Triangular mesh of a rotor zone with three blades, beside a close-up of the refined mesh around a circular cavity in a blade — Computational mesh: the rotating zone with the three blades (left), and the boundary-layer mesh around the dimple (right). Own simulation.

Dimpled blades for a vertical-axis wind turbine

Dr Mohammad Ghaffari · 2017 · Industry

Context

A vertical-axis wind turbine manufacturer wanted more power from its straight-bladed Darrieus rotor. Darrieus turbines are simple to build and work in any wind direction, but they are less efficient than horizontal-axis machines and weak at low speed. One proposed fix is to cut a small cavity, or dimple, into each blade. The project tested whether a dimple helps, and if so where it should sit, how big it should be and what shape it should have.

My role

I was the CFD engineer on the project, from model set-up through to the blade recommendation.

Approach

Two-dimensional unsteady simulation of a three-bladed, straight-bladed rotor in OpenFOAM, with a sliding mesh for the rotating zone and the SST k-ω turbulence model.
Rotor of 1.03 m diameter and 1.46 m height with NACA 0021 blades of 0.0858 m chord, at a wind speed of 9 m/s, matching a reference wind-tunnel test.
Mesh-independence check on four grids. The third grid gave a power coefficient of 0.0143 against 0.0147 on the finest, and was used for all runs.
Parameter sweep of the dimple: position (pressure or suction side, at a quarter, half or three quarters of the chord), diameter (2–8% of chord) and shape (circular, square or triangular).

Figures

Plot of power coefficient against tip speed ratio, simulation curve against experimental points — Power coefficient against tip speed ratio, compared with the wind-tunnel results of Castelli et al. (2011). Own simulation.

Power coefficient curves for the plain blade and four dimple diameters — Power coefficient for dimple diameters of 2% to 8% of chord, against the plain NACA 0021 blade. Own simulation.

Four plots of torque against rotation angle, dimpled blade against plain blade — Rotor torque over three revolutions at four tip speed ratios, dimpled blade against plain NACA 0021. Own simulation.

Two greyscale vorticity fields around a three-bladed rotor, dimpled blades beside plain blades — Vorticity around the rotor at the same instant, dimpled blades (left) and plain blades (right), at the optimum tip speed ratio. Own simulation.

Outcome

The simulated power curve follows the wind-tunnel data of Castelli et al. (2011) up to a tip speed ratio of 2.6. Beyond that the blades stall, and the two-dimensional model over-predicts power.
The best blade had a circular dimple of 8% of chord on the pressure side, near the leading edge.
With that blade, the power coefficient rose by 18% at the optimum tip speed ratio (λ = 2.6) and by 25% on average, against the plain NACA 0021 blade.
Torque swings over each revolution were smaller, and the vortices shed from the dimpled blades were smaller and died out faster.

Vertical-axis wind turbine
OpenFOAM
Sliding mesh
SST k-ω

Commercial project. Details generalised.