Verification
Checked against references, including the less good results
These are steady RANS results, the kind every practical CFD tool gives. Below is how close they come to textbooks, measurements and EN 1991-1-4, case by case, with the deviations that look good and the ones that don't.
Within 4 %
5 of 7 scored cases
The pipe expansion, the cube, the silo, pipe friction at Re 10⁶ and the flat plate. The bend counts once, on the medium mesh.
Less good
Friction −8.2 %, the bend up to −11.4 %
Pipe friction reads low at Re 10⁵, and the bend's K moves with the mesh. Both are explained below.
Last full run
28 October 2026
The flow reference suite, on a 12-core desk PC. The pipe-bend example was run again on 29 October.
Flow inside parts
Pipes, expansions and bends
| Case | Laminaro | Reference | Source | Deviation |
|---|---|---|---|---|
| Sudden pipe expansion, aird/D = 0.5 · 2.1 M cells | K 0.5594 | K 0.5625 | Borda–Carnot, (1 − (d/D)²)² | −0.5 % |
| Pipe friction, water, Re 10⁶smooth pipe · 387 k cells | f 0.01141 | f 0.01164 | Colebrook (1939) | −2.0 % |
| Pipe friction, air, Re 10⁵smooth pipe · 387 k cells | f 0.01651 | f 0.01799 | Colebrook (1939) | −8.2 % |
| 90° bend, R/D 1.5, water, Re 2·10⁵60 D inlet · coarse / medium / fine: 0.34 / 0.99 / 2.97 M cells | K 0.1744 K 0.1756 K 0.1684 | K 0.17–0.210.19 used for the deviation | Idelchik, diagram 6-1 (friction excluded) | −8.2 % −7.6 % −11.4 % |
| 90° bend, first set-upshort 20 D inlet · 603 k cells | K 0.1481 | K 0.19 | Idelchik, diagram 6-1 | −22.1 % |
The bend, honestly. All three meshes land inside or just under Idelchik's 0.17–0.21, but they don't converge in a clean order, so we can't extrapolate a mesh-independent value. The first set-up's −22 % was the measuring method, not the flow: over its short inlet, straight-pipe friction is about 82 % of the measured loss, and subtracting Colebrook's friction instead of the solver's own made the bend look too small. The long-inlet set-up above measures the friction in developed flow.
Pipe friction. At Re 10⁶ Laminaro is 2 % under Colebrook; at Re 10⁵ it's 8 % under. In a study where friction dominates (a long straight pipe at a low velocity), expect the pressure drop to read a few percent low.
Flow around parts
Bluff bodies and wind on the ground
| Case | Laminaro | Reference | Source | Deviation |
|---|---|---|---|---|
| Cube, face-on, free stream2.2 M cells | Cd 1.055 | Cd 1.05 | Hoerner (1965) | +0.5 % |
| Silo on open groundlog-law wind · 1.07 M cells | cf 0.3538 | cf 0.350 | EN 1991-1-4 §7.9, mean-flow reference | +1.1 % |
| Flat plate, face-on, free stream1.8 M cells | Cd 1.216 | Cd 1.17 | Fail, Lawford & Eyre (1957); Hoerner (1965) | +3.9 % |
| Cube on the ground, wind face-onSilsoe 6 m cube · coarse / medium / fine: 0.56 / 1.50 / 3.96 M cells | Cd 0.988 Cd 0.953 Cd 0.930 | —mesh study | Richards & Hoxey (2012) | GCI 5.7 % |
The silo and the Eurocode. EN 1991-1-4 gives cf = cf0·ψλ = 0.753 × 0.66 = 0.497, to be used with the wind pressure at the top of the silo, a deliberately safe simplification. A silo in a real log-law wind feels less: for this profile the mean dynamic pressure over the height is 70.45 % of the value at the top, so the fair comparison is 0.497 × 0.7045 = 0.350. Reading the slenderness as λ = l/b instead of 2l/b gives 0.329, and Laminaro would then be +7.5 %.
The cube on the ground is a mesh-convergence check rather than a scored case: the drag falls from 0.988 to 0.930 as the mesh is refined, the grid convergence index on the fine mesh is 5.7 %, and the extrapolated value is 0.888. It shows how much the mesh level moves a bluff-body force, which is why Laminaro reports a ± and suggests a finer mesh when it matters.
Method
How the cases are run
- Each case is written and solved by the same pipeline that runs your studies, with OpenFOAM's steady incompressible solver and the turbulence model Laminaro would pick.
- Deviation = (Laminaro − reference) / reference. The reference and its source are named on every row.
- The whole suite runs again whenever a release changes the physics or the way cases are written.
- Where a reference turned out not to be like-for-like (the Eurocode silo, the short-inlet bend), the reason is written down rather than the number quietly replaced.
Honest tolerances
What to expect on your part
| Kind of result | Typical deviation |
|---|---|
| Pipe friction | a few % |
| Fittings: bends, expansions, loss coefficients | ± 10 % |
| Bluff-body forces: drag, lift, Cd | ± 10–20 % |
These are the limits of steady RANS turbulence modelling, not of one product. Most cases above land well inside them. Two don't: pipe friction at Re 10⁵ is outside "a few %", and the bend on the fine mesh is just outside ± 10 %.