Guide
Two-equation RANS models need turbulence quantities at every inlet: the turbulent kinetic energy k and a dissipation quantity (ε or ω). You rarely measure these directly. You know a turbulence intensity and a length scale, or a viscosity ratio. This calculator converts what you know into the values your solver needs, and produces ready-to-paste boundary-condition snippets.
With freestream velocity U, turbulence intensity I (as a fraction), turbulent length scale Lt and the model constant Cμ = 0.09:
Pick whichever pair of quantities you actually have:
The calculator derives k, ε, ω and the remaining quantity consistently from the pair you provide.
| Situation | Turbulence intensity I | Length scale Lt |
|---|---|---|
| Wind tunnel, clean freestream, external aerodynamics | 0.1 – 1 % | A few percent of the body length is a common assumption |
| Fully developed pipe or duct flow | Estimate: I ≈ 0.16 ReDh−1/8 (roughly 3–5 % for Re from 10⁴ to 10⁶) | Lt ≈ 0.07 Dh |
| Flow behind grids, in turbomachinery, in combustors and engine ports | 5 – 20 % | Set by the size of the upstream obstruction or passage |
| Atmospheric boundary layer, urban flows | 10 – 30 % near the ground | Depends on the height above ground and roughness |
The factor 0.07 is based on the maximum mixing length in fully developed turbulent pipe flow, which is why it is applied to the pipe or hydraulic diameter. When you have no information, 5 % intensity with a length scale of about 5–10 % of the inlet dimension is a common default, but the results are then only as good as that assumption.
| Air, external flow | Water in a 100 mm pipe | |
|---|---|---|
| Inputs | U = 10 m/s, I = 5 %, Lt = 0.05 m; ρ = 1.2047 kg/m³, μ = 1.8205×10⁻⁵ Pa·s | U = 3 m/s, Dh = 0.1 m; ρ = 998.2 kg/m³, μ = 1.0×10⁻³ Pa·s |
| Intensity, length | I = 5 %, Lt = 0.05 m | Re = 2.99×10⁵, so I ≈ 3.3 %; Lt = 0.07 Dh = 7 mm |
| k | 0.375 m²/s² | 0.0148 m²/s² |
| ε | 0.755 m²/s³ | 0.0422 m²/s³ |
| ω | 22.4 1/s | 31.7 1/s |
| μt/μ | ≈ 1,110 | — |
The first column is a good illustration of a common surprise: at 5 % intensity and a 5 cm length scale in air, the inlet eddy-to-molecular viscosity ratio is above 1,000, far above the 1 to 10 typical of a clean freestream. That much eddy viscosity thickens boundary layers and can trigger early transition. If it is unrealistic for your case, lower the intensity or the length scale.
Different codes use different but equivalent conventions. The calculator generates inlet entries for:
fixedValue entries for k and epsilon or omega, plus the turbulentMixingLengthDissipationRateInlet alternative.Always check that the snippet matches your model variant (k-ε versus k-ω SST) and your solver version’s naming.
For internal flows use the pipe estimate I ≈ 0.16 Re−1/8, which gives roughly 3 to 5 % for Reynolds numbers between 10⁴ and 10⁶. For clean external flows 0.1 to 1 % is typical. If your inlet is downstream of a fan, valve or bend, expect 5 to 10 % or more.
Solvers use slightly different definitions of the dissipation rate, some with Cμ3/4 and some with other empirical constants. The calculator lists the variants so you can pick the one that matches your code. If your solver documentation gives a formula, use that one.
For separated or free-shear flows and transitional boundary layers it can change results significantly. For fully turbulent internal flows it mainly affects the development length near the inlet, since the turbulence quickly adjusts to the wall-generated field.
The standard value 0.09 used by the standard k-ε and by k-ω SST. You can reset to defaults in the calculator.
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