scholarly journals Exchange flow of two immiscible fluids and the principle of maximum flux

2011 ◽  
Vol 682 ◽  
pp. 132-159 ◽  
Author(s):  
R. R. KERSWELL
Keyword(s):  
Viscous Fluid ◽  
Annular Flow ◽  
Viscosity Ratio ◽  
Cylindrical Tube ◽  
Immiscible Fluids ◽  
Exchange Flow ◽  
Two Phase ◽  
Full Circle ◽  
Flow Situation ◽  
Principle Of Maximum

The steady, coaxial flow in which two immiscible, incompressible fluids of differing densities move past each other slowly in a vertical cylindrical tube has a continuum of possibilities due to the arbitrariness of the interface between the fluids. By invoking the presence of surface tension to at least restrict the shape of any interface to that of a circular arc or full circle, we consider the following question: which flow will maximise the exchange when there is only one dividing interface Γ? Surprisingly, the answer differs fundamentally from the better-known co-directional two-phase flow situation where an axisymmetric (concentric) core-annular solution always optimises the flux. Instead, the maximal flux state is invariably asymmetric either being a ‘side-by-side’ configuration where Γ starts and finishes at the tube wall or an eccentric core-annular flow where Γ is an off-centre full circle in which the more viscous fluid is surrounded by the less viscous fluid. The side-by-side solution is the most efficient exchanger for a small viscosity ratio β ≲ 4.60 with an eccentric core-annular solution optimal otherwise. At large β, this eccentric solution provides 51% more flux than the axisymmetric core-annular flow which is always a local minimiser of the flux.

Core–annular flow in a periodically constricted circular tube. Part 1. Steady-state, linear stability and energy analysis

2001 ◽  
Vol 432 ◽  
pp. 31-68 ◽  
Author(s):  
CHARALAMPOS KOURIS ◽  
JOHN TSAMOPOULOS
Keyword(s):  
Weber Number ◽  
Annular Flow ◽  
Viscosity Ratio ◽  
Solid Wall ◽  
Immiscible Fluids ◽  
Straight Tube ◽  
Neutral Stability ◽  
Ohnesorge Number ◽  
Dimensionless Numbers ◽  
Two Phase

The concentric, two-phase flow of two immiscible fluids in a tube of sinusoidally varying cross-section is studied. This geometry is often used as a model to study the onset of different flow regimes in packed beds. Neglecting gravitational effects, the model equations depend on five dimensionless parameters: the Reynolds and Weber numbers, and the ratios of density, viscosity and volume of the two fluids. Two more dimensionless numbers describe the shape of the solid wall: the constriction ratio and the ratio of its maximum radius to its period. In addition to the effect of the Weber number, which depends on both the fluid and the flow, the effect of the Ohnesorge number J has been examined as it characterizes the fluid alone. The governing equations are approximated using the pseudo-spectral methodology while the Arnoldi algorithm has been implemented for computing the most critical eigenvalues that correspond to axisymmetric disturbances. Stationary solutions are obtained for a wide parameter range, which may exhibit flow recirculation at the expanding portion of the tube. Extensive calculations are made for the dependence of the neutral stability boundaries on the various parameters. In most cases where the steady solution becomes unstable it does so through a Hopf bifurcation. Exceptions to this are cases where the viscosity ratio is O(10−3) and, then, the most unstable eigenvalue remains real. Generally, steady core–annular flow in this geometry is more susceptible to instability than in a straight tube and, in similar ranges of the parameters, it may be generated by different mechanisms. Decreasing the thickness of the annular fluid, inverse Weber number or the Ohnesorge number or the density of the core fluid stabilizes the flow. For stability reasons, the viscosity ratio must remain strictly below unity and it has an optimum value that maximizes the range of allowed Reynolds numbers.

Liquid-Liquid Two-Phase Flow Patterns and Mass Transfer Characteristics in a Circular Microchannel

2012 ◽  
Vol 482-484 ◽  
pp. 89-94
Author(s):  
Xu Bin Zhang ◽  
Dan Chen ◽  
Yan Wang ◽  
Wang Feng Cai
Keyword(s):  
Mass Transfer ◽  
Annular Flow ◽  
Flow Patterns ◽  
Immiscible Fluids ◽  
Viscous Force ◽  
Inertia Force ◽  
Transfer Coefficients ◽  
Two Phase ◽  
Transfer Characteristics ◽  
Circular Microchannel

In this paper, flow patterns and mass transfer characteristics of two immiscible fluids in a T-junction circular microchannel were investigated. Four flow patterns, i.e. slug flow, irregular flow, parallel flow and annular flow, were captured by a CCD method, which were resulted from the competition among interfacial tension, viscous force and inertia force. Besides, the overall volumetric mass transfer coefficients ka for the four flow patterns was determined experimentally. The values of ka are in the range of 0.006~0.545s−1 and mainly dependent on the superficial velocity and the flow pattern regime.

