CFD tutorial no. 12 — Aerodynamic airfoil CFD

The airfoil database, put to the test

This aerodynamic airfoil CFD tutorial compares a polar from Heliciel's database against a three-dimensional calculation.

Aerodynamic airfoil CFD: tutorial comparing against the airfoil database

CFD tutorial no. 12 of 20. The steps described here are those of the HELICIEL CFD Tool window, opened from Heliciel: they assume the PRO CFD/BEM upgrade is active. The preset values quoted are those of the catalogue shipped with the software; the numerical results depend on your geometry and your operating point, and should be read from the software.

Heliciel's BEM relies on polars : for each airfoil, lift and drag as a function of angle of attack and Reynolds number. These polars come from the software's airfoil database, computed by its numerical wind tunnel. An aerodynamic airfoil CFD calculation lets you put them to the test — and above all understand why the two can never match exactly.

The exercise : take an airfoil from the database, turn it into a high-aspect-ratio wing, calculate it at several angles of attack, and compare.

Prerequisites : an airfoil available in Heliciel's airfoil database ;
Duration : one calculation per angle of attack — allow half a day for a meaningful sweep ;
What you get out of it : knowing in which range to trust a polar, and where it stops being valid.

Tutorial outline:

Where the database polars come from
Building the test wing
Sweeping the angle of attack
Comparing, and correcting for aspect ratio
Stall, difficult ground
What this check is used for

1: Where the database polars come from

The polars in Heliciel's airfoil database are produced by its numerical airfoil wind tunnel, a boundary-layer solver coupled to a panel method, rebuilt and optimized for Heliciel. They describe an infinite-span airfoil, at a given Reynolds number, with a fixed transition criterion.

This origin explains both their strengths and their limits. A polar of this kind is extremely fast to obtain, it handles the laminar-to-turbulent transition correctly, and it's reliable in the linear range. On the other hand, by construction it ignores anything three-dimensional, and it loses reliability once stall has set in.

An airfoil CFD calculation, on the other hand, resolves a three-dimensional flow around an actual wing : it captures the tip effects, but its turbulence model doesn't predict transition. The two approaches are therefore complementary in their flaws, which is the best reason to compare them.

Heliciel airfoil database interface with the Cl Cd polar of a selected airfoil
Heliciel's airfoil database and an airfoil's polar: the starting point for the comparison

2: Building the test wing

In Heliciel, build a rectangular wing, with a high aspect ratio, carrying the airfoil to be tested over its whole span, with no twist. The higher the aspect ratio, the closer the centre section gets to the polar's two-dimensional behaviour.

Then File > New CFD case (from the current model). In the Flow tab, set the velocity to obtain the Reynolds number your polar was established at : it's the comparability condition most often forgotten.

Check the Symmetry box if you want to halve the mesh : the domain is then truncated at the mid-plane, and the loaded model is a half-wing whose span is already correct. Remember that this box locks the Insert tab — no consequence here, since nothing is being inserted.

Preset : Wing Level 3 · Fine at minimum. A polar is decided by differences of a few percent ; a coarse mesh doesn't have the resolution needed to settle it.

3: Sweeping the angle of attack

Each angle of attack is one calculation. Set the angle of attack in the flow parameters, mesh, calculate, read off lift and drag in the Matrix Me! table, then move to the next one.

A useful sweep : from 0° to 12° in 2° steps in the linear range, then from 12° to 20° in 1° steps to approach stall. Plan on ten to fifteen calculations.

Note at each point : the angle of attack, lift, drag, cell count, convergence status. That last one isn't a luxury : near stall, some points converge poorly, and you need to know which ones before you plot a curve.

overlay of the database polar and the CFD-calculated points on the same graph
The database polar and the CFD points on the same graph: the gap can be read, and it can be explained

4: Comparing, and correcting for aspect ratio

Overlay your calculated points on the database polar. Three discrepancies are expected, and you need to attribute them correctly before concluding anything :

The lift slope is lower in CFD. This is the finite-aspect-ratio effect : your wing has tips, the polar doesn't. This gap isn't an error, it's corrected by lifting-line theory — the same one Heliciel's BEM applies ;
Drag is higher in CFD. Two causes add up : the induced drag from the tip vortices, absent from the polar, and the lack of transition in the turbulence model, which makes the whole chord turbulent when a real portion of it is laminar ;
The stall angle differs. See the next step.

The right way to compare is therefore to strip the aspect-ratio effect out of your CFD results before comparing them against a two-dimensional polar. Without this correction, you're measuring the planform of your test wing, not the airfoil.

5: Stall, difficult ground

This is the range where both methods become fragile, each in its own way.

The polar loses its reliability once separation has set in : the method it comes from isn't made for a massively separated flow.

Steady-state CFD, meanwhile, inherits the limits of its turbulence model : the wing model underestimates separation, and beyond roughly fifteen to twenty degrees, the result becomes qualitative — it indicates a trend, not a value. A real stall is also often unsteady, which a steady-state calculation cannot represent by construction.

The practical consequence : for a clearly stalled airfoil, don't ask either method for a number. Use CFD to see where separation begins — the flow-lines and velocity-cut displays show it clearly — not to establish a coefficient.

The pressure distribution along the chord: the plateau that gives separation away

6: What this check is used for

Three concrete uses for a successful comparison :

Qualify an airfoil before using it on a blade : know in which angle-of-attack range its polar can be trusted, and where it stops being trustworthy ;
Investigate a BEM/CFD gap on a propeller : if the airfoil's polars have been checked, the gap comes from elsewhere — three-dimensional corrections, tip effects, or the mesh ;
Document an airfoil choice in a study file, with two independent methods rather than one.

Heliciel's airfoil database has its own editing tools — creating families by progressively morphing one airfoil into another, editing existing polars — which let you correct a clearly aberrant point or substitute experimental readings for calculated values. A CFD check is a good prerequisite for this kind of intervention : it tells you whether intervention is warranted.

pressure field around a NACA airfoil calculated in CFD with the stagnation point and the upper-surface suction peak
The pressure field around the airfoil: what the polar sums up in two numbers

The collection of twenty CFD tutorials

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