Turbulence boundary conditions calculator

Turn turbulence intensity and a length scale or turbulent viscosity ratio into inlet k, ε, ω or ν̃ for your solver, and see what reaches your model.

Sources: Ansys Fluent, NASA TMR, Spalart and Rumsey 2007, Simcenter STAR-CCM+ documentation · Reviewed by Christoffer Johansson, M.Sc. · Updated October 2026

How to use the turbulence boundary conditions calculator

1. Choose the kind of boundary, a pipe or duct inlet, a free stream around a body, or a pair of values you know. If you already have k and ε or ω from a precursor run or a measurement, choose the fourth option, Check k and ε or ω you already have, to work back to the intensity, the length scale and the ratio.

2. Choose the turbulence model and the solver. The card beside the inputs (below them on a phone) shows what to enter, in that solver’s field names, with a Copy button on each value.

3. Enter the mean velocity U and pick the fluid. For a duct, give the hydraulic diameter too. The calculator then works out Re = U D_h/ν and estimates the intensity at the pipe core and the length scale 0.07 D_h, and you can type over both.

4. If your model sits some way downstream of the inlet, give the distance under Check the decay to your model to see what is left there, or ask for the inlet values that give a target at the model.

Typical turbulence intensity values

Turbulence intensity I (also written turbulent intensity) is the root-mean-square of the velocity fluctuations u′ divided by the mean velocity U, I = u′/U. As a rule of thumb it is well below 1 % for external flow around cars and aircraft, 1 to 5 % in large pipes, ventilation and low-speed flows, and 5 to 20 % in heat exchangers and turbomachinery (CFD Online). Ansys Fluent’s guide calls 1 % or less low and more than 10 % high. If you have a measured value, use it instead.

Typical turbulence intensity at CFD inlets, with sources
Flow	Turbulence intensity I	Source
Free stream in a modern low-turbulence wind tunnel	as low as 0.05 %	Ansys Fluent User’s Guide
Free stream for k–ω SST with sustaining terms, k = 10⁻⁶ U²	0.08 %	NASA TMR
External flow around cars, submarines and aircraft	well below 1 %	CFD Online
Large pipes, ventilation flows and low-speed (low Reynolds number) flows	1 to 5 %	CFD Online
Ansys CFX option Default Intensity and Autocompute Length Scale, “an approximate value for internal pipe flow”	3.7 %	Ansys CFX-Solver Theory Guide
Core of fully developed pipe or duct flow, 0.16 Re^−1/8	3.8 % at Re = 10⁵	Ansys Fluent User’s Guide
Fully developed smooth-pipe flow averaged over the pipe, 0.227 Re^−0.1	7.2 % at Re = 10⁵	Russo and Basse (2016)
High-speed flow inside heat exchangers, turbines and compressors	5 to 20 %	CFD Online

Note that the two pipe rows answer different questions. The Fluent formula estimates the intensity at the core of a fully developed duct flow, 4 % at Re = 50000. Russo and Basse fitted Princeton Superpipe measurements of the intensity averaged over the pipe, which comes out nearly twice as high. The calculator starts from the core value and shows the average beside it. Use the core value if your uniform inlet stands for the middle of the pipe flow, and the average if it should carry the turbulence of the whole cross-section. The choice matters, because k goes with the square of the intensity, and at the default the average gives 3.5 times the k of the core value.

Basse (2021) points out that the Fluent formula is printed without a reference and that its origin is unclear, although other codes use it too, a Simcenter STAR-CCM+ tutorial among them. We use it because it is the estimate in the solver documentation, with the measured average next to it. If the flow that reaches your inlet is under-developed and undisturbed, the Fluent guide suggests a low intensity instead.

Turbulent viscosity ratio

The turbulent viscosity ratio μ_t/μ, also called the eddy viscosity ratio or turbulence viscosity ratio, is the turbulent (eddy) viscosity divided by the molecular viscosity of the fluid. It equals ν_t/ν, and from k and ε or ω it is μ_t/μ = C_μ k²/(ν ε) = k/(ν ω). Simcenter STAR-CCM+ and Ansys Fluent call the input Turbulent Viscosity Ratio.

With an intensity and a length scale, the ratio grows in proportion to the velocity, the intensity and the length scale (equation 7). Air at 10 m/s with 5 % and 10 mm gives 221, while the external example below, 40 m/s and 0.5 %, needs only 0.11 mm for a ratio of 1.

