Interstitial Inlet Velocity - Boundary Conditions

Interstitial Inlet Velocity is a Dirichlet (fixed–value) velocity boundary for Euler‑Euler multiphase or porous‑media problems. The boundary condition converts the superficial (bulk) inlet velocity to the interstitial velocity that the solver actually transports by dividing bulk velocity U by the local phase fraction α.

This boundary condition is useful in multiphase flow simulations when both phases exist at the inlet. Application of Fixed Value for the velocity will result in the incorrect velocity for a given phase, because the prescribed velocity would be scaled by the phase fraction \(\alpha\). Therefore, the resulting mass flow rate through the boundary would be smaller than expected.

Boundary conditions such as Interstitial Inlet Velocity need the true phase velocity to satisfy the phase‑mass balance. Users, however, often know or specify the superficial velocity. The boundary condition therefore divides the user input by the local phase fraction \(\alpha\) to obtain the proper interstitial value that the solver stores in the velocity field.

Mathematically, the interstitial velocity is calculated as below:

\(\vec U_{interstitial} = \vec U_{inlet}/\alpha\)

where:
\(\vec U_{inlet}\) – superficial (bulk) velocity provided by the User,
\(\alpha\) – the local volume‑fraction of the phase.

In Euler‑Euler formulations the phase‑mass balance is written for the phase volumetric flux \(\alpha \vec U\). Measurements or design data are usually given as the superficial velocity. The boundary condition simply back‑calculates the velocity the phase really has while occupying only a fraction \(\alpha\) of the patch area.

This guarantees mass‑flux consistency without the user having to monitor α variations during a transient run.

The Interstitial Inlet Velocity is commonly used in multiphase problems. It calculates the true phase velocity based on the user-defined bulk velocity. However, its physical meaning varies depending on the problem being considered and the solver applied.

To define Interstitial Inlet Velocity in SimFlow the proper option must be selected from the drop-down menu for the velocity field - Figure 1.

In this section, we propose boundary conditions that are alternative to Interstitial Inlet Velocity. While they may fulfill similar purposes, they might be better suited for a specific application and provide a better approximation of physical world conditions.