Influence of inlet flow profiles on swirling flow dynamics in a finite-length pipe

The influence of various inlet swirling flow profiles on the manifold of steady axisymmetric states of flows in a straight, long circular pipe of a finite length L and on flow dynamics is investigated. The study is motivated by the bifurcation diagrams originally studied by Leclaire and Sipp [B. Leclaire and D. Sipp, J. Fluid Mech. 645, 81 (2010)] and explores, in all of their inflow cases, the relationship between bifurcation and flow evolution. Steady circumferential and axial velocities and azimuthal vorticity are prescribed at the inlet. A parallel flow state is set at the outlet. The outlet state of the steady problem may be determined by solutions of the axially independent Squire-Long equation. For each of the incoming flows studied, the solutions include the base columnar flow solution, a decelerated flow along the centerline, an accelerated flow along the centerline, a vortex-breakdown solution, and a wall-separation solution. These solutions correspond to respective steady states in the pipe. Branches of higher-order noncolumnar states that bifurcate at a sequence of critical swirl levels are also presented. The theoretical predictions are numerically realized by unsteady and inviscid flow simulations. The simulations clarify the base flow stability and the dynamics of initial perturbations to various attracting states. Results demonstrate that, depending on the inlet flow profile, the global minimum state of the energy function epsilon of the problem turns at a certain critical swirl level, denoted by omega(0) + epsilon (L) [where 0 < epsilon (L) << 1 and tends to zero with an increase of L], from the columnar state to become a centerline-decelerated flow state, a vortex-breakdown state, or a wall-separation state. The jump of the global minimum state of epsilon at omega = omega(0) + epsilon (L) together with the critical swirl of the columnar state at omega = omega(1) govern the evolution of pipe vortex flows. This analysis provides understanding of all possible axisymmetric flow evolution processes for various inlet profiles and swirl levels, and the domain of attraction of crucial states.