Typical turbulent viscosity ratio μ_t/μ at CFD boundaries, with sources
Boundary	Model	μ_t/μ	Source
Free-stream boundary of an external flow	two-equation models	typically 1 to 10	Ansys Fluent User’s Guide
Free stream for a transition model (natural or low-turbulence bypass transition), with the inlet intensity chosen to reach the target at the leading edge	k–ω SST with a transition model	about 1 to 10	Ansys Fluent Theory Guide; Simcenter STAR-CCM+ documentation
Free stream	Spalart–Allmaras	0.21 to 1.29 (ν̃/ν = 3 to 5)	NASA TMR
Far field in Menter’s original SST recommendation	k–ω SST	10⁻⁵ to 10⁻²	NASA TMR
Ambient value near the body, held with sustaining terms	two-equation models	2 × 10⁻⁷ Re_c (chord Reynolds number), so 0.2 at Re_c = 10⁶ and 2 at 10⁷	Spalart and Rumsey (2007)
Ansys CFX, Default Intensity and Autocompute Length Scale (I = 3.7 %)	k–ε and k–ω	37	Ansys CFX-Solver Theory Guide
Pipe or duct inlet set with I = 0.16 Re^−1/8 and ℓ = 0.07 D_h	any	0.0075 Re^7/8, so 24 at Re = 10⁴, 178 at 10⁵ and 1340 at 10⁶	our arithmetic from the Fluent rules

These values differ by orders of magnitude because they describe different places. Fluent’s 1 to 10 and Menter’s 10⁻⁵ to 10⁻² are values for the boundary itself. Fluent’s is small enough not to swamp the boundary layers of an external flow, and Menter’s decays further on the way in (NASA TMR). The Spalart–Allmaras range and Spalart and Rumsey’s ambient values describe what should be left near the body, and free decay cannot always bring a two-equation inlet value down to them (Spalart and Rumsey).

Which of the two you set depends on what you know upstream. If the flow reaches your inlet through a pipe or a duct, you know its size and can set the length scale, 0.07 D_h in fully developed flow, the largest mixing length there (Ansys Fluent User’s Guide). Around a car or an aircraft there is no such length. Set the ratio there instead, and check what is left at the model.

Turbulent length scale: three definitions

The turbulent length scale ℓ (or turbulence length scale) describes the size of the large eddies that carry the turbulent kinetic energy. In fully developed duct flow the eddies cannot be larger than the duct, and the usual estimate is ℓ = 0.07 D_h, where D_h = 4A/P is the hydraulic diameter, four times the cross-section area divided by the wetted perimeter. Solvers do not all mean the same thing by ℓ, though, and their definitions differ by up to a factor of 11.1.

To-scale drawing of a pipe of hydraulic diameter Dh with one turbulent length scale in three definitions: classical 0.0383 Dh, mixing length 0.07 Dh (Simcenter STAR-CCM+, Ansys Fluent, OpenFOAM) and dimensional 0.426 Dh (Ansys CFX); the factors between them are 1.83, 6.09 and 11.1. — One length scale in the three definitions, drawn to scale against the hydraulic diameter of a fully developed pipe flow.

The mixing length, ℓ = C_μ^3/4 k^3/2/ε, is the definition behind ℓ = 0.07 D_h and ℓ = 0.4 δ₉₉ in the Ansys Fluent User’s Guide. Simcenter STAR-CCM+, Ansys Fluent, the OpenFOAM mixing-length inlet conditions and this calculator use it. Ansys CFX uses the dimensional length k^3/2/ε, which is 6.09 times longer for the same turbulence. The classical length C_μ k^3/2/ε, as in Wilcox’s book and CFD Online’s calculator, is 0.55 times the mixing length, and with it ν_t = √k ℓ.

Turbulent length scale definition by solver
Solver	Inlet setting	Definition	Pipe-flow length scale
Simcenter STAR-CCM+	Turbulence Specification: Intensity + Length Scale (Turbulent Length Scale)	Mixing length	0.07 D_h
Ansys Fluent	Intensity and Length Scale, or Intensity and Hydraulic Diameter	Mixing length	0.07 D_h
OpenFOAM (openfoam.com)	turbulentMixingLengthDissipationRateInlet or turbulentMixingLengthFrequencyInlet, mixingLength	Mixing length	0.07 D_h
OpenFOAM (openfoam.org, development version)	turbulentEpsilon or turbulentOmega, mixingLength	Mixing length	0.07 D_h
Ansys CFX	Intensity and Length Scale	Dimensional	0.426 D_h
CFD Online’s turbulence calculator	Turbulence length scale TuL	Classical	0.0383 D_h

If your solver uses the dimensional definition, multiply the length scale from this calculator by 6.09. To test which definition a solver uses, set 10 m/s, an intensity of 5 % (0.05 in Simcenter STAR-CCM+ and OpenFOAM) and a length scale of 0.01 m on any inlet, initialise, and read ε on the boundary. The mixing length gives 3.773 m²/s³, the classical definition 2.067 and the dimensional one 22.96.

