Turbulence boundary conditions calculator
Turn turbulence intensity into inlet k, ε, ω and ν̃ for common RANS models.
1Flow and turbulence intensity
Air at 20 °C and 1 atm.
Low: external flow and good wind tunnels. Medium: pipes and ventilation. High: heat exchangers, turbomachinery, after complex geometry.
Estimate the intensity for pipe flow
–
Fully developed pipe or duct flow. Typing a Reynolds number fills in the intensity above.
Turbulent kinetic energy k
m²/s²
- Velocity fluctuation u′ = U I
- –
- Turbulence intensity I
- –
k = ³⁄₂ (U I)², assuming isotropic fluctuations.
2Turbulence length scale
Pipe or duct: ℓ ≈ 0.07 Dh. Downstream of a boundary layer: ℓ ≈ 0.4 δ.
Use the hydraulic diameter
–
Dh = 4A/P. Typing a diameter fills in the length scale above.
Free stream: 1–10. Internal flows: 10–100. Fully turbulent flows: 100–1000.
Turbulent dissipation rate ε
m²/s³
- Specific dissipation rate ω
- –
- Turbulent viscosity νt
- –
- Eddy viscosity ratio μt/μ
- –
- Turbulence Reynolds number Uℓ/ν
- –
3Values for your turbulence model
k–ω SST
Specific dissipation rate ω
1/s
- Turbulent kinetic energy k
- –
k–ε
Turbulent dissipation rate ε
m²/s³
- Turbulent kinetic energy k
- –
Spalart–Allmaras
Modified viscosity ν̃
m²/s
- Ratio ν̃/ν
- –
Solved from νt = ν̃ fv1, not the shortcut ν̃ ≈ νt.
Simcenter STAR-CCM+ inlet settings
Set these on the inlet boundary under Physics Conditions and Physics Values. Simcenter STAR-CCM+ takes the intensity as a fraction, not a percentage.
Turbulence Specification: Intensity + Length Scale
- Turbulence Intensity
- –
- Turbulent Length Scale
- –
Or enter the transported values directly
- Turbulent Kinetic Energy
- –
- Turbulent Dissipation Rate (k–ε)
- –
- Specific Dissipation Rate (k–ω)
- –
- Modified Diffusivity (Spalart–Allmaras)
- –
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How to use the turbulence boundary conditions calculator
1. Choose the fluid and how you will specify turbulence. Use the length scale for internal flows with a known hydraulic diameter, and the viscosity ratio for external flows where no length scale is obvious.
2. Enter the inlet velocity and the turbulence intensity. Pick one of the typical levels, or estimate the intensity of fully developed pipe flow from its Reynolds number. The turbulent kinetic energy k updates as you type.
3. Enter the length scale or the eddy viscosity ratio. For a duct, the hydraulic diameter helper fills in ℓ ≈ 0.07 Dh.
4. Copy the values for your turbulence model from step 3, or copy the Simcenter STAR-CCM+ inlet settings in one go.
Length scale or viscosity ratio?
Both methods start from the turbulence intensity I, which gives k. They differ in how they fix the second quantity, ε or ω.
Intensity and length scale works best when the upstream geometry is well defined. Pipes, ducts and channels have a hydraulic diameter, and ℓ ≈ 0.07 Dh is a reliable starting point for fully developed flow.
Intensity and viscosity ratio suits external flows around vehicles, wings or buildings, where a meaningful length scale is hard to define. The eddy viscosity ratio μt/μ says directly how much the turbulent viscosity exceeds the molecular viscosity: about 1–10 in a free stream, 10–100 in internal flows and 100 or more in fully developed turbulence.
