THE TIME-ASYMPTOTIC BEHAVIOR OF VORTEX BREAKDOWN IN TUBES

Numerical solutions of unsteady, viscous, swirling flows that experience vortex breakdown in a pipe were obtained. Solutions were computed assuming rotational symmetry and frictionless flow at the pipe wall. Both time-independent and time-varying (ramp to steady-state) vortex properties were specified at the inlet. Time-asymptotic solutions were found to be in agreement with results of calculations using the governing equations in steady-state form. However, where, as a function of vortex strength, multiple equilibrium solutions of the Navier-Stokes were admissible, time-asymptotic behavior was found to be sensitive to initial condition and the rate at which vortex strength was varied at the inlet. Time-asymptotic solutions either exhibited vortex breakdown (i.e., reversed flow was present) or were quasi-cylindrical in nature.