Annular Film

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John Tsamopoulos - One of the best experts on this subject based on the ideXlab platform.

  • Unsteady extrusion of a viscoelastic Annular Film: II. Linearized model and its analytical solution
    Journal of Non-newtonian Fluid Mechanics, 2020
    Co-Authors: Kostas D Housiadas, John Tsamopoulos
    Abstract:

    Abstract The unsteady extrusion of a viscoelastic Film from an Annular and axisymmetric die is examined, when the gravitational and the capillary forces in the Film are small relative to the viscous forces. The Oldroyd-B constitutive equation is employed. This moving boundary problem is solved by mapping the inner and outer liquid/air interfaces of the extruded Film onto fixed ones and by transforming the governing equations accordingly. The ratio of the Film thickness to its inner radius at the exit of the die is small in relevant processes with polymer melts and is used as the small parameter, e , in a regular perturbation expansion of the governing equations. It is shown that when the St and Ca −1 numbers are of appropriately small magnitude, the base state in the perturbation scheme is a uniformly falling Film. The effect of these dimensionless numbers is demonstrated by analytically calculating the next order solution in a Taylor expansion in the Reynolds number. It is found that the present results agree very well with the numerical ones calculated by solving a large nonlinear equation set in [K. Housiadas, J. Tsamopoulos, Unsteady extrusion of a viscoelastic Film I. General model and its numerical solution, J. Non-Newtonian Fluid Mech. 1999, in press], when the dimensionless numbers are as small as required by the present analysis. The present analysis also shows where and which auxiliary conditions should be applied in this problem.

  • Unsteady extrusion of a viscoelastic Annular Film: I. General model and its numerical solution
    Journal of Non-newtonian Fluid Mechanics, 2020
    Co-Authors: Kostas D Housiadas, John Tsamopoulos
    Abstract:

    Abstract The unsteady extrusion of a viscoelastic Film from an Annular and axisymmetric die is examined. This moving boundary problem is solved by mapping the inner and outer liquid/air interfaces of the extruded Film onto fixed ones, and by transforming the governing equations accordingly. The ratio of the Film thickness to its inner radius at the exit of the die is used as the small parameter, e, in a regular perturbation expansion of the governing equations. Forces applied on the Film give rise to four dimensionless numbers: Stokes, Capillary, Reynolds and Deborah. When the Oldroyd-B model is used, the dimensionless retardation time also arises. For typical fluid properties and process conditions, the Stokes and Deborah numbers are O(e0), i.e. much larger than the other relevant dimensionless numbers. In such cases, the base state is significantly deforming with time and it is calculated numerically by solving a partial differential system of equations in time and the axial direction. Special attention is required for its accurate numerical solution. It was found that gravity plays the most important role in the process by accelerating the Film, deflecting its inner and outer surfaces towards its axis of symmetry and decreasing its thickness around the middle of its length. For typical values of the De number, its increase leads to deceleration of the Film that has less curved interfaces and more uniform thickness along its length. These effects become apparent, if the St number is of order one; if it is smaller, the effects of fluid elasticity decrease considerably. For typical values of the Ca and Re numbers, and of the retardation time of the fluid, their influence on the process is small.

  • Two- and three-dimensional instabilities in the Film blowing process
    Journal of Non-newtonian Fluid Mechanics, 2007
    Co-Authors: Kostas D Housiadas, George Klidis, John Tsamopoulos
    Abstract:

    Abstract We examine the Film blowing process (FBP), which is widely used for manufacturing biaxially stretched Films of polymeric materials. The viscoelastic property of the material is taken into account by employing the Upper Convected Maxwell, the Oldroyd-B or the Phan-Thien and Tanner constitutive model. In contrast to all previous theoretical works, which followed the now classical method developed by Pearson and Petrie [J.R.A. Pearson, C.J.S. Petrie, The flow of a tubular Film. Part 1. Formal mathematical representation, J. Fluid Mech. 40 (1) (1970) 1–19; J.R.A. Pearson, C.J.S. Petrie, The flow of a tubular Film. Part 2. Interpretation of the model and discussion of solutions, J. Fluid Mech. 42 (3) (1970) 609–625], we analyze the process by starting with the general three-dimensional mass and momentum balances and by formally and systematically applying the thin-Film approximation. This procedure results in two-dimensional dynamic balances in both the axial and azimuthal directions. Although these balances are highly non-linear and more complicated than the original momentum balance, they are reduced by one spatial dimension and, more importantly, they are more general than the classical ones, whereas they are developed in a rigorous and straightforward manner. When we assume axial symmetry and steady state, we recover the earlier model equations. However, this new methodology allows us to examine not only axisymmetric, but also non-axisymmetric disturbances to this base flow and to retain the time derivatives in all the governing equations. This procedure is an extension of our earlier one used to study transient Annular extrusion [K. Housiadas, J. Tsamopoulos, Unsteady flow of an axisymmetric Annular Film under gravity, Phys. Fluids 10 (10) (1998) 2500–2516; K. Housiadas, J. Tsamopoulos, Unsteady extrusion of a viscoelastic Annular Film: I. General model and its numerical solution, J. Non-Newton. Fluid Mech. 88 (3) (2000) 229–259], which also involved the thin-Film approximation and three moving interfaces, but under the assumption of axial symmetry. Viscous, elastic, inertial, gravitational and capillary forces are included in our model. The base state is computed using finite differences to simultaneously predict bubble shape, Film thickness, velocity, pressure and polymer extra-stress profiles. Subsequently, its linear stability is examined to two- and three-dimensional disturbances by solving the full eigenvalue problem to determine the stability regions of the process. It is shown that under typical operating conditions the bubble becomes unstable first to non-axisymmetric disturbances, although two-dimensional instability is also predicted by our model, in agreement with recent experiments.

  • The steady Annular extrusion of a Newtonian liquid under gravity and surface tension
    International Journal for Numerical Methods in Fluids, 2000
    Co-Authors: Kostas D Housiadas, Georgios C. Georgiou, John Tsamopoulos
    Abstract:

    The steady extrusion of a Newtonian liquid through an Annular die and its development outside and away from the die are studied under the influence of gravitational and surface tension forces. The finite element method (FEM) is used for the simulations. The positions of the inner and outer free surface profiles are calculated simultaneously with the other unknown fields, i.e. using the Newton–Raphson iterative scheme. The effects of three relevant parameters, i.e. the Reynolds, the Stokes and the capillary numbers, on the shape of the Annular Film are studied for two values of the inner to the outer diameter ratio, corresponding to a thick and a thin Annular Film respectively. A one-dimensional model for the extrudate region, valid for thin Annular Films, is also presented, and its predictions are compared with the two-dimensional finite element calculations. Despite the fact that it is valid away from the die exit, the one-dimensional model predicts satisfactorily the effects of the Stokes and capillary numbers. Copyright © 2000 John Wiley & Sons, Ltd.

  • unsteady flow of an axisymmetric Annular Film under gravity
    Physics of Fluids, 1998
    Co-Authors: Kostas D Housiadas, John Tsamopoulos
    Abstract:

    The unsteady flow of an Annular and axisymmetric Film under gravity is examined. This moving boundary problem is solved by mapping the inner and the outer interface of the Film in the radial direction onto fixed ones and by transforming the governing equations accordingly. The ratio of the Film thickness to its inner radius at the exit of the die is small in relevant processes with polymer melts. This ratio, e, is used as the small parameter in a perturbation expansion of the general Navier–Stokes equations. Forces applied on the Film include gravity, surface tension, inertia, and viscous forces. Their ratios give rise to three dimensionless numbers, St, Ca, and Re. When these dimensionless numbers are up to order one, the base state is quite deformed and it is calculated numerically by simultaneously solving three nonlinear partial differential equations in time and the axial direction. Intuitively it is expected that when the dimensionless numbers are small the base state in the perturbation scheme is a...

Kostas D Housiadas - One of the best experts on this subject based on the ideXlab platform.