Typical turbulence intensities
The turbulence intensity is the ratio of the velocity fluctuations to the mean velocity, I = u′/U. Typical inlet values:
| Intensity | Typical flows |
|---|---|
| Below 1 % | External flow around streamlined bodies such as aircraft. Quiet wind tunnels with turbulence screens reach below 0.05 %. |
| 1–5 % | External flow around cars and buildings, ordinary wind tunnels, large ventilation ducts, low-Reynolds-number internal flows. |
| 5–10 % | Fully developed pipe and duct flow, flow after conditioning elements, HVAC systems. |
| 10–20 % | Flow after complex geometry, heat exchangers, turbomachinery stages, strongly recirculating flows. |
For fully developed pipe flow, the core intensity follows from the Reynolds number based on the hydraulic diameter, I ≈ 0.16 ReDh−1/8, which the calculator offers as a helper. In turbomachinery the length scale is often set to about 5 % of the channel height at the stage inlet; behind a grid or a screen it is close to the bar size.
One length scale, three definitions
Solvers do not all mean the same thing by the turbulence length scale. Three definitions are common:
Classical: ℓ = Cμk3/2/ε, with Cμ = 0.09. The smallest of the three, about 0.038 Dh in fully developed pipe flow.
Mixing length: ℓ = Cμ3/4k3/2/ε, about 1.8 times the classical value and about 0.07 Dh in pipe flow. This calculator uses this definition.
Dimensional: ℓ = k3/2/ε, about 11 times the classical value and about 0.42 Dh in pipe flow.
| Solver | Definition | Pipe-flow estimate |
|---|---|---|
| Simcenter STAR-CCM+ | Mixing length | ℓ ≈ 0.07 Dh |
| Ansys Fluent | Mixing length | ℓ ≈ 0.07 Dh |
| OpenFOAM (mixing-length inlet) | Mixing length | ℓ ≈ 0.07 Dh |
| Ansys CFX | Dimensional | ℓ ≈ 0.42 Dh |
If your solver uses the dimensional definition, multiply the length scale from this calculator by 1/Cμ3/4 ≈ 6.1. Check the documentation of your solver version if you are unsure which definition it uses.
Formulas
The calculator uses the standard relations for incompressible RANS inlets with Cμ = 0.09.
k = ³⁄₂ (U I)2 (1)
Isotropic fluctuations, u′ = U I.
ε = Cμ3/4k3/2/ℓ, ω = k1/2/(Cμ1/4ℓ) (2)
From the intensity and the length scale.
νt = (μt/μ)ν, ε = Cμk2/νt, ω = k/νt (3)
From the intensity and the eddy viscosity ratio.
νt = Cμk2/ε = k/ω (4)
νt = ν̃ fv1, fv1 = χ3/(χ3 + cv13), χ = ν̃/ν, cv1 = 7.1 (5)
Spalart–Allmaras, solved for ν̃ with Newton’s method.
I ≈ 0.16 ReDh−1/8, ℓ ≈ 0.07 Dh (6)
Fully developed pipe or duct flow.
Assumptions: incompressible flow and isotropic turbulence at the inlet. For compressible flow above about Mach 0.3, check your solver’s documentation for density-weighted forms. The values describe the turbulence at the inlet; it decays on its way into the domain.
A note on Spalart–Allmaras
The one-equation Spalart–Allmaras model needs only the modified viscosity ν̃ at the inlet. A common shortcut is ν̃ ≈ νt, but that holds only at high eddy viscosity ratios, where the damping function fv1 approaches 1.
At free-stream levels the error is large: at μt/μ = 1 the correct value is ν̃/ν ≈ 4.6, not 1. For free-stream boundaries, NASA’s Turbulence Modeling Resource recommends setting ν̃/ν between 3 and 5, which corresponds to μt/μ ≈ 0.21–1.3. The calculator flags values outside that range when you use the viscosity ratio method.
Worked example: air at 10 m/s with 5 % intensity
Air at 20 °C (ν = 1.516 × 10−5 m²/s) enters at 10 m/s with 5 % intensity and a length scale of 10 mm. These are the calculator’s defaults.
k = ³⁄₂ (10 × 0.05)2 = 0.375 m²/s². With ℓ = 0.01 m, ε = 0.093/4 × 0.3753/2/0.01 = 3.77 m²/s³ and ω = 112 1/s. The turbulent viscosity is νt = 3.35 × 10−3 m²/s, an eddy viscosity ratio of 221, typical of an internal flow.
