Stability and dynamics of the flow past a bullet-shaped blunt body moving in a pipe

The flow past a bullet-shaped blunt body moving in a pipe is investigated through global linear stability analysis (LSA) and direct numerical simulation. A cartography of the bifurcation curves is provided thanks to LSA, covering the range of parameters corresponding to Reynolds number Re = [50-110], confinement ratio a/A = [0.01-0.92] and length-to-diameter ratio L/d = [2-10]. Results show that the first bifurcation is always a steady bifurcation associated to a non-oscillating eigenmode with azimuthal wavenumber m = +/- 1 leading to a steady state with planar symmetry. For weakly confined cases (a/A < 0.6), the second bifurcation is associated to an oscillating mode with azimuthal wavenumber m = +/- 1, as in the unconfined case. On the other hand, for the strongly confined case (a/A > 0.8), a destabilization of non-oscillating modes with vertical bar m vertical bar = 2, 3 and a restabilization of the m = +/- 1 eigenmodes are observed. The aspect ratio Lid is shown to have a minor influence for weakly confined cases and almost no influence for strongly confined cases. Direct numerical simulation is subsequently used to characterize the nonlinear dynamics. The results confirm the steady bifurcation predicted by LSA with excellent agreement for the threshold Reynolds. For weakly confined cases, the second bifurcation is a Hopf bifurcation leading to a periodic, planar-symmetric state in qualitative accordance with LSA predictions. For more confined cases, more complex dynamics is obtained, including a steady state with vertical bar m vertical bar = 3 geometry and aperiodic states.

Automated summary

The flow past a bullet-shaped blunt body moving in a pipe is investigated using global linear stability analysis (LSA) and direct numerical simulation. The results show that the confinement ratio and length-to-diameter ratio have an influence on the flow stability, with a destabilization and restabilization phenomenon observed for the strongly confined cases. The direct numerical simulation confirms the predictions made by LSA and reveals different dynamic states for weakly and strongly confined cases.