For an inlet with a turbulent boundary layer, the Fluent guide gives ℓ = 0.4 δ₉₉, where δ₉₉ is the boundary layer thickness, and the y+ calculator gives an estimate of δ. Behind a perforated plate or turning vanes, base ℓ on the size of the openings rather than on the duct. CFD Online suggests the size of the grid bars behind a grid and about 5 % of the channel height at a turbine stage inlet, without saying which definition it means.

How inlet turbulence decays before it reaches your model

In a uniform stream between the inlet and your model nothing produces turbulence, and a two-equation model only destroys it. Spalart and Rumsey (2007) give the result in closed form. With τ = 1 + β ω₀ x/U, ω falls as ω₀/τ and k as k₀ τ^−β*/β, with β = 0.0828 and β* = 0.09 for k–ω SST in the free stream. Standard k–ε, with C_ε2 = 1.92, follows the same law, and so do the transition guidelines in the Simcenter STAR-CCM+ documentation, while the Ansys Fluent Theory Guide prints the two constants the other way round.

Chart of turbulence intensity from the inlet to the model for air at 40 m/s: with 0.5 % and a turbulent viscosity ratio of 1 at the inlet, free decay leaves 0.150 % at 1 m and 0.066 % at 5 m (k–ω SST and standard k–ε); started with a ratio of 10, 0.206 % is left at 5 m; Spalart–Allmaras keeps ν̃/ν at 4.62. — Intensity against the distance from the inlet for the external example below, with inlet viscosity ratios of 1 and 10 (k–ω SST and standard k–ε), and the constant ν̃ of Spalart–Allmaras.

Take the external example, air at 40 m/s with I = 0.5 % and μ_t/μ = 1 at the inlet. With k–ω SST or standard k–ε you will see the intensity drop to 0.150 % after 1 m and 0.066 % after 5 m. The ratio falls far less, to 0.72 at 5 m, because in Spalart and Rumsey’s solution ν_t decays with a power of about −0.09 against −1.1 for k.

Realizable k–ε has a different destruction term in its ε equation, ε²/(k + √(νε)) in place of ε²/k. In our integration of that form, as printed in the Ansys Fluent Theory Guide, the external example keeps 0.042 % at 1 m, and k falls to zero at about 1.2 m. If you run realizable k–ε, check the decay in a short run.

Raising the inlet intensity does not help you much. With μ_t/μ = 1 at the inlet, no inlet intensity brings more than 0.067 % to a model 5 m downstream, because a higher intensity at the same ratio means a higher ω, and ω at a distance x can never exceed U/(β x). This means that if you need more turbulence at the model, you raise the viscosity ratio at the inlet. Keeping 0.2 % at 5 m needs a ratio of at least 6.55 there, and an inlet of 0.36 % with μ_t/μ = 11 gives 0.2 % and 10 at the model.

For transition models the Ansys Fluent Theory Guide recommends a low inlet ratio, about 1 to 10, and the Simcenter STAR-CCM+ documentation aims for a free-stream ratio of 1 to 10 for natural transition and for bypass transition at low free-stream turbulence. Our post on transition modelling in Simcenter STAR-CCM+ explains the models.

Spalart–Allmaras behaves differently. Without vorticity there is no production, and far from walls the destruction term is insignificant, so ν̃ and ν_t stay as you set them.

To hold the free-stream turbulence of a two-equation model all the way to the model, the alternative to inflated inlet values is a sustaining (ambient) source, which cancels the destruction when k and ω equal the ambient values. The SST-sust version in the NASA TMR uses k_amb = 10⁻⁶ U², an intensity of 0.08 %. Simcenter STAR-CCM+ has it for the k–ω and k–ε models as the fluid region’s Turbulence Source Option, Ambient, with the values taken from the inflow boundary, and OpenFOAM (openfoam.com) as decayControl in k–ω SST.

