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Journal ArticleDOI

Dynamics of the axisymmetric core-annular flow. II. The less viscous fluid in the core, saw tooth waves

13 Feb 2002-Physics of Fluids (American Institute of Physics)-Vol. 14, Iss: 3, pp 1011-1029
TL;DR: In this paper, the authors studied the nonlinear dynamics of the concentric, two-phase flow of two immiscible fluids in a circular tube, where the viscosity ratio of the fluid in the annulus to that in the core of the tube, μ, is larger than or equal to unity.
Abstract: The nonlinear dynamics of the concentric, two-phase flow of two immiscible fluids in a circular tube is studied when the viscosity ratio of the fluid in the annulus to that in the core of the tube, μ, is larger than or equal to unity. For these values of the viscosity ratio the perfect core-annular flow (CAF) is linearly unstable and it is necessary to keep the ratio of the thickness of the annulus to the radius of the tube small so that the solutions remain uniformly bounded. The simulations are based on a pseudospectral numerical method while special care has been taken in order to minimize as far as possible the effect of the boundary conditions imposed in the axial direction allowing for multiple waves of different lengths to develop and interact. The time integration originates with the analytical solution for the pressure driven, perfect CAF or the perfect CAF seeded with either the most unstable mode or random disturbances. Quite regular wave patterns are predicted in the first two cases, whereas m...
Citations
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Journal ArticleDOI
TL;DR: In this article, a review highlights the profound and unexpected ways in which viscosity varying in space and time can affect flow and the most striking manifestations are through alterations of flow stability, as established in model shear flows and industrial applications.
Abstract: This review highlights the profound and unexpected ways in which viscosity varying in space and time can affect flow. The most striking manifestations are through alterations of flow stability, as established in model shear flows and industrial applications. Future studies are needed to address the important effect of viscosity stratification in such diverse environments as Earth's core, the Sun, blood vessels, and the re-entry of spacecraft.

231 citations


Cites background from "Dynamics of the axisymmetric core-a..."

  • ...Kouris & Tsamopoulos (2002) found sawtooth waves in their simulations....

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Journal ArticleDOI
TL;DR: In this article, the stability of miscible two-fluid flow in a horizontal channel is examined, where flow dynamics are governed by the continuity and Navier-Stokes equations coupled to a convective-diffusion equation for the concentration of the more viscous fluid through a concentration-dependent viscosity.
Abstract: The stability of miscible two-fluid flow in a horizontal channel is examined. The flow dynamics are governed by the continuity and Navier–Stokes equations coupled to a convective-diffusion equation for the concentration of the more viscous fluid through a concentration-dependent viscosity. Our analysis of the flow in the linear regime delineates the presence of convective and absolute instabilities and identifies the vertical gradients of viscosity perturbations as the main destabilizing influence in agreement with previous work. Our transient numerical simulations demonstrate the development of complex dynamics in the nonlinear regime, characterized by roll-up phenomena and intense convective mixing; these become pronounced with increasing flow rate and viscosity ratio, as well as weak diffusion.

111 citations

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the linear stability of variable viscosity, miscible core-annular flows and showed that the flow is stable at any Reynolds number when the magnitude of the viscosities ratio is less than a critical value.
Abstract: The linear stability of variable viscosity, miscible core-annular flows is investigated. Consistent with pipe flow of a single fluid, the flow is stable at any Reynolds number when the magnitude of the viscosity ratio is less than a critical value. This is in contrast to the immiscible case without interfacial tension, which is unstable at any viscosity ratio. Beyond the critical value of the viscosity ratio, the flow can be unstable even when the more viscous fluid is in the core. This is in contrast to plane channel flows with finite interface thickness, which are always stabilized relative to single fluid flow when the less viscous fluid is in contact with the wall. If the more viscous fluid occupies the core, the axisymmetric mode usually dominates over the corkscrew mode. It is demonstrated that, for a less viscous core, the corkscrew mode is inviscidly unstable, whereas the axisymmetric mode is unstable for small Reynolds numbers at high Schmidt numbers. For the parameters under consideration, the switchover occurs at an intermediate Schmidt number of about 500. The occurrence of inviscid instability for the corkscrew mode is shown to be consistent with the Rayleigh criterion for pipe flows. In some parameter ranges, the miscible flow is seen to be more unstable than its immiscible counterpart, and the physical reasons for this behaviour are discussed. A detailed parametric study shows that increasing the interface thickness has a uniformly stabilizing effect. The flow is least stable when the interface between the two fluids is located at approximately 0.6 times the tube radius. Unlike for channel flow, there is no sudden change in the stability with radial location of the interface. The instability originates mainly in the less viscous fluid, close to the interface.

94 citations


Cites background from "Dynamics of the axisymmetric core-a..."

  • ...Kouris & Tsamopoulos (2001a, 2002a) investigated both linear and nonlinear dynamics of core– annular flows in periodically constricted circular tubes, whereas Wei & Rumschitzki (2002a, b) modelled the core–annular flows in an asymptotically corrugated tube....