Hydromagnetic Mixed Convective Two-Phase Flow of Couple Stress and Viscous Fluids in an Inclined Channel

2014 ◽  
Vol 69 (10-11) ◽  
pp. 553-561 ◽  
Author(s):  
Zaheer Abbas ◽  
Jafar Hasnain ◽  
Muhammad Sajid
Keyword(s):  
Viscous Fluid ◽  
Couple Stress ◽  
Mhd Flow ◽  
Immiscible Fluids ◽  
Two Phase ◽  
Fully Developed Flow ◽  
Closed Form Solutions ◽  
Inclined Channel ◽  
Electrically Conducting ◽  
Flow And Heat Transfer

AbstractAn analysis is carried out to study magnetohydrodynamic (MHD) flow and heat transfer of two immiscible fluids in an inclined channel. The channel is filled with couple stress fluid in one region and a viscous fluid in the other region. The viscous fluid is assumed to be electrically conducting. The governing equations are modelled using the fully developed flow conditions. A closed form solutions of velocity and the temperature profiles are obtained by using perturbation method. The physical interpretation of the emerging parameters of interest on the velocity and temperature distributions are shown through graphs and discussed in detail.

scholarly journals Numerical simulations of the behaviour of a drop in a square pipe flow using the two-phase lattice Boltzmann method

2011 ◽  
Vol 369 (1945) ◽  
pp. 2528-2536 ◽  
Author(s):  
Yuta Kataoka ◽  
Takaji Inamuro
Keyword(s):  
Lattice Boltzmann Method ◽  
Pipe Flow ◽  
Lattice Boltzmann ◽  
Weber Number ◽  
Viscosity Ratio ◽  
Reynolds Numbers ◽  
Immiscible Fluids ◽  
Two Phase ◽  
Pipe Section ◽  
Boltzmann Method

The lattice Boltzmann method for multi-component immiscible fluids is applied to simulations of the behaviour of a drop in a square pipe flow for various Reynolds numbers of 10< Re <500, Weber numbers of 0< We <250 and viscosity ratios of η =1/5, 1, 2 and 5. It is found that, for low Weber numbers, the drop moves straight along a stable position on the diagonal line of the pipe section, and it moves along the centre axis of the pipe for larger Weber numbers. We obtain the boundary of the two different behaviours of the drop in terms of Reynolds number, Weber number and viscosity ratio.

Dynamics of a viscous thread surrounded by another viscous fluid in a cylindrical tube under the action of a radial electric field: breakup and touchdown singularities

2011 ◽  
Vol 683 ◽  
pp. 27-56 ◽  
Author(s):  
Q. Wang ◽  
D. T. Papageorgiou
Keyword(s):  
Viscous Fluid ◽  
Electric Field ◽  
Electric Fields ◽  
Viscosity Ratio ◽  
Cylindrical Tube ◽  
Radial Electric Field ◽  
Boundary Element Methods ◽  
Annular Region ◽  
Two Fluids ◽  
Jet Breakup

AbstractThe nonlinear dynamics of a viscous filament surrounded by a second viscous fluid arranged in a core-annular configuration when a radial electric field acts in the annular region, are studied analytically and computationally using boundary element methods. The flow is characterized by the viscosity ratio, an electric Weber number measuring the strength of the electric field, a geometrical parameter measuring the thickness of the undisturbed annular region, as well as a computational parameter that fixes the wavenumber of the undulations. Axisymmetric solutions are computed by direct numerical simulations in the Stokes limit for general values of the parameters when the two fluids have equal viscosities, and an asymptotic theory is carried out to produce a novel evolution equation for thin film dynamics valid when the undisturbed annular thickness is small and the viscosity ratio is of order one. It is established (in agreement with previous computations in the absence of electric fields) that a sufficiently thick annulus enables thread breakup while a sufficiently thin one (approximately one fifth of the undisturbed thread radius for the case of equal viscosities, for instance) suppresses pinching and drives the interface to approach the tube wall asymptotically without actually touching it. The present simulations show that the electric field affects the dynamics drastically in several ways. First, it promotes interfacial wall touchdown in finite time and a comparison between direct simulations and the asymptotic solutions are in fair agreement. Second, the electric field acts to suppress pinching in the sense that solutions that lead to jet breakup due to a thick enough viscous annulus are driven to wall touchdown. When pinching takes place we find that the ultimate pinching solutions are self-similar and recover the non-electrified ones to leading order for the range of parameters studied.

