CFD Tutorial no. 11 — Drag and lift CFD

Accounting for the forces

This drag and lift CFD tutorial shows where the forces come from, and how to read their breakdown.

Drag and lift CFD: tutorial for calculating the forces

CFD Tutorial no. 11 of 20. The actions described here are those of the HELICIEL CFD tool window, opened from Heliciel: they assume the PRO CFD/BEM extension 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 in the software.

A CFD solver does not calculate forces. It calculates pressure and velocity fields; the forces are derived from them, by integration over the surfaces. Understanding this step changes the way you read a drag and lift CFD result — and lets you catch the most common mistakes.

Prerequisites: a completed calculation, on a wing or a propeller;
Duration: half an hour of reading;
What you get out of it: knowing exactly what each number in the results table covers.

Tutorial outline:

From pressure to force
Pressure and friction, two parts to distinguish
Wing case: lift, drag, Cx and Cz
Propeller case: thrust and torque
Reading the force table
Classic interpretation mistakes

1: From pressure to force

On each small mesh face touching the object, the fluid exerts two actions: a pressure, perpendicular to the face, and a shear stress, tangent to the face. Multiplied by the face area, they give an elementary force.

The total force is the sum of these contributions over all the faces of a given boundary. The moment is calculated the same way, by multiplying each elementary force by its lever arm relative to the chosen axis.

This mechanism has a practical consequence: the accuracy of the forces depends directly on the quality of the surface mesh. A blade described by faces that are too large integrates an averaged pressure, and a poorly meshed boundary layer distorts the shear stress — and therefore the entire friction drag.

diagram of normal pressure and tangential shear on a surface mesh face
On each face: a perpendicular pressure and a tangential shear. The forces are the sum of all of this

2: Pressure and friction, two parts to distinguish

Heliciel PRO CFD/BEM separates, for each boundary, the part due to pressure and the viscous part. This separation is not cosmetic: it is the first diagnostic tool for a result.

On a blade, the thrust must come mostly from pressure. It is the difference between the pressure side and the suction side that does the work;
The viscous part represents friction. It is small on a well-profiled blade, and it is always resistive;
On a hub or a duct wall, a large viscous part signals parasitic friction. If it dominates the axial moment, the power it consumes is not propulsion, it is loss.

Hub friction and duct-wall friction are not set from the interface: Heliciel decides according to the case type — slip hub in a closed duct, friction hub on a free rotor — and writes its choice into the case's heliciel_benchmark.txt, where it stays readable. A reopened case keeps the value it had. This is a typical example of what presets take care of: a decision that, if wrong, would distort the torque without ever making the calculation fail.

3: Wing case — lift, drag, Cx and Cz

For a wing case, the flow goes toward +X, and the breakdown is direct: drag is the component of the force along X, lift is the component along Z. The coefficients follow by dividing by the dynamic pressure and the reference area.

Drag itself breaks down into two terms that CFD separates naturally:

pressure drag, or form drag, linked to the pressure distribution around the airfoil and to any separation;
friction drag, the integral of the wall shear stress.

Watch the convention: this breakdown into drag and lift only makes sense for wing cases, the only ones that use these quantities. For a propeller, the flow goes toward −X and the reading is different.

table of a wing's Cx and Cz coefficients with pressure and friction separated
A wing's coefficients, with the pressure part and the friction part separated

4: Propeller case — thrust and torque

For a propeller, two quantities matter: the axial force along the rotation axis, which is the rotor's thrust or drag depending on whether it propels or captures energy; and the moment about that same axis, which is the torque.

Torque multiplied by angular speed gives the shaft power. This is the junction point with the mechanical design: motor, gearbox, shaft, blade structure.

The sign distinguishes the two families of machines. A propulsive propeller consumes torque; a capturing rotor — wind turbine, tidal turbine, turbine — produces one. An unexpected sign flip is almost always explained by the axis convention, never by the physics: remember that the flow goes toward −X for a propeller while the rotation axis stays +X.

One last point on what is integrated: CFD sums over all declared solid boundaries — blades, hub, and depending on the case, duct or inserted object. Heliciel's BEM, by contrast, returns the forces of the blades. Do not compare a total to a part.

table of a propeller's forces with axial force and moment per boundary rotor hub duct
The forces of a rotor, boundary by boundary: blades, hub, duct. The total is not the blade

5: Reading the force table

The Matrix Me! button on the Results tab opens the case's numerical table: the aerodynamic quantities, boundary by boundary, with their breakdown.

In Phase 2, a methodological point matters. Unsteady forces oscillate at the blade-passing frequency; the value that counts as the result is the average over the last revolution, not the value of the last time step. Quoting a single instant means quoting the peak or the trough of an oscillation.

This same force convergence serves as the calculation's stopping criterion: the monitor compares the average over two sliding windows and cleanly stops when the relative variation drops below its threshold. Forces and convergence are therefore the same subject, seen from two sides — tutorial no. 7 covers the other side.

comparison of CFD forces and BEM forces for the same propeller with the per-boundary breakdown
CFD forces alongside BEM forces: what each total covers must be known before comparing

6: Classic interpretation mistakes

Four traps, all encountered in practice:

Comparing a CFD total to a BEM blade. The hub drags and rubs: including it is enough to create a discrepancy that will wrongly be blamed on the method;
Forgetting the reference area. A coefficient without its reference area is not a coefficient, it is a number;
Quoting an instantaneous Phase 2 force while presenting it as a steady-state result;
Ignoring numerical diffusion. A first-order upwind scheme — the one used by the Stable preset, and by Phase 2 — smooths gradients and tends to overestimate drag. That is the price of stability, and it must be known when comparing two calculations run with different schemes.

The natural next step: tutorial no. 12, which applies all of this to an isolated airfoil and compares it against the polars in Heliciel's database.

The collection of twenty CFD tutorials

« Previous: Reading a pressure map | Next: Checking an airfoil polar »

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