Turbulence formulas: k, ε, ω and turbulent viscosity

These are the relations the calculator uses for a uniform inlet, with C_μ = 0.09 in standard k–ε and β* = 0.09 in k–ω SST. All quantities are per unit mass, so for a compressible inlet we use ν = μ/ρ at the inlet’s static conditions.

Turbulence intensity formula

Turbulence intensity is the root-mean-square velocity fluctuation u′ over the mean velocity U, and with isotropic turbulence u′ = √(2k/3). Equation (2) gives the Ansys Fluent estimate at the core of fully developed pipe flow and the Russo and Basse average over the pipe.

I = u′/U = √(2k/3)/U (1)
Root-mean-square fluctuation over the mean velocity (Ansys Fluent User’s Guide; CFD Online).

I_core ≈ 0.16 Re^−1/8, I_avg ≈ 0.227 Re^−0.1, ℓ ≈ 0.07 D_h, Re = U D_h/ν (2)
Fully developed pipe flow: core intensity and mixing length (Ansys Fluent User’s Guide), average intensity (Russo and Basse 2016).

The pipe estimate changes slowly with the Reynolds number, from 5.1 % at the core at Re = 10⁴ to 2.8 % at 10⁶.

Turbulent kinetic energy k

Turbulent kinetic energy k is the kinetic energy of the velocity fluctuations per unit mass, ½ (u′_x² + u′_y² + u′_z²), in m²/s². At an inlet where the three fluctuations are equal, it follows from the intensity as in (3).

k = ³⁄₂ (U I)² (3)
Isotropic inlet turbulence (Ansys Fluent User’s Guide; Ansys CFX; OpenFOAM; Simcenter STAR-CCM+ documentation).

Doubling the intensity gives four times as much k.

Turbulent dissipation rate ε

The turbulent dissipation rate ε is the rate at which turbulent kinetic energy is dissipated, per unit mass, in m²/s³. Equation (4) gives it from the mixing length or from the turbulent viscosity ratio.

ε = C_μ^3/4 k^3/2/ℓ, ε = C_μ k²/(ν μ_t/⁠μ) (4)
From the mixing length and from the ratio (Ansys Fluent User’s Guide; OpenFOAM; Simcenter STAR-CCM+ documentation).

For the same k, a length scale twice as long gives half the ε.

Specific dissipation rate ω

The specific dissipation rate ω is ε divided by C_μ k, in 1/s, and it is the second variable of the k–ω models. Equation (5) gives it from the mixing length or from the ratio.

ω = k^1/2/(C_μ^1/4 ℓ) = ε/(C_μ k), ω = k/(ν μ_t/⁠μ) (5)
Ansys Fluent User’s Guide; OpenFOAM; Simcenter STAR-CCM+ documentation, with β* = C_μ = 0.09.

This means that at a fixed ratio ω grows with the square of the intensity, which is why a high inlet intensity decays fast.

Turbulent viscosity and the viscosity ratio

The turbulent viscosity ν_t, or eddy viscosity, is the viscosity that a RANS model adds to the molecular one, in m²/s. At an inlet it follows from (6), and with an intensity and a mixing length from (7).

ν_t = C_μ k²/ε = k/ω, μ_t/⁠μ = ν_t/⁠ν (6)
Inlet relation for k–ε and k–ω (Ansys Fluent User’s Guide).

μ_t/⁠μ = C_μ^1/4 √(3/2) U I ℓ/ν ≈ 0.67 U I ℓ/ν (7)
From (3), (4) and (6) for a mixing length ℓ, as in Basse (2021), eq. 4.

This is the inlet relation. Inside the boundary layer k–ω SST limits the eddy viscosity, μ_t = ρ a₁ k/max(a₁ ω, Ω F₂), and k/ω is not SST’s general formula. In realizable k–ε, C_μ is not a constant, so the ratio a solver reports for the same k and ε can differ from the value here.

Note that all of this assumes a uniform inlet with isotropic turbulence. If the boundary layer or the developed profile at the inlet matters for your result, the Ansys Fluent User’s Guide recommends a profile from measurements or empirical formulas rather than one value.

Spalart–Allmaras inlet value: the modified viscosity

The one-equation Spalart–Allmaras model transports a modified viscosity ν̃ (nuTilda in OpenFOAM, Modified Diffusivity in Simcenter STAR-CCM+), not the eddy viscosity itself. The eddy viscosity follows from it through a damping function f_v1, which is close to 1 only when ν̃ is much larger than ν.

