Computational Modelling of Unsteady Rotor Effects
Duncan McNae – PhD candidate
Professor J Michael R Graham
Summary
Background
Numerical Model
Results
Ongoing Work
Summary
Background
Numerical Model
Results
Ongoing Work
Background – Blade loads and fatigue
 Fatigue life is a major consideration for rotor blade design
 Flow unsteadiness:
- Turbulent flow structures
- Waves
SeaGen rotor, Marine Current Turbines Ltd.
Background – Unsteady Flow Effects
Key principle:
– Dynamic Inflow
Fluctuations in flow speed cause changes in the loading on
the rotor, and therefore the strength of vorticity trailing into
the wake is not constant. The induced velocity field takes
time to develop as a result.
Burton et al. 2001
Burton et al
Summary
Background
Numerical Model
Results
Ongoing Work
Numerical Model
Numerical modelling techniques:
 Blade Element Momentum Theory (BEM)
 Potential Flow / Vortex Methods
 Computational Fluid Dynamics (CFD)
Numerical Model
Numerical modelling techniques:
 Blade Element Momentum Theory (BEM)
 Potential Flow / Vortex Methods
 Computational Fluid Dynamics (CFD)
Numerical Model – The Vortex Lattice Method
The blade–wake system can be represented
by a lattice of “vortex rings”, or “panels”.
This concept is derived from potential flow
theory.
Vortex rings are distributed on the blade
camber line, and the wake panels are free –
they move with the flow.
Representation of a vortex ring
Γ = circulation strength
A system of equations is formed with the use
of a zero-flow-normal boundary condition at
the center of each panel – the “collocation
points”.
Biot–Savart Law
Numerical Model – The wake
At each time step, a row of wake panels is
released from the trailing edge of the blade.
The circulation strength of each wake panel
is determined to be the strength of it's
corresponding panel on the trailing edge of
the blade.
At each time step, the nodes of the wake
lattice move with the local flow velocity,
(including the influence of all wake and blade
Panels) – this is computationally expensive.
Numerical Model – Loads
The loading contribution of each panel is calculated using the following:
This is a form of the unsteady Kutta-Joukowski equation.
Numerical Model – Validation
Validation of the unsteady vortex lattice method (VLM):
 Flat plate steady case
 Flat plate unsteady
 Rotor
Numerical Model – Validation
For a simple flat plate wing case (AR=8), the VLM has been
compared with “Tornado”, which is a similar program that has
been developed for aircraft design.
Numerical Model – Validation
Unsteady flat plate oscillations, vs Theodorsens theory:
Numerical Model
– Coefficient of Power:
– Coefficient of Thrust:
Numerical Model – Validation
 Validation of rotor loads against
BEM model
 Range of tips speed ratios (TSR)
 Inviscid flat plate approximation
for BEM coefficients
Rotor Blade Properties (3 bladed)
Root
Tip
Radius (m)
0.3
1
Chord (m)
0.2
0.1
Pitch Angle
30
0
Numerical Model – Demonstration
Numerical Model – Demonstration
Review
Background
Numerical Model
Results
Ongoing Work
Numerical Model – Results
Example load case:
Comparison of a step increase in flow velocity
against a step change in pitch angle.
The step change in pitch is -2 degrees.
The step change in free stream flow velocity
is set to match the thrust loading after the
transients have diminished. (1.08x increase)
The Imperial College turbine blade shape has
been used for the computational modelling.
– Ø 0.4m
– 2 Blades
– Free stream flow velocity = 1m/s
– Tip speed ratio = 5
Numerical Model – Results
Axial thrust force shown vs. time (in rotor rotations) for the two cases:
The simulations are first started impulsively, and allowed to reach a
steady condition before the changes are applied.
Numerical Model – Results
With the reverse case:
Pitch change:
+2 degrees
Flow change:
0.91
Numerical Model – Results
Induced velocity at the tip (μ = 0.95)
Numerical Model – Results
Induced velocity, thrust and angle of incidence at three radial sections:
Numerical Model – Results
Numerical Model – Results
Numerical Model – Results
Numerical Model – Results
Matching induced velocity in the tip region:
Free stream velocity after change = 1.2
Numerical Model – Results
Higher tip speed ratio example (TSR = 7)
Flow speed after change = 1.12 m/s
Numerical Model – Results
Higher Tip Speed Ratio – Induced velocities
Numerical Model – Results
Different turbine geometry, 3 blades.
Numerical Model – Results
Numerical work on flow oscillation:
- The vortex lattice code can be used to model sinusoidal flow oscillations
Numerical Model – Results
Numerical work on flow oscillation:
- The vortex lattice code can be used to model sinusoidal flow oscillations
Mean tip speed ratio: 5
Current number: 0.2
Free stream velocity: 1m/s
Review
Background
Numerical Model
Results
Ongoing Work
Experiment
 Imperial College Aeronautics
Department water flume
 Strain gauge measuring out of
plane bending moment is
located at blade root
 Wireless telemetry system
Ongoing Work
 Comparison of numerical model with common engineering
model – (e.g. Pitt and Peters for dynamic inflow)
 Numerical improvements
 Comparison of VLM with experimental data
 Investigate more load cases:
- wave motion
Conclusion
A vortex lattice method solver has been created to model flow
unsteadiness in power generating turbines
The effect of flow unsteadiness and dynamic inflow on rotor
loading has been demonstrated
Dynamic inflow has been shown to be significant for some
unsteady cases.
Thanks,
Duncan McNae
Reverse Case Mirrored
Numerical Model – Results
Flexible blade