OpenFOAM Inlet Boundary Conditions: velocity, pressure, turbulence

Inlet boundary conditions are among the most common sources of divergence and poor results in OpenFOAM. Getting velocity, pressure, and turbulence quantities right at the inlet is fundamental to any simulation.

By CFDpilot · Updated April 2026

Velocity inlet (fixedValue)

The standard velocity inlet specifies a uniform velocity normal to the patch:

// 0/U
inlet
{
    type        fixedValue;
    value       uniform (10 0 0);   // 10 m/s in x-direction
}

For an inlet normal to a surface where the direction isn't purely axial, specify the exact vector. The magnitude must match your Reynolds number target.

Pressure at the inlet

When velocity is fixed at the inlet, pressure must be free to float — use zeroGradient:

// 0/p
inlet
{
    type        zeroGradient;
}

Never fix both velocity and pressure at the same patch — this over-constrains the problem and causes divergence.

Pressure-driven flow (no fixed velocity)

If you drive the flow by a pressure difference rather than a fixed velocity:

// 0/p — fixed pressure at inlet
inlet
{
    type        fixedValue;
    value       uniform 101325;   // Pa (absolute)
}

// 0/U — velocity is computed, must allow backflow
inlet
{
    type        pressureInletOutletVelocity;
    value       uniform (0 0 0);
}

Turbulence quantities at the inlet: k and epsilon

For k-ε and k-ω SST, you need to specify turbulence intensity I and a length scale L at the inlet. Typical values: I = 5% (0.05) for internal flows, L = 0.07 × hydraulic diameter.

// k = 1.5 * (U * I)^2
// Example: U=10 m/s, I=0.05 → k = 1.5 * (10*0.05)^2 = 0.375 m²/s²

// epsilon = C_mu^0.75 * k^1.5 / L
// C_mu = 0.09, L = 0.07 * D_h
// Example: L=0.07m → epsilon = 0.09^0.75 * 0.375^1.5 / 0.07 ≈ 0.14 m²/s³

// 0/k
inlet
{
    type        fixedValue;
    value       uniform 0.375;
}

// 0/epsilon
inlet
{
    type        fixedValue;
    value       uniform 0.14;
}

Turbulence at the inlet: omega (k-omega SST)

// omega = k^0.5 / (C_mu^0.25 * L)
// Example: k=0.375, L=0.07 → omega ≈ 14.9 s⁻¹

// 0/omega
inlet
{
    type        fixedValue;
    value       uniform 14.9;
}

turbulentIntensityKineticEnergyInlet

OpenFOAM provides a convenience BC that computes k automatically from intensity and a reference velocity. This avoids manual calculation:

// 0/k
inlet
{
    type            turbulentIntensityKineticEnergyInlet;
    intensity       0.05;
    value           uniform 0.375;
}

turbulentMixingLengthDissipationRateInlet

The companion BC to compute epsilon automatically from a mixing length:

// 0/epsilon
inlet
{
    type            turbulentMixingLengthDissipationRateInlet;
    mixingLength    0.07;   // L = 0.07 * D_h in metres
    value           uniform 0.14;
}

// 0/omega — equivalent for k-omega SST
inlet
{
    type            turbulentMixingLengthFrequencyInlet;
    mixingLength    0.07;
    value           uniform 14.9;
}

These BCs recompute the turbulence quantities from k each time step, ensuring consistency with any updated k field at the inlet.

nut at the inlet

// 0/nut — computed from k and epsilon/omega at inlet
inlet
{
    type        calculated;
    value       uniform 0;
}

Non-uniform velocity profiles at the inlet

For fully developed pipe or channel flow, the inlet velocity should reflect the real profile rather than a uniform plug flow. Two approaches:

1. Power-law profile via codedFixedValue:

// 0/U — turbulent power-law profile (1/7 power law)
inlet
{
    type            codedFixedValue;
    value           uniform (0 0 0);
    name            powerLawInlet;
    code
    #{
        const fvPatch& p = this->patch();
        const vectorField& Cf = p.Cf();
        vectorField& U = *this;
        scalar R = 0.05;      // pipe radius [m]
        scalar Umax = 12.0;   // centreline velocity [m/s]
        forAll(Cf, i)
        {
            scalar r = mag(Cf[i] - vector(0,0,0));  // radial distance
            U[i] = vector(Umax * pow(1.0 - r/R, 1.0/7.0), 0, 0);
        }
    #};
}

2. Mapped inlet from a precursor simulation:

// 0/U — mapped from a periodic precursor channel
inlet
{
    type        mapped;
    offset      (0 0 0);
    interpolationScheme cellPoint;
    setAverage  false;
    value       uniform (10 0 0);
}

The mapped approach requires matching the inlet patch geometry to an internal region of a precursor periodic simulation. This is the most physically accurate method for turbulent inflow generation in LES.

Inlet boundary conditions for compressible solvers

For rhoSimpleFoam and rhoPimpleFoam, pressure is now a thermodynamic quantity with units Pa. Total pressure inlets are often more physical than fixed static pressure:

// 0/p — total pressure inlet for compressible flow
inlet
{
    type        totalPressure;
    p0          uniform 101325;   // total (stagnation) pressure [Pa]
    value       uniform 101325;
}

// 0/U — must allow the solver to set direction
inlet
{
    type        pressureInletOutletVelocity;
    value       uniform (0 0 0);
}

// 0/T — temperature at inlet
inlet
{
    type        fixedValue;
    value       uniform 300;   // 300 K
}

Turbulence intensity guidelines by application

Selecting the right turbulence intensity requires understanding the physical context of the inlet:

• Wind tunnel free stream: I = 0.1–1%. Very low turbulence, clean inflow.
• Pipe and duct internal flows: I = 3–6%. Use I = 0.16 × Re^(-1/8) for developed pipe flow.
• Flows past bluff bodies: I = 5–10% depending on upstream geometry.
• HVAC and ventilation flows: I = 10–20% near diffusers and grilles.
• Gas turbine combustors: I = 15–25%. Highly turbulent mixing environments.

Common mistakes

• k = 0 at inlet — causes division by zero in epsilon/omega equation; use a small positive value (1e-6 minimum)
• epsilon = 0 at inlet — same problem; always provide a physically motivated value
• Velocity and pressure both fixed — over-constrains the system, solver diverges immediately
• Wrong turbulence intensity — I = 1% for very clean flows, 5% for typical internal flows, up to 20% for highly turbulent jets
• Mismatched hydraulic diameter in L — for non-circular ducts, L = 0.07 × D_h where D_h = 4 × Area / Perimeter
• Using uniform (0 0 0) for velocity with a fixed pressure inlet — this creates a zero-velocity initial condition that is physically inconsistent; use potentialFoam to initialise the velocity field