Turbulence k-Epsilon Boundary Calculator

Computational fluid dynamics & boundary specification: Calculate turbulent kinetic energy ($k$), dissipation rate ($arepsilon$), specific dissipation ($omega$), and eddy viscosity ratio ($mu_t / mu$).

Inlet Inflow & Geometric Scales

Mean Velocity U (m/s): Inlet bulk flow velocity

Turbulence Intensity I (%): Low < 1%, Medium 5%, High > 10%

Length Scale Input Mode: Geometry definition

Characteristic Dimension (m): D_h or turbulent eddy scale ℓ

Kinematic Viscosity ν (m²/s): Air ~1.5e-5, Water ~1.0e-6 m²/s

C_μ Empirical Constant: Standard k-ε closure (0.09)

Inlet Boundary Variables

Turbulent Kinetic Energy (k)

k = ³/₂ · (U · I)² (m²/s²)

Dissipation Rate (ε)

ε = C_μ^(¾) · k^(1.5) / ℓ (m²/s³)

Specific Dissipation (ω)

ω = k^(½) / (C_μ^¼ · ℓ) (s⁻¹)

Eddy Viscosity Ratio (μ_t / μ)

Turbulent / Molecular viscosity

Turbulent Length Scale (ℓ)

Integral eddy size

Turbulent Velocity RMS (u')

Fluctuating velocity scale

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Frequently Asked Questions

What is typical turbulence intensity for external aerodynamics?

For external vehicle aerodynamics (automotive, aerospace flight), free-stream turbulence intensity is typically low (I ≈ 0.1% to 1.0%). For internal combustion engine manifolds, turbomachinery, and heat exchangers, intensity is high (I ≈ 5% to 15%).

How does k decay between the inlet and the test object?

In empty domains, k and ε decay according to d(k)/dt = -ε. If the inlet is set far upstream of an airfoil, turbulence can decay by over 80% before reaching the leading edge. Modified ambient source terms or shorter inlet distances prevent this decay.

Can k and ω be directly transferred into OpenFOAM?

Yes. In OpenFOAM, specify type "turbulentIntensityKineticEnergyInlet" for k and "turbulentMixingLengthDissipationRateInlet" for epsilon/omega, using the exact values computed above in the 0/ folder.