Transitions and instabilities of flow in a symmetric channel with a suddenly expanded and contracted part

Mizushima, Jiro; Shiotani, Y.

doi:10.1017/s0022112001003743

Cited by 33 publications

(32 citation statements)

References 7 publications

(9 reference statements)

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“…The flow in a planar X-junction exhibits two bifurcations as the Reynolds number is increased from zero. A similar bifurcation pattern has been observed in a channel with a sudden expansion (Fearn et al 1990;Fani et al 2012), contraction (Chiang & Sheu 2002), or both (Mizushima & Shiotani 2000). The flow first bifurcates to an asymmetric steady state through a pitchfork bifurcation.…”

Section: Introductionsupporting

confidence: 70%

The planar X-junction flow: stability analysis and control

et al. 2014

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The bifurcations and control of the flow in a planar X-junction are studied via linear stability analysis and direct numerical simulations. This study reveals the instability mechanisms in a symmetric channel junction and shows how these can be stabilized or destabilized by boundary modification. We observe two bifurcations as the Reynolds number increases. They both scale with the inlet speed of the two side channels and are almost independent of the inlet speed of the main channel. Equivalently, both bifurcations appear when the recirculation zone(s) reach a critical length. A two-dimensional stationary global mode becomes unstable first, changing the flow from a steady symmetric state to a steady asymmetric state via a pitchfork bifurcation. The core of this instability, whether defined by the structural sensitivity or the disturbance energy production, is at the edges of the recirculation bubbles, which are located symmetrically along the walls of the downstream channel. The energy analysis shows that the first bifurcation is due to a lift-up mechanism. We develop an adjustable control strategy for the first bifurcation with distributed suction/blowing at the walls. The linearly optimal wall-normal velocity distribution is computed through a sensitivity analysis and is shown to delay the first bifurcation from Re = 82.5 to Re = 150. This stabilizing effect arises because blowing at the walls weakens the streamwise velocity gradient around the recirculation zone and hinders the lift-up.At the second bifurcation, a three-dimensional stationary global mode with a span-wise wavenumber of order unity becomes unstable around the asymmetric steady state. Nonlinear three-dimensional simulations at the second bifurcation display transition to a nonlinear cycle involving growth of a three-dimensional steady structure, time-periodic secondary instability, and nonlinear breakdown restoring a two-dimensional flow. Finally, we show that the sensitivity to wall suction at the second bifurcation is as large as it is at the first bifurcation, providing a possible mechanism for destabilization.

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Section: Introductionsupporting

confidence: 70%

The planar X-junction flow: stability analysis and control

et al. 2014

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“…All these observations confirm that even if experimental setups are geometrically and hydraulically symmetric, asymmetric flow patterns can develop under certain geometric and hydraulic conditions, as shown for instance by Stovin [5,6]. Kolyshkin and Ghidaoui (2003) summarize similar findings for wake flows [10], including notably the detailed analysis of shallow flows behind various obstacles carried out by Chen and Jirka [11] Shiotani (1996, 2001) [12,13] have studied experimentally and numerically flows in symmetric channels with a suddenly expanded and contracted part for Reynolds numbers lower than 1,500 (in the approaching channel). The present study investigates flows with Reynolds numbers one to two orders of magnitude higher.…”

Section: Introductionsupporting

confidence: 68%

Experimental and numerical analysis of flow instabilities in rectangular shallow basins

et al. 2008

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Free surface flows in several shallow rectangular basins have been analyzed experimentally, numerically and theoretically. Different geometries, characterized by different widths and lengths, are considered as well as different hydraulic conditions. First, the results of a series of experimental tests are briefly depicted. They reveal that, under clearly identified hydraulic and geometrical conditions, the flow pattern is found to become nonsymmetric, in spite of the symmetrical inflow conditions, outflow conditions and geometry of the basin. This non-symmetric motion results from the growth of small disturbances actually present in the experimental initial and boundary conditions. Second, numerical simulations are conducted based on a depth-averaged approach and a finite volume scheme. The simulation results reproduce the global pattern of the flow observed experimentally and succeed in predicting the stability or instability of a symmetric flow pattern for all tested configurations. Finally, an analytical study provides mathematical insights into the conditions under which the symmetric flow pattern becomes unstable and clarifies the governing physical processes.

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“…These results are consistent with the nonlinear nature of the governing equations, enabling the system to converge towards different steady states depending on the initial conditions. Similarly, multiple steady-state solutions were observed for transitions at low Reynolds numbers (Mizushima and Shiotani 2001).…”

Section: Resultsmentioning

confidence: 73%