On the oscillatory hydrodynamic instability of gravitational thermal flows of liquid metals in variable cross-section containers

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Abstract

Natural convective flows of liquid metals in open or closed ducts and containers play a relevant role in a variety of applications in mechanical, materials and nuclear engineering. This analysis follows and integrates the line of inquiry started in past authors’ work about the typical properties of these flows and associated hierarchy of bifurcations in rectangular geometries. The Navier Stokes and energy equations are solved in their time-dependent and non-linear formulation to investigate the onset and evolution of oscillatory disturbances and other effects breaking the initially unicellular structure of the flow. It is shown that a kaleidoscope of oscillatory patterns is made possible by the new degree of freedom represented by the opposite inclination of the walls with respect to the horizontal direction. Even minute variations in the geometry and/or initial conditions can cause significant changes. Multiple states exist which can replace each other in given sub-regions of the space of parameters. Observed regimes include: stationary convection, weakly oscillating rolls, coalescing rolls, traveling waves, and modulated (pulso-traveling) disturbances. Most interestingly, traveling waves can propagate either in the downstream or the upstream direction according to whether the walls are converging or diverging.
LanguageEnglish
Article number064106
Number of pages18
JournalPhysics of Fluids
Volume29
Issue number6
DOIs
Publication statusPublished - 14 Jun 2017

Fingerprint

liquid metals
containers
Liquid metals
traveling waves
Containers
Flow of fluids
disturbances
Hydrodynamics
hydrodynamics
engineering
Nuclear engineering
mechanical engineering
Bifurcation (mathematics)
Geometry
convective flow
cross sections
geometry
ducts
Ducts
coalescing

Keywords

  • liquid metals
  • thermal flows
  • bifurcations
  • Navier Stokes equations
  • oscillatory disturbances
  • traveling waves

Cite this

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title = "On the oscillatory hydrodynamic instability of gravitational thermal flows of liquid metals in variable cross-section containers",
abstract = "Natural convective flows of liquid metals in open or closed ducts and containers play a relevant role in a variety of applications in mechanical, materials and nuclear engineering. This analysis follows and integrates the line of inquiry started in past authors’ work about the typical properties of these flows and associated hierarchy of bifurcations in rectangular geometries. The Navier Stokes and energy equations are solved in their time-dependent and non-linear formulation to investigate the onset and evolution of oscillatory disturbances and other effects breaking the initially unicellular structure of the flow. It is shown that a kaleidoscope of oscillatory patterns is made possible by the new degree of freedom represented by the opposite inclination of the walls with respect to the horizontal direction. Even minute variations in the geometry and/or initial conditions can cause significant changes. Multiple states exist which can replace each other in given sub-regions of the space of parameters. Observed regimes include: stationary convection, weakly oscillating rolls, coalescing rolls, traveling waves, and modulated (pulso-traveling) disturbances. Most interestingly, traveling waves can propagate either in the downstream or the upstream direction according to whether the walls are converging or diverging.",
keywords = "liquid metals, thermal flows, bifurcations, Navier Stokes equations, oscillatory disturbances, traveling waves",
author = "Marcello Lappa and Hermes Ferialdi",
note = "This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Lappa, M., & Ferialdi, H. (2017). On the oscillatory hydrodynamic instability of gravitational thermal flows of liquid metals in variable cross-section containers. Physics of Fluids, 29(6), [064106], and may be found at https://doi.org/10.1063/1.4985197.",
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N1 - This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Lappa, M., & Ferialdi, H. (2017). On the oscillatory hydrodynamic instability of gravitational thermal flows of liquid metals in variable cross-section containers. Physics of Fluids, 29(6), [064106], and may be found at https://doi.org/10.1063/1.4985197.

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N2 - Natural convective flows of liquid metals in open or closed ducts and containers play a relevant role in a variety of applications in mechanical, materials and nuclear engineering. This analysis follows and integrates the line of inquiry started in past authors’ work about the typical properties of these flows and associated hierarchy of bifurcations in rectangular geometries. The Navier Stokes and energy equations are solved in their time-dependent and non-linear formulation to investigate the onset and evolution of oscillatory disturbances and other effects breaking the initially unicellular structure of the flow. It is shown that a kaleidoscope of oscillatory patterns is made possible by the new degree of freedom represented by the opposite inclination of the walls with respect to the horizontal direction. Even minute variations in the geometry and/or initial conditions can cause significant changes. Multiple states exist which can replace each other in given sub-regions of the space of parameters. Observed regimes include: stationary convection, weakly oscillating rolls, coalescing rolls, traveling waves, and modulated (pulso-traveling) disturbances. Most interestingly, traveling waves can propagate either in the downstream or the upstream direction according to whether the walls are converging or diverging.

AB - Natural convective flows of liquid metals in open or closed ducts and containers play a relevant role in a variety of applications in mechanical, materials and nuclear engineering. This analysis follows and integrates the line of inquiry started in past authors’ work about the typical properties of these flows and associated hierarchy of bifurcations in rectangular geometries. The Navier Stokes and energy equations are solved in their time-dependent and non-linear formulation to investigate the onset and evolution of oscillatory disturbances and other effects breaking the initially unicellular structure of the flow. It is shown that a kaleidoscope of oscillatory patterns is made possible by the new degree of freedom represented by the opposite inclination of the walls with respect to the horizontal direction. Even minute variations in the geometry and/or initial conditions can cause significant changes. Multiple states exist which can replace each other in given sub-regions of the space of parameters. Observed regimes include: stationary convection, weakly oscillating rolls, coalescing rolls, traveling waves, and modulated (pulso-traveling) disturbances. Most interestingly, traveling waves can propagate either in the downstream or the upstream direction according to whether the walls are converging or diverging.

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