The residence-time algorithm is used on flow through a converging-diverging duct. This case is selected because of the unusual nature of the solver. This axi-symmetric (with swirl) system computes the streamfunction as part of the state-vector. This allows the simple calculation of the zero streamfunction or separation surface. All residence time calculations are done in full 3D by spinning the 2D geometry and producing 16 azimuthal sections. The cells are all hexahedra except those at the centerline that are represented as prisms. The following examples were computed with a Reynolds number of 200 and a swirl ratio of 1.75. The duct walls are treated with a slip condition. The solver was run in a transient mode but the input conditions produce a stable flow. Residence-time is calculated for both inviscid incompressible and constant viscosity and density cases.

The top image displays the duct and a rake of streamlines generated from the upstream region. It is clear that something interesting is occurring at the converging part of the pipe.

The separation bubble is fully displayed just downstream of the converging section as shown in second image. This is an iso-surface of the streamfunction with value 0.

The characteristic time for this problem is about 24. This is found by looking at an iso-surface of residence-time and finding the time where the major portion of the flow exits the domain. A value greater than that needs to be selected to differentiate old fluid from the core flow. The third image displays an iso-surface of residence-time at the value of 40.

The bottom image displays the comparsion of the streamfunction (transparent) and the residence-time isosurface.