The bifurcation structure is presented for an axisymmetric swirling flow in a constricted pipe, using the pipe geometry of Beran and Culick [J. Fluid Mech. 242, 491 (1992)]. The flow considered has been restricted to a two‐dimensional parameter space comprising the Reynolds number Re and the relative swirl V0 of the incoming swirling flow. The bifurcation diagram is constructed by solving the time‐dependent axisymmetric Navier–Stokes equations. The stability of the steady results presented by Beran and Culick, obtained from a steady axisymmetric Navier–Stokes code, has been confirmed. Further, the steady solution branch has also been extended to much larger V0 values. At larger V0, a stable unsteady solution branch has been identified. This unsteady branch coexists with the previously found stable steady solution branch and originates via a turning point bifurcation. The bifurcation diagram is of the type described by Benjamin [Proc. R. Soc. London Ser. A 359, 1 (1978)] as the canonical unfolding of a pitchfork bifurcation. This type of bifurcation structure in the two‐dimensional parameter space (Re,V0), suggests the possibility of hysteresis behavior over some part of parameter space, and this is observed in the present study. The implications of this on the theoretical description of vortex breakdown and the search for a criterion for its onset are discussed.
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November 1994
Research Article|
November 01 1994
On the bifurcation structure of axisymmetric vortex breakdown in a constricted pipe
J. M. Lopez
J. M. Lopez
Department of Mathematics and Earth System Science Center, The Pennsylvania State University, University Park, Pennsylvania 16802
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Physics of Fluids 6, 3683–3693 (1994)
Article history
Received:
April 05 1994
Accepted:
July 20 1994
Citation
J. M. Lopez; On the bifurcation structure of axisymmetric vortex breakdown in a constricted pipe. Physics of Fluids 1 November 1994; 6 (11): 3683–3693. https://doi.org/10.1063/1.868359
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