ν_t = ν̃ f_v1, f_v1 = χ³/(χ³ + c_v1³), χ = ν̃/⁠ν, c_v1 = 7.1 (8)
Spalart–Allmaras (NASA TMR), solved for ν̃ with a bracketed Newton method.

Log–log chart of the Spalart–Allmaras ν̃/ν against the turbulent viscosity ratio μt/μ with the NASA TMR free-stream band ν̃/ν 3 to 5 (μt/μ 0.210 to 1.294): at μt/μ = 1 the model needs ν̃/ν = 4.62, where the shortcut ν̃ = νt gives 1; at 10 the curve gives 12.05 and at 100 the two agree. — The Spalart–Allmaras ν̃/ν from equation (8) against the turbulent viscosity ratio on log axes, with the shortcut ν̃ = ν_t dashed and the free-stream band of the NASA TMR shaded.

At free-stream levels the difference is large. With μ_t/μ = 1 the damping function is only f_v1 = 0.216, and ν̃ has to be 4.62 times ν to give that eddy viscosity. The NASA TMR gives ν̃/ν = 3 to 5 for the free stream, which means μ_t/μ of 0.21 to 1.29, with 3 somewhat better at the lowest Reynolds numbers (Spalart and Rumsey 2007). At μ_t/μ = 10 the shortcut ν̃ = ν_t is 17 % low, and at 100 the two differ by 0.04 %.

The case that goes wrong is typing ν̃ = ν, a ν̃/ν of 1, in the belief that it sets μ_t/μ = 1. It sets μ_t/μ = 0.0028, about 360 times less than intended. Spalart and Rumsey note that some user interfaces do not make clear whether ν̃ or ν_t is being set, and that this matters most at exactly these low values.

Solvers also differ in how they turn an intensity and a length scale into ν̃. In Simcenter STAR-CCM+ the Turbulent Viscosity Ratio method solves ν̃ through f_v1, as this calculator does, while Intensity + Length Scale sets ν̃ equal to the ν_t of the mixing-length relations. Ansys Fluent’s formula for the same inputs, ν̃ = √1.5 U I ℓ, gives 1.83 times that ν_t. For a free-stream boundary we therefore set the ratio, or enter the Modified Diffusivity from the card directly.

Simcenter STAR-CCM+ inlet settings

In Simcenter STAR-CCM+ you set the inlet turbulence on the boundary, under Regions > [region] > Boundaries > [boundary] > Physics Conditions > Turbulence Specification, and the values appear under its Physics Values. The same choices exist on Velocity Inlet, Stagnation Inlet, Mass Flow Inlet, Free Stream and Pressure Outlet boundaries.

For each model the Simcenter STAR-CCM+ documentation (version 2606) gives these choices.

k–ω SST and the other k–ω models: Turbulence Specification Intensity + Length Scale with Turbulence Intensity and Turbulent Length Scale, Intensity + Viscosity Ratio with Turbulence Intensity and Turbulent Viscosity Ratio, or K + Omega with Turbulent Kinetic Energy and Specific Dissipation Rate.
k–ε models: the same, with K + Epsilon, Turbulent Kinetic Energy and Turbulent Dissipation Rate in place of the k–ω pair. The Elliptic Blending k–ε models also ask for a Reduced Stress Function with each method.
Spalart–Allmaras: Turbulent Viscosity Ratio, Modified Turbulent Diffusivity with the value Modified Diffusivity, or Intensity + Length Scale with a Cmu coefficient.

Sketch of a duct inlet of hydraulic diameter Dh = 100 mm with the mean velocity U = 10 m/s, the turbulence intensity I = u′/U and eddies of size ℓ = 0.07 Dh = 7 mm, next to the Simcenter STAR-CCM+ settings for k–ω SST: Regions > Fluid > Boundaries > Inlet > Physics Conditions > Turbulence Specification, Intensity + Length Scale; Physics Values, Turbulence Intensity 0.04 and Turbulent Length Scale 0.007 m. — The default duct inlet and where its values go in Simcenter STAR-CCM+, with Turbulence Intensity as a fraction.

Turbulence Intensity is a fraction, 0.04 for 4 %, because the documentation computes k = ³⁄₂ (I v)² with I as a fraction and v the local velocity. Note that it advises against the intensity-based methods where the velocity field is initialised to zero, since k is then zero too. The length scale is the mixing length, as in this calculator, so 7 mm goes in as 0.007 m.

