The bubble-slug flow pattern transition and instabilities of void fraction waves

Matuszkiewicz, A.; Flamand, J.C.; Bouré, J. A.

doi:10.1016/0301-9322(87)90029-2

Cited by 54 publications

(8 citation statements)

References 5 publications

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“…That the onset of vertical slug fl ow results from an instability of bubbly flow is not currently accepted. However there exists strong experimental evidence (Matuszkiewicz et al 1987), as well as theoretical justification from linear stability theory (Boure 1988), that the void fraction waves-that is waves of volume fraction of gas-become unstable when the gas flow rate is increased. The under standing of the onset of slugging is still fragmentary and the obvious limits of the linear stability theory suggest that nonlinear analyses must be developed.…”

Section: Introductionmentioning

confidence: 98%

Modeling of Two-Phase Slug Flow

Fabre¹,

Liné²

1992

Annu. Rev. Fluid Mech.

297

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Section: Introductionmentioning

confidence: 98%

Modeling of Two-Phase Slug Flow

Fabre¹,

Liné²

1992

Annu. Rev. Fluid Mech.

297

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“…A more clear distinction between the other three models can be made if we study the dependence of the growth rate σ r on the wavenumber k for values of the void fraction close to the critical. Since it is reasonable to accept that the frequency of the fastest growing mode will be close (as an order of magnitude) to the frequency of the (generally nonlinear) waves measured in the experiments we can use some of the conclusions of Matuszkiewicz et al (1987). They observed that it increases with increasing value of the void fraction.…”

Section: Linear Stability Analysismentioning

confidence: 81%

“…It is proportional to ρ 1 and in that case ρ 2 ρ 1 . In an experimental study Matuszkiewicz, Flamand & Bouré (1987) found that a uniform bubbly flow can undergo a transition at values of the void fraction larger than 0.25. Since the expressions for δ e and µ d contain free parameters of order of 1, however, this quantitative criterion is not decisive.…”

Section: Linear Stability Analysismentioning

confidence: 99%

“…A natural choice for a characteristic length is the wavelength l of the void-fraction waves observed in the experiments. Matuszkiewicz et al (1987) indicate that the typical wavelength for bubble flow is 0.3 m. The most obvious choice for a characteristic velocity is the velocity v 0 of the undisturbed uniform dispersion given by (3.1). For model (i) the dimensionless momentum equation (obtained from 2.18) then reads †…”

Section: Weakly Nonlinear Analysismentioning

confidence: 99%

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A comparative study of two-phase flow models relevant to bubble column dynamics

1999

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Multiphase flow modelling is still a major challenge in fluid dynamics and, although many different models have been derived, there is no clear evidence of their relevance to certain flow situations. That is particularly valid for bubbly flows, because most of the studies have considered the case of fluidized beds. In the present study we give a general formulation to five existing models and study their relevance to bubbly flows. The results of the linear analysis of those models clearly show that only two of them are applicable to that case. They both show a very similar qualitative linear stability behaviour. In the subsequent asymptotic analysis we derive an equation hierarchy which describes the weakly nonlinear stability of the models. Their qualitative behaviour up to first order with respect to the small parameter is again identical. A permanent-wave solution of the first two equations of the hierarchy is found. It is shown, however, that the permanent-wave (soliton) solution is very unlikely to occur for the most common case of gas bubbles in water. The reason is that the weakly nonlinear equations are unstable due to the low magnitude of the bulk modulus of elasticity. Physically relevant stabilization can eventually be achieved using some available experimental data. Finally, a necessary condition for existence of a fully nonlinear soliton is derived.

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“…Brennen 2005), but it is not known what determines the transition between these. One suggestion for the bubbly to slug transition is that bubbly flow becomes unstable to kinematic waves as the bubble volume (void) fraction increases (Matuszkiewicz et al 1987). A common feature of two-phase flow models is that they can be ill-posedy in certain circumstances (e.g.…”

Section: The Day After Tomorrowmentioning

confidence: 99%

A note on the derivation of the quasi-geostrophic potential vorticity equation

Fowler

2011

Geophysical & Astrophysical Fluid Dynamics

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The derivation of the quasi-geostrophic potential vorticity equation of mathematical meteorology is usually done using fairly sophisticated techniques of perturbation theory, but stops short of deriving self-consistently the stratification parameter of the mean atmospheric state. In this note we suggest how this should be done within the confines of the theory, and as a consequence we raise the possibility that the atmosphere could become globally unstable, with dramatic consequences.

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The bubble-slug flow pattern transition and instabilities of void fraction waves

Cited by 54 publications

References 5 publications

Modeling of Two-Phase Slug Flow

Modeling of Two-Phase Slug Flow

A comparative study of two-phase flow models relevant to bubble column dynamics

A note on the derivation of the quasi-geostrophic potential vorticity equation

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