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  • ...More recently, nonlinear simulations of such immiscible flows have been conducted by several authors, among them Li & Renardy (1999) and Kouris & Tsamopoulos (2001b, 2002b)....

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Journal ArticleDOI
TL;DR: In this paper, the effect of buoyancy on pressure-driven flow of two miscible fluids in inclined channels via direct numerical simulations was studied, where the flow dynamics were governed by the continuity and Navier-Stokes equations, without the Boussinesq approximation, coupled to a convective-diffusion equation for the concentration of the more viscous fluid through a concentrationdependent viscosity and density.
Abstract: We study the effect of buoyancy on pressure-driven flow of two miscible fluids in inclined channels via direct numerical simulations. The flow dynamics are governed by the continuity and Navier–Stokes equations, without the Boussinesq approximation, coupled to a convective-diffusion equation for the concentration of the more viscous fluid through a concentration-dependent viscosity and density. The effect of varying the density ratio, Froude number, and channel inclination on the flow dynamics is examined, for moderate Reynolds numbers. We present results showing the spatiotemporal evolution of the flow together with an integral measure of mixing.

70 citations

Journal ArticleDOI
TL;DR: In this paper, the authors report on experiments with two miscible fluids of equal density but different viscosities, injected co-currently and concentrically into a cylindrical pipe.
Abstract: We report on experiments with two miscible fluids of equal density but different viscosities. The fluids were injected co-currently and concentrically into a cylindrical pipe. The resulting base state is an axisymmetric parallel flow. The ratio of the two fluid flow rates determines the relative amount of the fluids, thus the radius of the inner core fluid. Depending on this radius and the total flow rate, two different and unstable axisymmetric patterns, denoted by mushrooms and pearls, were observed. We delineate the diagram of occurrence of the two patterns as a function of the various parameters.

67 citations

References
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Book
01 Jan 1979
TL;DR: In this paper, the authors examined the relationship between transport properties and pore structure of porous material and presented models of pore structures with a discussion of how such models can be used to predict the transport properties of porous media.
Abstract: This book examines the relationship between transport properties and pore structure of porous material. Models of pore structure are presented with a discussion of how such models can be used to predict the transport properties of porous media.

3,638 citations

Book
01 Jan 1950
TL;DR: In this article, the authors provide fundamental instruction in heat transfer while employing the methods and language of industry using a course given at the Polytechnic Institute of Brooklyn over a period of years.
Abstract: It is the object of this text to provide fundamental instruction in heat transfer while employing the methods and language of industry. This treatment of the subject has evolved from a course given at the Polytechnic Institute of Brooklyn over a period of years. The possibilities of collegiate instruction patterned after the requirements of the practicing process engineer were suggested and encouraged by Dr. Donald F. Othmer, Head of the Department of Chemical Engineering. The inclusion of the practical aspects of the subject as an integral part of the pedagogy was intended to serve as a supplement rather than a substitute for a strong foundation in engineering fundamentals. These points of view have been retained throughout the writing of the book.

955 citations

Journal ArticleDOI
TL;DR: In this paper, the authors characterized the transition to chaos of the solutions to the Kuramoto-Sivashinsky equation through extensive numerical simulation, and showed that the attracting solution manifolds undergo a complex bifurcation sequence including multimodal fixed points, invariant tori, traveling wave trains, and homoclinic orbits.

310 citations

Journal ArticleDOI
TL;DR: In this paper, the existence and role of solitary waves in the instability of a fluid layer flowing down an inclined plane was studied and the long-term evolution was shown to be a slow relaxation to a steady state in a moving frame.
Abstract: We study the existence and the role of solitary waves in the instability of a fluid layer flowing down an inclined plane. The approach presented is fully nonlinear. Solitary waves steady in a moving frame are described by homoclinic trajectories of an associated ordinary differential equation. They are searched numerically for a given value of viscosity and surface tension. Several kinds of solitary waves can exist, characterized by their number n of humps. We investigate the stability of these waves by integrating the initial-value problem directly. Solitary waves with more than 1 hump did not appear in the simulation, and moreover a catastrophic behaviour took place for too large a Reynolds number (R [gsim ] R*1) or too large an amplitude, suggesting a finite-time singularity. The long-term evolution is shown to be a very slow relaxation to a steady state in a moving frame. The relation to the experimental observation of localized wavetrains is also discussed.

284 citations

Journal ArticleDOI
TL;DR: In this article, the stability of a steady, axisymmetric, laminar, primary flow composed of two fluids flowing concentrically in a straight circular tube is investigated by the method of small perturbations.
Abstract: The stability of a steady, axisymmetric, laminar, primary flow composed of two fluids flowing concentrically in a straight circular tube is investigated by the method of small perturbations. Both asymmetric and axisymmetric disturbances to the primary flow are considered. It is demonstrated that, regardless of the size of the Reynolds number, no situations are encountered for which the primary flow is stable to both types of disturbances, simultaneously. The primary cause of instability is found to be the difference in viscosities of the two fluids.

259 citations