In the continuum’s Initial Conditions the intensity methods put a turbulent velocity scale in place of v in k = ³⁄₂ (I v)². Since version 2602 that scale follows the initial velocity by default (Turbulent Velocity Scale Specification: Use Initial Velocity), so an initial velocity equal to the inlet speed gives the initial field the same k as the inlet. With a zero initial velocity the scale falls back to 1 m/s, so choose Specified and enter the inlet speed instead. Johan Bernander’s post “Initializing with existing solutions in Simcenter STAR-CCM+” shows the tree from before 2602, when Turbulent Velocity Scale was a value of its own.

If you have questions about the inlet of your own case, you are welcome to ask us through the form at the end of the page. Our support engineers also teach Simcenter STAR-CCM+ in our training courses.

Worked examples: inlet k, ε and ω

Duct inlet, the calculator’s default. Air at 20 °C flows at 10 m/s in a duct with a hydraulic diameter of 100 mm. The duct size sets both the intensity, 4.0 % at the core for Re = 65960, and the length scale, 7 mm.

Air at 10 m/s with 5 % intensity and a 10 mm length scale. k = ³⁄₂ (10 × 0.05)² = 0.375 m²/s². With ℓ = 0.01 m, ε = 0.09^3/4 × 0.375^3/2/0.01 = 3.77 m²/s³ and ω = 112 1/s. The turbulent viscosity is ν_t = 3.35 × 10⁻³ m²/s, a turbulent viscosity ratio of 221, in the range of the duct inlets in the viscosity-ratio table.

External flow with the model 5 m downstream. Air flows at 40 m/s with 0.5 % intensity and μ_t/μ = 1 at the inlet. Spalart–Allmaras needs ν̃/ν = 4.62, inside the NASA TMR range, and keeps it to the model, while the intensity of k–ω SST is down to 0.066 % there.

The three worked examples, air at 20 °C (ν = 1.516 × 10⁻⁵ m²/s)
Quantity	Duct inlet	10 m/s, 5 %, 10 mm	External, 40 m/s
Mean velocity U (m/s)	10	10	40
Turbulence intensity I	4.0 %	5 %	0.5 %
Length scale ℓ (mixing length)	7 mm	10 mm	0.113 mm
Turbulent viscosity ratio μ_t/μ	124	221	1
k (m²/s²)	0.240	0.375	0.06
ε (m²/s³)	2.76	3.77	21.4
ω (1/s)	128	112	3958
ν_t (m²/s)	1.878 × 10⁻³	3.354 × 10⁻³	1.516 × 10⁻⁵
ν̃/ν (Spalart–Allmaras)	124	221	4.62
I at 5 m, k–ω SST and standard k–ε	–	–	0.066 %

We checked all three by hand and with the engine’s tests (below).

References and changelog

References

Ansys Fluent 12.0 User’s Guide, section 7.3.2, and Theory Guide, sections 4.4.3 and 4.7.3, Ansys, Inc., 2009 (public copy): the inlet rules, equations (1) to (6) and realizable k–ε. Basse (2021) cites the same pipe formula from the 2021 R1 release.

Ansys CFX-Solver Theory Guide, Release 2025 R2, section 1.9.1.2, Ansys, Inc. (ansyshelp.ansys.com).

Simcenter STAR-CCM+ documentation, version 2606, Siemens Digital Industries Software, 2026: the RANS boundary conditions, the boundary and region references of the turbulence models, the Transition Guidelines and the tutorial on boundary settings (Siemens Support Center, login required).

OpenFOAM, the documentation of the turbulence inlet conditions and kOmegaSST (openfoam.com) and of the Foundation development version (openfoam.org).

P. R. Spalart and S. R. Allmaras, “A one-equation turbulence model for aerodynamic flows”, La Recherche Aérospatiale, no. 1, 5–21, 1994, first presented as AIAA Paper 92-0439, 1992.

Turbulence Modeling Resource, at NASA Langley until February 2026 and now at tmbwg.github.io, guided by the AIAA Turbulence Model Benchmarking Working Group: the Spalart–Allmaras, Menter SST and Wilcox k–ω pages.

P. R. Spalart and C. L. Rumsey, “Effective inflow conditions for turbulence models in aerodynamic calculations”, AIAA Journal 45(10), 2544–2553, 2007, doi:10.2514/1.29373 (NASA NTRS).

F. R. Menter, “Two-equation eddy-viscosity turbulence models for engineering applications”, AIAA Journal 32(8), 1598–1605, 1994, doi:10.2514/3.12149.

