STABILITY AND EXISTENCE OF MULTIPLE SOLUTIONS FOR VISCOUS-FLOW IN SUDDENLY ENLARGED CHANNELS

Instability of two-dimensional symmetric flows through channels with a symmetrical expansion about their centerline was studied. A numerical solution of viscous flow in two-dimensional channels with symmetric changes in width is presented. The channel semi-angles range from 10° to 90°, with width ratios up to 3, and Reynolds number based on the small width of up to 400. Two types of calculations for the flowfield were made, one for a full channel and the second for a half channel assuming symmetry. Using linear stability analysis the stability limit for the half-domain calculation is then shown to be the minimum Reynolds number for which an asymmetric full-flowfield solution can be obtained. For example, for a 1 : 3 expansion ratio the critical Reynolds number for stability changes from 82 for the 90° semi-angle to 147 for the 10° semi angle. A linear disturbance was applied and a time-dependent finite element solver was used to isolate the least stable mode and the corresponding eigenvalue. The eigenvalues corresponding to the least stable modes for all cases were real, indicating that the instability was local. The least stable mode was found to have a shape which indicates that this disturbance is due to the Coanda effect. This causes the change from symmetric to asymmetric flow pattern for Re > Recr. The disturbance eigenfunction is antisymmetric for the linear regime of disturbances studied here. © 1990.