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.
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 and 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 , which is generally prescribed at an outlet.
At a free/entrainment boundary, the basic outﬂow conditions, and , 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.
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.