Computational Modelling of Unsteady Rotor Effects

1. Computational Modelling of Unsteady Rotor Effects Duncan McNae – PhD candidate Professor J Michael R Graham

2. Summary Background Numerical Model Results Ongoing Work

3. Summary Background Numerical Model Results Ongoing Work

4. 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.

5. 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 Burton et al. 2001

6. Summary Background Numerical Model Results Ongoing Work

7. Numerical Model Numerical modelling techniques: • Blade Element Momentum Theory (BEM) • Potential Flow / Vortex Methods • Computational Fluid Dynamics (CFD)

8. Numerical Model Numerical modelling techniques: • Blade Element Momentum Theory (BEM) • Potential Flow / Vortex Methods • Computational Fluid Dynamics (CFD)

9. 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. 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”. Representation of a vortex ring Γ = circulation strength Biot–Savart Law

10. 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.

11. Numerical Model – Loads The loading contribution of each panel is calculated using the following: This is a form of the unsteady Kutta-Joukowski equation.

12. Numerical Model – Validation Validation of the unsteady vortex lattice method (VLM): • Flat plate steady case • Flat plate unsteady • Rotor

13. 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.

14. Numerical Model – Validation Unsteady flat plate oscillations, vs Theodorsens theory:

15. Numerical Model – Coefficient of Power: – Coefficient of Thrust:

16. 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)

17. Numerical Model – Demonstration

18. Numerical Model – Demonstration

19. Review Background Numerical Model Results Ongoing Work

20. 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

21. 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.

22. Numerical Model – Results With the reverse case: Pitch change: +2 degrees Flow change: 0.91

23. Numerical Model – Results Induced velocity at the tip (μ = 0.95)

24. Numerical Model – Results Induced velocity, thrust and angle of incidence at three radial sections:

25. Numerical Model – Results

26. Numerical Model – Results

27. Numerical Model – Results

28. Numerical Model – Results Matching induced velocity in the tip region: Free stream velocity after change = 1.2

29. Numerical Model – Results Higher tip speed ratio example (TSR = 7) Flow speed after change = 1.12 m/s

30. Numerical Model – Results Higher Tip Speed Ratio – Induced velocities

31. Numerical Model – Results Different turbine geometry, 3 blades.

32. Numerical Model – Results Numerical work on flow oscillation: - The vortex lattice code can be used to model sinusoidal flow oscillations

33. 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

34. Review Background Numerical Model Results Ongoing Work

35. Experiment • Imperial College Aeronautics Department water flume • Strain gauge measuring out of plane bending moment is located at blade root • Wireless telemetry system

36. 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

37. 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.

38. Thanks, Duncan McNae

39. Reverse Case Mirrored

40. Numerical Model – Results Flexible blade