This propeller boundary layer tutorial shows the prism layers, explains y+ and links both to the chosen preset.

Start with tutorial no. 1

All of a blade's friction drag, and a good part of its stall, plays out in a very thin film of fluid stuck to its surface. This film is called the propeller boundary layer, and the way the mesh describes it determines what the calculation can or cannot say.

The experiment : mesh the same geometry with two neighbouring presets that mainly differ in their boundary layers — on a wing, Wing Level 3 and Level 4, which share the same background grid, the same surface and edge levels, and differ only by snapping and layers (10 against 12) —, and look at what changes at the leading edge and in the velocity profile near the wall.

• Prerequisites : tutorial no. 3 recommended, it lays out the preset vocabulary ;
• Duration : two meshes and one calculation ;
• What you get out of it : knowing which preset your question requires — and which would be a waste.

• Tutorial outline:

1. What a boundary layer physically is
2. y+, in one useful definition
3. What each preset stacks
4. Looking at the layers in the viewer
5. Seeing a separation
6. Choosing based on the question asked

1: What a boundary layer physically is

At the surface of a blade, the fluid sticks : its velocity there is zero. A little further out, it moves at the flow velocity. Between the two, the velocity goes from zero to its full value : this is the boundary layer, and the gradient it contains is what produces the friction.

This layer has a structure. Right next to the wall, a very thin zone where viscosity dominates. Further out, a logarithmic zone where turbulence takes over. Further still, the connection to the free stream.

A CFD calculation has two ways of handling it : resolve it, by placing enough cells inside it to describe the gradient ; or model it, by placing the first cell in the logarithmic zone and letting a wall law make the connection. The first is expensive and gives access to separation ; the second is more than enough for global forces.

The surface mesh of a multi-blade marine propeller (the propeller of tutorial no. 13): the triangulated skin on which the prism layers are stacked; the layers themselves are not visible at this scale

2: y+, in one useful definition

y+ is a wall distance made dimensionless by the flow's own quantities. What matters, in practice, is the regime your first cell falls into :

• y+ on the order of 1 : the first cell is in the viscous zone. The boundary layer is resolved, separation is accessible. This is the domain of the finest meshes ;
• y+ between 30 and 100 : the first cell is in the logarithmic zone, and a wall law handles the connection. Global forces are correct, the fineness of separation is not ;
• in between : the buffer zone, where neither treatment is optimal. This is the region you try to avoid.

Heliciel's wing presets fix the number of layers, their expansion ratio and the thickness of the last one : they do not aim at a specific y+. The y+ obtained depends on the velocity and the chord of your case, and is verified on the calculation. One measurement exists : on a hydrofoil calculated at Level 2, the first cell actually delivered gave a y+ of about 20.8, i.e. in the buffer zone described above. The software manual also notes that, without a transition model, aiming at a y+ of 1 would bring nothing more than a y+ of the order of 20 : OpenFOAM's wall laws are not very sensitive to it.

3: What each preset stacks

A preset fixes three things for the layers : their number, their expansion ratio — the thickness ratio from one layer to the next — and the thickness of the last one.

Note the direction of the expansion ratio : the closer it is to 1, the closer the layer thicknesses are to each other, and so the smoother the transition to the volume mesh. A high ratio saves cells but creates a step between the last layer and the first volume cell.

On the propeller side, the progression is wider : the Express level stacks no layers at all — it's for geometry diagnostics, not friction — while the Reference level stacks twenty at a ratio of 1.04. For a free rotor, Levels 1 to 8 stack 0, 1, 2, 2, 3, 6, 10 and 20 layers respectively.

The "Other presets available" list: each Libre Level 1 to 8 fixes surface refinement, background mesh, rotating interface (NCC) and number of boundary layers (BL, 0 to 20) in one go. These are not settings to hunt down one by one

4: Looking at the layers in the viewer

After meshing : Show menu, uncheck 3D model, check CFD mesh (Cyan), then zoom in on the leading edge with the scroll wheel. The layers appear as a stack of thin slats parallel to the surface, distinct from the volume mesh.

Three defects can be spotted by eye :

• layers missing in places : the stacking could not happen, usually at a sharp angle or a narrow gap ;
• layers crushed at the trailing edge, where two surfaces come close together ;
• a step between the last layer and the volume, a sign of an expansion ratio too ambitious for the available cell size.

On a propeller, one zone deserves particular attention : the blade tip, and even more so the gap between the blade tip and a duct. This is where the boundary layers of two surfaces meet, where the cells become tiny, and where an unsteady calculation eventually chokes. The Show > Highlight problem cells menu points them out.

Overview of a propeller in its duct, skin coloured by pressure (scale in Pa on the right). It locates the walls where the boundary layer forms; the wall velocity gradient is not resolved in this image

5: Seeing a separation

When the boundary layer can no longer climb back up the adverse pressure gradient on the upper surface, it separates. Three tell-tale signs, in the Results tab :

• the Flow lines leave the surface and form a recirculation zone ;
• a velocity cut near the wall shows a reversal of the flow direction ;
• the surface pressure flattens out downstream of the separation point, instead of rising steadily.

A warning is needed here : a separation observed on a wall-law mesh (high y+) is not a measured separation, it is a suggested one. The turbulence model used for wings underestimates separation, and a wall law lacks the required fineness. If separation is your topic, you need to move up a preset — and know that even then, once stall has set in, the result stays qualitative.

Streamlines around the marine propeller of tutorial no. 13: they wind into the wake. This is the view to inspect for separation (lines leaving the surface and recirculating); here none is clearly identifiable

6: Choosing based on the question asked

There is no absolute right level : there is a level suited to the question.

And the rule that overrides all the others : check the mesh convergence. As long as your quantity moves when you refine, you are measuring the mesh. When it no longer moves, you are measuring the propeller.

The collection of twenty CFD tutorials

« Previous: Turbulence models  |  Next: Reading a pressure map »

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+ (you are here)
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
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, choice of rotation speed, performance curves. CFD comes after them, to verify and to see.