D. C. Wilcox, Turbulence Modeling for CFD, 3rd ed., DCW Industries, 2006: the Wilcox 2006 k–ω model, with the constants as listed by the Turbulence Modeling Resource.

F. Russo and N. T. Basse, “Scaling of turbulence intensity for low-speed flow in smooth pipes”, Flow Measurement and Instrumentation 52, 101–114, 2016, doi:10.1016/j.flowmeasinst.2016.09.012, and N. T. Basse, “Scaling of global properties of fluctuating and mean streamwise velocities in pipe flow”, Physics of Fluids 33, 065127, 2021 (arXiv).

CFD Online, CFD-Wiki pages Turbulence intensity, Turbulence length scale, Turbulence free-stream boundary conditions and Hydraulic diameter, and the turbulence calculator.

Y. A. Çengel and J. M. Cimbala, Fluid Mechanics: Fundamentals and Applications, McGraw-Hill, Tables A-3 and A-9 (the fluid presets).

Volupe blog: C. Johansson, “Transition modelling in Simcenter STAR-CCM+” (2022); J. Bernander, “Initializing with existing solutions in Simcenter STAR-CCM+” (2023); F. Vesting, “Enhancing turbulence models in Simcenter STAR-CCM+” (2024).

How we checked the numbers

We test the calculation engine in Node.js with over 52000 checks, all passing on 28 October 2026. Among them are the 0.210438 and 1.294234 of the NASA TMR for the Spalart–Allmaras solve, a Runge–Kutta integration and Table 1 of Spalart and Rumsey (2007) for the decay, Fluent’s 4 % at Re = 50000, and the conversions against their inverses. The three worked examples are also done by hand.

Changelog

October 2026. We rebuilt the calculator around the type of boundary, with the values in the field names of Simcenter STAR-CCM+ or OpenFOAM. New are the decay to your model, the check of k and ε or ω you already have, and a link that keeps your inputs. Earlier versions of this page said that Simcenter STAR-CCM+ uses a length scale other than the mixing length. Its documentation shows the mixing length, which the calculator’s formulas already used.

27 October 2026. We fixed the Spalart–Allmaras solve. For μ_t/μ between 0.503 and 0.799 the Newton iteration in earlier versions returned ν̃/ν between 0.51 and 1.0 in almost every case, where 3.80 to 4.33 is right. It now uses a bracketed Newton method, tested as described above.

Questions about inlet turbulence

Calculator reviewed by

Christoffer Johansson

Senior Application Specialist, M.Sc.

Questions about boundary conditions? We reply within one day.

Ask a technical question →

What turbulence intensity should I use?

Use a measured value if you have one, from the rig or the wind tunnel. Without one, CFD Online gives well below 1 % for external flow around cars and aircraft, 1 to 5 % for large pipes and ventilation, and 5 to 20 % in heat exchangers and turbomachinery. For the core of fully developed pipe flow, the Ansys Fluent formula, 0.16 times the Reynolds number to the power −1/8, gives 4 % at Re = 50000. Averaged over the pipe it is nearly twice that.

How do I calculate turbulent kinetic energy from turbulence intensity?

Use k = 1.5 (U I)², where U is the mean velocity and I the intensity as a fraction. It assumes isotropic fluctuations, the same u′ = U I in every direction. For air at 10 m/s and 5 % intensity, k = 1.5 × (10 × 0.05)² = 0.375 m²/s². Ansys Fluent, Ansys CFX, OpenFOAM’s intensity inlet condition and Simcenter STAR-CCM+ use the same relation.

What turbulent viscosity ratio should I use?

At the free-stream boundary of an external flow, typically 1 to 10 for two-equation models (Ansys Fluent User’s Guide), and 0.21 to 1.29 for Spalart–Allmaras, which is the ν̃/ν of 3 to 5 in the NASA TMR. At a duct inlet set from the hydraulic diameter, the ratio follows from the Reynolds number, 124 for air at 10 m/s in a 100 mm duct. For a free stream, check what is left at your model after the decay.

Should I use intensity and length scale, or intensity and turbulent viscosity ratio?

Use the length scale when the flow comes through a pipe or duct of known size, ℓ = 0.07 Dh in fully developed flow. Use the turbulent viscosity ratio for a free stream, where there is no obvious length, with typically 1 to 10 for two-equation models (Ansys Fluent) or 0.21 to 1.29 for Spalart–Allmaras (NASA TMR). For the two-equation models both start from the intensity, which sets k.