For an external case, take 40 m/s, 0.5 % intensity and μt/μ = 1. Then k = 0.06 m²/s², ω = 3 960 1/s and ν̃/ν = 4.62, inside the free-stream guideline.
References and changelog
References
H. K. Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, 2nd ed., Pearson, 2007: inlet values of k and ε from intensity and length scale.
D. C. Wilcox, Turbulence Modeling for CFD, 3rd ed., DCW Industries, 2006: the k–ω model and the relation between ω, k and ε.
P. R. Spalart and S. R. Allmaras, “A one-equation turbulence model for aerodynamic flows”, AIAA Paper 92-0439, 1992.
NASA Langley Research Center, Turbulence Modeling Resource: free-stream values for the Spalart–Allmaras model.
CFD Online, Turbulence length scale and Turbulence intensity: length-scale conventions and the pipe-flow estimate.
Review
Reviewed by Christoffer Johansson, M.Sc., Senior Application Specialist at Volupe. Version 2.0.
Changelog
October 2026: new interface with the same formulas; automated checks confirm identical results to the previous version. The calculator now updates as you type and no longer depends on the site’s script optimiser to start. Decimal commas are accepted (1,5e-5 used to be read as 1). The Spalart–Allmaras check now flags ν̃/ν outside 3–5 for the viscosity ratio method; before, it could never trigger. The note on length-scale definitions was corrected, and Simcenter STAR-CCM+ inlet settings were added.
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Questions about inlet turbulence
Calculator reviewed by
Christoffer Johansson
Senior Application Specialist, M.Sc.
Questions about boundary conditions? We reply within one day.
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What turbulence intensity should I use?
It depends on the flow. External aerodynamics around cars, wings or buildings: 1–5 %. Pipes and ducts: about 5–10 %. Heat exchangers, turbomachinery and flows behind complex geometry: 10–20 %. For fully developed pipe flow, estimate the core value from I ≈ 0.16 Re−1/8.
Should I use intensity and length scale, or intensity and viscosity ratio?
Use the length scale for internal flows where you know the geometry, with ℓ ≈ 0.07 Dh. Use the viscosity ratio for external flows where a length scale is hard to define, with μt/μ between about 1 and 10 for free-stream conditions.
Which values do k–ω SST, k–ε and Spalart–Allmaras need?
k–ε needs k and ε, k–ω SST needs k and ω, and Spalart–Allmaras needs ν̃. Most solvers, Simcenter STAR-CCM+ included, also accept the intensity with a length scale or viscosity ratio and convert them internally, so the calculator also shows what those inputs mean.
Why is the Spalart–Allmaras ν̃ not equal to the turbulent viscosity?
The model defines νt = ν̃ fv1, and the damping function fv1 approaches 1 only at high eddy viscosity ratios. At free-stream levels fv1 is well below 1, so ν̃ is much larger than νt: at μt/μ = 1, ν̃/ν ≈ 4.6. The calculator solves the full relation.
How do I enter these values in Simcenter STAR-CCM+?
On the inlet boundary, choose the turbulence specification under Physics Conditions, for example Intensity + Length Scale, and enter the values under Physics Values. The turbulence intensity is entered as a fraction, 0.05 for 5 %. You can also specify the transported quantities directly. Step 3 lists both sets and copies them in one go.
Does the turbulence length scale mean the same in every solver?
No. Simcenter STAR-CCM+, Ansys Fluent and the OpenFOAM mixing-length inlet use ℓ = Cμ3/4k3/2/ε, as this calculator does. Ansys CFX uses k3/2/ε, which is about 6.1 times larger for the same turbulence.
Can Volupe help me set up inlet turbulence in Simcenter STAR-CCM+?
Yes. Our application engineers help Simcenter STAR-CCM+ users choose turbulence models and boundary conditions, and check how the inlet turbulence develops through the domain, as part of support or in a training course. Use the form below and choose Technical question.
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