This aircraft propeller CFD software tutorial compares cruise and static thrust, and shows why the latter is harder.

Start with tutorial no. 1

An aircraft propeller does not work the same way on take-off and in cruise — and this is not just a matter of setting : it is a different physics, which the aircraft propeller CFD software handles with different requirements.

The exercise : calculate the same propeller at two operating points, in cruise then at zero advance speed, and observe what makes the second one significantly trickier.

• Prerequisites : an aerial propeller designed in Heliciel — aircraft, ultralight, drone ;
• Duration : two calculations, one of which will need a Phase 2 ;
• What you get out of it : knowing when Phase 1 is enough, and when it is not.

• Tutorial outline:

1. The advance ratio, in one line
2. First calculation: cruise
3. Second calculation: static thrust
4. Why static thrust requires Phase 2
5. Blade tip speed and the incompressibility assumption
6. The case of small propellers

1: The advance ratio, in one line

It all comes down to one number. The advance ratio J compares the distance the aircraft travels during one propeller revolution to that propeller's diameter : J = V / (n·D), with V the advance speed, n the rotation speed in revolutions per second and D the diameter.

In cruise, J is high : the propeller advances quickly through the fluid, and the wake it produces is carried far behind it before the next blade arrives. At zero speed, J equals zero : nothing carries the wake away, and it stays there.

This difference governs everything else, and in particular the choice of calculation phases.

2: First calculation — cruise

File > New CFD case (from current model) with the project's cruise operating point. Flow tab : check the flow speed and the rotation speed.

Preset Free Level 5 — Study for a quantitative result. Mesh, then Phase 1.

This calculation is the easy case. The wake is evacuated, the interaction between one blade and the previous one's wake is weak, and the steady calculation in the rotating frame represents the situation well. When J is high, as here (J = 1.87), Phase 1 is enough : Phase 2 would not change much and would cost far more (on the static case treated below, 18 min of Phase 2 against 1 min 18 for Phase 1). Note that this does not mean Phase 1 matches the designer. On the screenshot of this cruise case, the CFD blade thrust (776 N) stays about 35 % below the BEM value (1,186 N) : this BEM/CFD gap exists in cruise too, and is read with tutorial no. 6.

In the Results tab, check Flow lines : the helical wake goes straight downstream, regular, and moves away. This is the visual signature of a well-advanced operating point.

In cruise: the wake goes straight downstream and moves away. Each blade works in clean fluid

3: Second calculation — static thrust

Take the same propeller, the same rotation speed, and set the flow speed to zero. This is the static thrust configuration : ground test, vertical take-off, a multirotor's hover.

Create a new case and calculate Phase 1. You will get a result : the induced velocity field through the rotor disc is correctly calculated, and the integrated forces are of the right order of magnitude, but not stabilised (table below).

But look at the Flow lines : there is no longer any upstream flow to carry anything away. Fluid only arrives because the propeller sucks it in, and the blade-tip vortices go nowhere. They build up around the rotor disc and form a helical vortex tube that stays in place.

At static thrust: the vortices no longer leave. They coil around the disc and stay there

4: Why static thrust requires Phase 2

The steady calculation freezes the blades' angular position. As long as the wake moves away, this approximation is benign. When the wake stays, it stops being so : each blade actually crosses the vortex left by the previous one, and this interaction is unsteady by nature.

This is why Phase 2 becomes recommended at low or zero advance speed. It makes the mesh actually rotate, each blade genuinely crosses the structures left by the others, and the resulting forces carry the real oscillations.

Running Phase 2 is described in tutorial no. 5.

The same static-thrust point, calculated in Phase 1 then in Phase 2 : the real rotation still removes 18 % of thrust from Phase 1. That is the gap the frozen rotation ignored, and the reason why, at static thrust, the value to keep is the Phase 2 one.

5: Blade tip speed and the incompressibility assumption

A caveat specific to fast aerial propellers, and one better known before launching a calculation than after : the solver used treats an incompressible flow. As a general rule, this assumption holds up to a Mach number of about 0.3, i.e. roughly 100 m/s in air. The cruise case shown above (Mach 0.322 at the blade tip, 109.6 m/s) already exceeds it slightly.

Now, what matters for a blade is not the advance speed, it is the relative tip speed, which combines advance and rotation speed. A two-metre propeller at 2 700 rpm already has a blade tip above 280 m/s.

Heliciel displays the blade tip speed in its BEM project : that is the figure to check before launching a CFD calculation. Beyond the incompressibility domain, the calculation will still return a result, and that result will underestimate drag and torque, with no message warning you of it. It is a model limitation, not a setting error.

6: The case of small propellers

Drone propellers pose the opposite problem : they are not too fast, they are too small. Two consequences :

• The Reynolds number is low. Since the turbulence model does not predict the transition between laminar and turbulent regimes, it treats the whole chord as turbulent even though a real part of it is not : the computed drag is pessimistic. The order of magnitude remains useful, the absolute value should be taken with this caveat ;
• Blade thickness is tiny. On a 250 mm rotor, a blade is a few millimetres thick, while the background cell is much larger. The fast presets simply do not resolve it : it is invisible to the mesh. The quantitative floor remains Free Level 5 — Study, and there is no shortcut.

A multirotor in hover actually stacks both difficulties from this chapter : zero advance speed and small scale. It is the most demanding case in the aerial domain, and the one where comparing against BEM is most instructive.

Results panel of a cruise case (1.80 m propeller, 7 blades, J = 1.87, blade tip Mach 0.322): thrust, torque, shaft power and efficiency. This is not a drone propeller: it illustrates how forces are computed, valid for any aerial propeller

The full set of twenty CFD tutorials

« Previous: Fan in a closed duct  |  Next: The optimisation loop »

1. First CFD propeller simulation
2. Reading the OpenFOAM case folder
3. Choosing the mesh preset
4. The MRF zone and Phase 1
5. Phase 2 with sliding mesh
6. Comparing BEM and CFD
7. Reading the convergence of a run
8. Turbulence models
9. Boundary layer and y+
10. Reading a pressure map
11. Where the forces come from
12. Checking an airfoil polar
13. Marine propeller and cavitation
14. Wind turbine and tidal turbine
15. Fan in a closed duct
16. Aircraft propeller, cruise and static thrust (you are here)
17. The optimisation loop
18. Calibrating on a reference
19. From the hull to the propeller
20. The deliverable calculation file

This series accompanies the Heliciel design tutorials, which cover the BEM part: blade design, rotation speed choice, performance curves. CFD comes after them, to verify and to see.

Short, jargon-free version of this tutorial: the aircraft propeller CFD case study, cruise and static thrust in pictures.