How much energy does it take from the wind, with what load on the mast? The wake in pictures.

All the CFD case studies

A wind turbine in CFD does the opposite of a propeller: instead of pushing the air, it lets itself be pushed and takes energy from it. The Heliciel designer draws the rotor and announces the shaft power; this case study shows, with the CFD (Computational Fluid Dynamics, numerical simulation of the flow) bench, the wind slowing down as it crosses the rotor, the wake widening behind it, and the two numbers that matter to the designer of a wind machine: the power recovered and the load the rotor transmits to the mast.

The 4 m three-blade rotor in perspective. The streamlines, coloured by speed, go from yellow-green (free wind) to blue (slowed) as they cross the rotor, and spread apart behind it: the stream tube widens. This is the signature of a machine that takes energy from the fluid, the opposite of a propeller whose jet narrows.

• Contents:

1. The machine and the wind
2. The two faces of the blade
3. The wind turbine wake in CFD: the wind slows down
4. Power and load on the mast: the wind turbine CFD figures
5. Take-aways

1: The machine and the wind

The CFD computation was run with the Level 5 preset: 235,000 cells, 7 min 20 of meshing, then 1 min 04 for the first phase (frozen rotor, simulated rotation) and 29 minutes for the second (really rotating rotor), on a 6-core desktop PC. The second phase stopped on its own, forces settled.

2: The two faces of the blade

The rotor seen facing the wind, as from the ground in front of the machine. The whole exposed face is yellow-red: the wind presses on it. The red border along the leading edges marks where the air strikes the blade head-on.

The same rotor seen from behind, nacelle side. The back of the blades is blue, in suction, especially towards the blade tips. It is the difference between the two faces, pressed on the yellow side and sucked on the blue side, that turns the rotor.

A wind turbine blade is a wing that rotates: the windward face is its lower surface, the back its upper surface. The colours say where the load concentrates: towards the blade tips, where the relative speed is highest. This is where the blade must be most carefully made, and where it wears.

3: The wind turbine wake in CFD: the wind slows down

Vertical cut of the speed, side view. The wind arrives from the right in yellow-green (free wind, 5.5 m/s). Behind the rotor, on the left, a large blue zone: the wind has lost part of its speed, this is the energy the rotor has taken from it. The slowed wake is wider than the rotor and extends far behind: a second turbine placed there would receive less wind.

Cut perpendicular to the axis, just behind the rotor: the blue-green disc of slowed wind, surrounded by free wind in yellow-green. Its diameter already exceeds that of the rotor.

These two pictures illustrate what every wind turbine designer knows from theory and rarely sees: the rotor cannot stop the wind, it slows it down. If it stopped it, nothing would pass through any more and it would recover nothing. Betz's theory places the best compromise: a wind slowed to two thirds of its speed at the rotor, and to one third far behind it. The colours of the section do not allow this ratio to be read precisely; they show the phenomenon, and the bench probe gives the value at each point.

4: Power and load on the mast: the wind turbine CFD figures

The results panel after the first phase: 223 N of thrust on the blades, 19.1 N·m of torque, 334 W at the shaft, power coefficient Cp 0.28. The designer's reference is recalled above: 231 N and 35.9 N·m. The bench's percentage deviations refer to the blades, the only part the designer computes.

Two very different results in the same table, and they must be read separately:

• The thrust is confirmed to within 3 %. It is the axial load the wind exerts on the rotor, the one that loads the mast, the foundations and the bearing. On the blades, the two CFD phases give 223 and 225 N against the designer's 231 N; the hub adds 6 N, and the total load transmitted to the mast is 229 to 231 N. To size the structure, this is the figure to take, and it is solid.
• The torque, however, is much lower in CFD: 20 N·m against 36. The bench announces it itself in its alerts: "torque not reliable". On a wind turbine, the torque is a small difference between the pressure force that drives the blades and their friction. The bench adds that "the fully turbulent assumption remains debatable": on a blade with a 28 cm chord at 5.5 m/s, part of the air layer attached to the blade is probably laminar, which the turbulence model does not represent. This is the most probable explanation of the gap, not a certainty. The CFD power is therefore not to be retained here: the nominal power remains the designer's, and CFD is worth it for the thrust, the wake and the pictures.

This is a general lesson, valid beyond this case: CFD is not uniformly reliable on every quantity. Axial loads, integrated over the whole surface, are robust; torques of lightly loaded machines depend on fine details. The Heliciel CFD bench flags this in its alerts, and this page repeats it so that nobody replaces a catalogue power by a poorly resolved CFD torque.

5: Take-aways

• The rotor slows the wind, it does not stop it: the velocity cut shows the blue wake, wider than the rotor, extending far behind.
• The thrust is confirmed to within 3 % by CFD on the blades, in both phases: 229 to 231 N on the mast, hub included, for this 4 m rotor in a 20 km/h wind. This is the structural figure.
• The CFD torque is to be read with the bench alert: underestimated here, it does not replace the designer's power on a lightly loaded machine.
• About 37 minutes in total on a desktop PC: 7 min 20 of meshing, then 30 minutes for the two phases of the computation.

The CFD case studies

« Previous: Drone propeller CFD: hover  |  Next: Tidal turbine CFD: a 16 m rotor in the current »

1. Understanding a CFD result in five pictures
2. Boat propeller CFD: thrust and pressure on the blades
3. Aircraft propeller CFD: cruise and static thrust
4. Drone propeller CFD: hover
5. Wind turbine CFD: power and wake (you are here)
6. Tidal turbine CFD: a 16 m rotor in the current
7. Ducted fan CFD: duct and radiator
8. Wing CFD and hydrofoil: lift and drag

These case studies complement the Heliciel design tutorials (in French), which cover the BEM side: blade design, choice of speed, performance curves. To go further into the method, the technical collection of twenty tutorials remains available.