  • Unsteady extrusion of a viscoelastic Annular Film: II. Linearized model and its analytical solution
    Journal of Non-newtonian Fluid Mechanics, 2020
    Co-Authors: Kostas D Housiadas, John Tsamopoulos
    Abstract:

    Abstract The unsteady extrusion of a viscoelastic Film from an Annular and axisymmetric die is examined, when the gravitational and the capillary forces in the Film are small relative to the viscous forces. The Oldroyd-B constitutive equation is employed. This moving boundary problem is solved by mapping the inner and outer liquid/air interfaces of the extruded Film onto fixed ones and by transforming the governing equations accordingly. The ratio of the Film thickness to its inner radius at the exit of the die is small in relevant processes with polymer melts and is used as the small parameter, e , in a regular perturbation expansion of the governing equations. It is shown that when the St and Ca −1 numbers are of appropriately small magnitude, the base state in the perturbation scheme is a uniformly falling Film. The effect of these dimensionless numbers is demonstrated by analytically calculating the next order solution in a Taylor expansion in the Reynolds number. It is found that the present results agree very well with the numerical ones calculated by solving a large nonlinear equation set in [K. Housiadas, J. Tsamopoulos, Unsteady extrusion of a viscoelastic Film I. General model and its numerical solution, J. Non-Newtonian Fluid Mech. 1999, in press], when the dimensionless numbers are as small as required by the present analysis. The present analysis also shows where and which auxiliary conditions should be applied in this problem.

  • Unsteady extrusion of a viscoelastic Annular Film: I. General model and its numerical solution
    Journal of Non-newtonian Fluid Mechanics, 2020
    Co-Authors: Kostas D Housiadas, John Tsamopoulos
    Abstract:

    Abstract The unsteady extrusion of a viscoelastic Film from an Annular and axisymmetric die is examined. This moving boundary problem is solved by mapping the inner and outer liquid/air interfaces of the extruded Film onto fixed ones, and by transforming the governing equations accordingly. The ratio of the Film thickness to its inner radius at the exit of the die is used as the small parameter, e, in a regular perturbation expansion of the governing equations. Forces applied on the Film give rise to four dimensionless numbers: Stokes, Capillary, Reynolds and Deborah. When the Oldroyd-B model is used, the dimensionless retardation time also arises. For typical fluid properties and process conditions, the Stokes and Deborah numbers are O(e0), i.e. much larger than the other relevant dimensionless numbers. In such cases, the base state is significantly deforming with time and it is calculated numerically by solving a partial differential system of equations in time and the axial direction. Special attention is required for its accurate numerical solution. It was found that gravity plays the most important role in the process by accelerating the Film, deflecting its inner and outer surfaces towards its axis of symmetry and decreasing its thickness around the middle of its length. For typical values of the De number, its increase leads to deceleration of the Film that has less curved interfaces and more uniform thickness along its length. These effects become apparent, if the St number is of order one; if it is smaller, the effects of fluid elasticity decrease considerably. For typical values of the Ca and Re numbers, and of the retardation time of the fluid, their influence on the process is small.

  • Two- and three-dimensional instabilities in the Film blowing process
    Journal of Non-newtonian Fluid Mechanics, 2007
    Co-Authors: Kostas D Housiadas, George Klidis, John Tsamopoulos
    Abstract:

