Vortex dynamics in confined counter-current shearing flows with applications to mixing

A numerical investigation has been performed for the time-dependent motion of a constant property, Newtonian fluid in a counter-current shearing flows configuration. In the geometry of interest, two initially separated streams are made to flow counter to each other at bulk average velocities U1 and U2 along the streamwise (x-coordinate) direction through a pair of stacked, straight, parallel channels. The channels have width W, height H/2 and length L, and are separated by a pair of thin plates with a discontinuity in length Lm centered at L/2. The counter-flowing streams interact dynamically in the space shared by the two channels, defined by the discontinuity between plates. This problem consists of a very simple Cartesian geometry with well posed initial and boundary conditions and yet, for the conditions explored, the resulting physics is highly non-linear and complex. Starting from rest, the counter-flowing streams in the shared space region initially display the characteristics of a two-dimensional saddle point flow when observed along the spanwise (z  -coordinate) direction. Soon thereafter, depending on the shapes of the velocity profiles imposed at the channel inlet planes and the respective Reynolds numbers of the opposing streams Re1,2≡U1,2H/2ν, two pairs of vortices aligned in the transverse (y-coordinate) direction appear that can be stable or unstable. If the inlet plane velocity profiles are symmetric and Re1 = Re2 = 300 or Re1 = 2 × Re2 = 300 each of the two channel vortex pairs counter-rotates and they are stable over long periods of time. If, however, the inlet velocity profiles are anti-symmetric one pair of anti-symmetric co-rotating vortices dominates the flow and they orbit around each other. For this case, if Re1 = Re2 < 200 the vortex pair merge and the resulting vortex structure is stable. In contrast, if Re1 = Re2 > 200, in the presence of stretching by the background saddle point flow the merging of the vortex pair is unstable and the resulting vortex structure ultimately collapses in a temporary burst of complex, three-dimensional, unsteady motion. Soon thereafter, the formation, merging and collapse of this vortex pair repeats. Aside from their intrinsic fundamental interest, the phenomena observed have potential applications for the controlled mixing of fluid streams at both low and high Reynolds numbers. Flow visualization results show how this can be achieved in a device consisting of a number of basic counter-current flow units concatenated in series.