On Instabilities in Horizontal Two-Phase Flow

1994 ◽  
Vol 59 (12) ◽  
pp. 2595-2603
Author(s):  
Lothar Ebner ◽  
Marie Fialová
Keyword(s):  
Differential Equation ◽  
Flow Regime ◽  
Slug Flow ◽  
Annular Flow ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Annular Flows ◽  
Flow Regime Maps

Two regions of instabilities in horizontal two-phase flow were detected. The first was found in the transition from slug to annular flow, the second between stratified and slug flow. The existence of oscillations between the slug and annular flows can explain the differences in the limitation of the slug flow in flow regime maps proposed by different authors. Coexistence of these two regimes is similar to bistable behaviour of some differential equation solutions.

Upward Vertical Two-Phase Flow Through an Annulus—Part II: Modeling Bubble, Slug, and Annular Flow

1992 ◽  
Vol 114 (1) ◽  
pp. 14-30 ◽  
Author(s):  
E. F. Caetano ◽  
O. Shoham ◽  
J. P. Brill
Keyword(s):  
Flow Pattern ◽  
Annular Flow ◽  
Two Phase Flow ◽  
Flow Behavior ◽  
Bubble Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Through ◽  
Physical Phenomena ◽  
Good Agreement

Mechanistic models have been developed for each of the existing two-phase flow patterns in an annulus, namely bubble flow, dispersed bubble flow, slug flow, and annular flow. These models are based on two-phase flow physical phenomena and incorporate annulus characteristics such as casing and tubing diameters and degree of eccentricity. The models also apply the new predictive means for friction factor and Taylor bubble rise velocity presented in Part I. Given a set of flow conditions, the existing flow pattern in the system can be predicted. The developed models are applied next for predicting the flow behavior, including the average volumetric liquid holdup and the average total pressure gradient for the existing flow pattern. In general, good agreement was observed between the experimental data and model predictions.

Measurement of Liquid Film Thickness in Micro Tube Annular Flow

2010 ◽  
Author(s):  
Hiroshi Kanno ◽  
Youngbae Han ◽  
Yusuke Saito ◽  
Naoki Shikazono
Keyword(s):  
Heat Transfer ◽  
Film Thickness ◽  
Liquid Film ◽  
Annular Flow ◽  
Liquid Film Thickness ◽  
Phase Flow ◽  
Two Phase ◽  
Micro Scale ◽  
Film Model ◽  
Annular Film

Heat transfer in micro scale two-phase flow attracts large attention since it can achieve large heat transfer area per density. At high quality, annular flow becomes one of the major flow regimes in micro two-phase flow. Heat is transferred by evaporation or condensation of the liquid film, which are the dominant mechanisms of micro scale heat transfer. Therefore, liquid film thickness is one of the most important parameters in modeling the phenomena. In macro tubes, large numbers of researches have been conducted to investigate the liquid film thickness. However, in micro tubes, quantitative information for the annular liquid film thickness is still limited. In the present study, annular liquid film thickness is measured using a confocal method, which is used in the previous study [1, 2]. Glass tubes with inner diameters of 0.3, 0.5 and 1.0 mm are used. Degassed water and FC40 are used as working fluids, and the total mass flux is varied from G = 100 to 500 kg/m2s. Liquid film thickness is measured by laser confocal displacement meter (LCDM), and the liquid-gas interface profile is observed by a high-speed camera. Mean liquid film thickness is then plotted against quality for different flow rates and tube diameters. Mean thickness data is compared with the smooth annular film model of Revellin et al. [3]. Annular film model predictions overestimated the experimental values especially at low quality. It is considered that this overestimation is attributed to the disturbances caused by the interface ripples.

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