4.6 Free (entrainment) boundaries

The basic set of boundary conditions for subsonic incompressible flow, introduced in Sec. 4.3 , relates to inlet, outlet and wall boundary regions. Sometimes a single boundary patch occupies a location which experiences both inflow and outflow.

PICT\relax \special {t4ht=

The figure above shows a 2D domain with an inlet and outlet, left and right respectively. The top boundary is free to allow:

  • inflow from the centre to the left side of the patch, through entrainment of fluid by the main flow from the inlet;
  • outflow at the right side of the patch, driven by a pressure gradient that emanates from the point where the flow impinges on the right wall.

Boundary conditions for eqn and eqn are therefore required which support both inflow and outflow at a single patch. The inlet flow speed is determined from the flow solution rather than being prescribed at the patch. This suggests a gradient condition on eqn, which is generally prescribed at an outlet.

PICT\relax \special {t4ht=

At a free/entrainment boundary, the basic outflow conditions, eqn and eqn, are generally not recommended. The figure above shows a snapshot from a simulation using those conditions. The solution oscillates between changing levels of inflow and outflow over the open boundary; the figure below shows the flow leading up to the snapshot above.

PICT\relax \special {t4ht=

The is no convergence towards a stable solution in this example of a simple flow in a regular 2D geometry. Moreover, solutions tend to diverge and “blow up” if the basic outflow conditions are applied at a free boundary for geometries and meshes that are even moderately complex. In the following sections we look at some alternative conditions that are applied at a free boundary to deliver stable, robust solutions.

Notes on CFD: General Principles - 4.6 Free (entrainment) boundaries