Which inlet values do k–ω SST, k–ε and Spalart–Allmaras need?

k–ε (k-epsilon) transports k and ε, k–ω SST (k-omega SST) transports k and ω, and Spalart–Allmaras transports only the modified viscosity ν̃. Simcenter STAR-CCM+ and Ansys Fluent also accept an intensity with a length scale or a viscosity ratio, and OpenFOAM accepts an intensity with a mixing length. For k, ε and ω they convert these with the relations on this page. For Spalart–Allmaras the conversion from an intensity and a length scale differs between solvers, so check which one yours uses.

Why is the Spalart–Allmaras modified viscosity not equal to the turbulent viscosity?

Because the model defines νt = ν̃ fv1, with fv1 = χ³/(χ³ + 7.1³) and χ = ν̃/ν. The damping function fv1 is close to 1 only at high viscosity ratios. At free-stream levels it is small, for μt/μ = 1 only 0.216, and ν̃/ν = 4.62. Typing ν̃ = ν instead gives μt/μ = 0.0028, about 360 times less than intended.

Does the turbulence length scale mean the same in every solver?

No. Simcenter STAR-CCM+, Ansys Fluent and OpenFOAM’s mixing-length inlet conditions use the mixing-length definition, as this calculator does. Ansys CFX uses the dimensional definition, which is 6.09 times larger for the same turbulence. The classical definition, used by CFD Online’s calculator, is 0.55 times the mixing length. Check your solver’s definition before you copy a length scale.

Why is the turbulence at my model lower than the value I set at the inlet?

Because in a uniform stream a two-equation model only destroys turbulence on its way to your model. With k–ω SST or standard k–ε, air at 40 m/s with 0.5 % and μt/μ = 1 at the inlet has 0.15 % left after 1 m and 0.066 % after 5 m, and realizable k–ε loses it faster at such a low ratio. A higher inlet ratio slows the decay (Spalart and Rumsey 2007). Spalart–Allmaras does not decay in a uniform stream.

How do I enter these values in Simcenter STAR-CCM+?

On the inlet boundary, set Turbulence Specification to Intensity + Length Scale under Physics Conditions, and enter Turbulence Intensity and Turbulent Length Scale under Physics Values. The intensity is a fraction, 0.05 for 5 %, and the length scale is the mixing length used here. For Spalart–Allmaras, choose Turbulent Viscosity Ratio, or Modified Turbulent Diffusivity with the Modified Diffusivity from the card. Copy settings copies these fields with your values.

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 inlet conditions, and check how the turbulence develops on its way to the model, in support cases and in our Simcenter STAR-CCM+ training courses. Use the form below and choose Technical question.

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Turbulence boundary conditions calculator

What to enter in Simcenter STAR-CCM+

How to use the turbulence boundary conditions calculator

Typical turbulence intensity values

Turbulent viscosity ratio

Turbulent length scale: three definitions

How inlet turbulence decays before it reaches your model

Turbulence formulas: k, ε, ω and turbulent viscosity

Turbulence intensity formula

Turbulent kinetic energy k

Turbulent dissipation rate ε

Specific dissipation rate ω

Turbulent viscosity and the viscosity ratio

Spalart–Allmaras inlet value: the modified viscosity

Simcenter STAR-CCM+ inlet settings

Worked examples: inlet k, ε and ω

References and changelog

References

How we checked the numbers

Changelog

Next in a CFD set-up

Turbulence model selector

y+ calculator

Grid Convergence Index (GCI) calculator

Questions about inlet turbulence

Christoffer Johansson

What turbulence intensity should I use?

How do I calculate turbulent kinetic energy from turbulence intensity?

What turbulent viscosity ratio should I use?

Should I use intensity and length scale, or intensity and turbulent viscosity ratio?

Which inlet values do k–ω SST, k–ε and Spalart–Allmaras need?

Why is the Spalart–Allmaras modified viscosity not equal to the turbulent viscosity?

Does the turbulence length scale mean the same in every solver?

Why is the turbulence at my model lower than the value I set at the inlet?

How do I enter these values in Simcenter STAR-CCM+?

Can Volupe help me set up inlet turbulence in Simcenter STAR-CCM+?

Talk to an engineer in your region

Lukas Johansson

Carl Wanngård

David Fabis

André Hau

Fredrik Liljedahl

Henrik Pahlitzsch

Mikel Sevilla

Ask us about Turbulence boundary conditions calculator

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