Lund coefficients (Cholesky decomposition aTa of Reynolds stress tensor)
εjeddy = normalised Gaussian random numbers
Compounded with the mean-velocity
eddy box
nominal inlet plane
Mean Flow
Turbulence
Reynolds stresses Length scales
Prescribed Inflow Statistics
Flow-Field
Zero inflow turbulence
Synthetic inflow turbulence - based on channel-flow simulation
Synthetic inflow turbulence - factored to match data at hub-height
Loads (Phase-Averaged; Whole Rotor)
Thrust Power
AU
thrustCT 2
021 ρ
AU
velocityangulartorqueCP 3
02
1 ρ
Loads ( One Cycle; One Blade)
Loads (Blade Bending Moment)
Grey: experiment
Green: zero onset turbulence
Purple: synthetic turbulence
ARU
momentbendingCM 2
021 ρ
Load Spectrum
Grey: experiment
Green: zero onset turbulence
Purple: synthetic turbulence
harmonics of rotor frequency
approach-flow turbulence
blade-generated turbulence
Observations From ReDAPT
In low onset turbulence, LES and RANS (k-w SST) produce similar – phase-averaged loads – low-frequency fluctuations (support tower; velocity shear)
Turbulence has a small effect on mean power
LES necessary to predict high-frequency blade-generated turbulent fluctuations
LES with realistic inlet turbulence necessary to predict full spectrum of frequencies.
The STREAM Code
• Finite-volume incompressible solver
• Multiblock structured meshes
• Surface-fitting moving mesh for free surface / sediment
• Advanced RANS turbulence models
• Pressure-velocity coupling: SIMPLE
• Parallelisation: domain decomposition by block; MPI
Actuator Representations
Replace the turbine ... by the reaction forces it imparts on the flow
Actuator disk
Blade-element momentum theory
Rotating actuator lines
Actuator Representations
Advantages :
Simple background mesh Simple turbine representation Easy to add, move or redesign turbines Decouples ambient flow from turbine
Disadvantages:
Limited near-field resolution No blade-generated turbulence Limited 3-d and boundary-layer effects
Rotating Actuator Lines
2/33
σ/)(
πσ
e)(
22p
p
xx
Fxf
))(Δ(ρ 2
21
DDLLrelp CCrcU eeF
Requires: - lift and drag coefficients CL(α,r), CD(α,r)
- chord distribution c(r)
- blade twist distribution β(r)
uax
urel
u +ray
D
L
F
dr
r
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
12.0 12.5 13.0 13.5 14.0 14.5 15.0
Po
we
r co
eff
icie
nt
(CP)
Time (tD/U)
Upstream turbine
Downstream turbine
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
12.0 12.5 13.0 13.5 14.0 14.5 15.0
Po
we
r co
eff
icie
nt
(CP)
Time (tD/U)
Upstream turbine
Downstream turbine
Turbines in Tandem
Waves – Free-Surface Methods
Smoothed particle hydrodynamics (SPH)
Volume of fluid (VOF)
Level-set methods
Surface-following (ALE)
f = 0
f = 1
f = 0
0 < f < 1
Free-Surface Movement in STREAM
Surface vertices interpolated from intermediate control points
Aim: no net volume flux through free surface
tVswept Δ)(Δ Au
Adjust control points iteratively
*ΔΔ)(Δ sweptcontrolh VtzA Au
Wave Types
Focused (“NewWave”)
)ωcos(η tkxA kdgk tanhω2
)ω(sechη 2 tkxA 34/3 dAk
)(/ω Adgkc
Regular
Solitary
Spectral n
nnnn txkaA )ωcos(η n random
n
n
nn
S
Sa
ωΔ
ωΔ
focusnfocusnn txk ω
])ω
ω(
4
5exp[
ω
ω
16
5)ω( 42
5
4
p
mo
pHS
Tools
Spline fitting of turbine profile
Vortex panel methods for CL(α), CD(α)
Blade-element momentum theory (BEMT) code
2-d finite-volume aerofoil code
Vortex Panel Methods
U0
i
i-1
u =0n
rut
π
Γ
N
j
j
ij
ij
i N
M
0
0 ΓUUFlow field:
Kutta condition: 0ΓΓ0 N
Future Work
Validation and improvement of actuator-line models Arrays of tidal turbines Turbines in waves Variable speed and pitch; control and operation