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Indexed by:Journal Papers
Date of Publication:2020-02-01
Journal:INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
Included Journals:EI、SCIE
Volume:147
ISSN No.:0017-9310
Key Words:Flow instability; Ledinegg instability; Flow excursion; Saddle-node bifurcation; Onset of flow instability; Hysteresis phenomenon
Abstract:Some new phenomena of Ledinegg instability are observed by portraying a complete flow excursion process via bifurcation analysis and experimental verification. A mathematical model consisting of two first-order nonlinear ordinary differential equations, is constructed via the lumped parameter method and verified through linear stability analysis. The results of bifurcation analysis show that Ledinegg instability corresponds to saddle-node bifurcation, which is consistent with previous literatures. The minimum point of the internal curve is not necessarily the onset of flow instability (OFI). It is equivalent, for the saddle-node bifurcation point, OR and the tangent point between two characteristic curves, to indicate flow excursion. The flow excursion process is unidirectional and irreversible at OFI, which decides that hysteresis phenomenon can be triggered by Ledinegg instability within the unstable bifurcation interval. Conversely, hysteresis phenomenon determines there exist two types of flow excursion and OFIs, namely, Type I and Type II which respectively correspond to decrease and increase in mass flux. Hysteresis phenomenon indicates not only that the system cannot autonomously returns to the original operating state once flow excursion occurs, but also that the sufficient and necessary condition of flow excursion is that current equilibrium state crosses over the corresponding OR in the same equilibrium branch. To avoid the occurrence of Ledinegg instability, a versatile quantitative criterion is developed by considering two characteristic forces simultaneously. Finally, experimental results verify the correctness of bifurcation analysis. (C) 2019 Elsevier Ltd. All rights reserved.