    Abstract We examine the Film blowing process (FBP), which is widely used for manufacturing biaxially stretched Films of polymeric materials. The viscoelastic property of the material is taken into account by employing the Upper Convected Maxwell, the Oldroyd-B or the Phan-Thien and Tanner constitutive model. In contrast to all previous theoretical works, which followed the now classical method developed by Pearson and Petrie [J.R.A. Pearson, C.J.S. Petrie, The flow of a tubular Film. Part 1. Formal mathematical representation, J. Fluid Mech. 40 (1) (1970) 1–19; J.R.A. Pearson, C.J.S. Petrie, The flow of a tubular Film. Part 2. Interpretation of the model and discussion of solutions, J. Fluid Mech. 42 (3) (1970) 609–625], we analyze the process by starting with the general three-dimensional mass and momentum balances and by formally and systematically applying the thin-Film approximation. This procedure results in two-dimensional dynamic balances in both the axial and azimuthal directions. Although these balances are highly non-linear and more complicated than the original momentum balance, they are reduced by one spatial dimension and, more importantly, they are more general than the classical ones, whereas they are developed in a rigorous and straightforward manner. When we assume axial symmetry and steady state, we recover the earlier model equations. However, this new methodology allows us to examine not only axisymmetric, but also non-axisymmetric disturbances to this base flow and to retain the time derivatives in all the governing equations. This procedure is an extension of our earlier one used to study transient Annular extrusion [K. Housiadas, J. Tsamopoulos, Unsteady flow of an axisymmetric Annular Film under gravity, Phys. Fluids 10 (10) (1998) 2500–2516; K. Housiadas, J. Tsamopoulos, Unsteady extrusion of a viscoelastic Annular Film: I. General model and its numerical solution, J. Non-Newton. Fluid Mech. 88 (3) (2000) 229–259], which also involved the thin-Film approximation and three moving interfaces, but under the assumption of axial symmetry. Viscous, elastic, inertial, gravitational and capillary forces are included in our model. The base state is computed using finite differences to simultaneously predict bubble shape, Film thickness, velocity, pressure and polymer extra-stress profiles. Subsequently, its linear stability is examined to two- and three-dimensional disturbances by solving the full eigenvalue problem to determine the stability regions of the process. It is shown that under typical operating conditions the bubble becomes unstable first to non-axisymmetric disturbances, although two-dimensional instability is also predicted by our model, in agreement with recent experiments.

  • The steady Annular extrusion of a Newtonian liquid under gravity and surface tension
    International Journal for Numerical Methods in Fluids, 2000
    Co-Authors: Kostas D Housiadas, Georgios C. Georgiou, John Tsamopoulos
    Abstract:

    The steady extrusion of a Newtonian liquid through an Annular die and its development outside and away from the die are studied under the influence of gravitational and surface tension forces. The finite element method (FEM) is used for the simulations. The positions of the inner and outer free surface profiles are calculated simultaneously with the other unknown fields, i.e. using the Newton–Raphson iterative scheme. The effects of three relevant parameters, i.e. the Reynolds, the Stokes and the capillary numbers, on the shape of the Annular Film are studied for two values of the inner to the outer diameter ratio, corresponding to a thick and a thin Annular Film respectively. A one-dimensional model for the extrudate region, valid for thin Annular Films, is also presented, and its predictions are compared with the two-dimensional finite element calculations. Despite the fact that it is valid away from the die exit, the one-dimensional model predicts satisfactorily the effects of the Stokes and capillary numbers. Copyright © 2000 John Wiley & Sons, Ltd.

  • unsteady flow of an axisymmetric Annular Film under gravity
    Physics of Fluids, 1998
    Co-Authors: Kostas D Housiadas, John Tsamopoulos
    Abstract:

    The unsteady flow of an Annular and axisymmetric Film under gravity is examined. This moving boundary problem is solved by mapping the inner and the outer interface of the Film in the radial direction onto fixed ones and by transforming the governing equations accordingly. The ratio of the Film thickness to its inner radius at the exit of the die is small in relevant processes with polymer melts. This ratio, e, is used as the small parameter in a perturbation expansion of the general Navier–Stokes equations. Forces applied on the Film include gravity, surface tension, inertia, and viscous forces. Their ratios give rise to three dimensionless numbers, St, Ca, and Re. When these dimensionless numbers are up to order one, the base state is quite deformed and it is calculated numerically by simultaneously solving three nonlinear partial differential equations in time and the axial direction. Intuitively it is expected that when the dimensionless numbers are small the base state in the perturbation scheme is a...

John R Thome - One of the best experts on this subject based on the ideXlab platform.

  • asymmetric Annular flow in horizontal circular macro channels basic modeling of liquid Film distribution and heat transfer around the tube perimeter in convective boiling
    International Journal of Heat and Mass Transfer, 2014
    Co-Authors: A W Mauro, John R Thome, Andrea Cioncolini, R Mastrullo
    Abstract:

    This paper presents the modeling of the liquid Film distribution and heat transfer during convective boiling in horizontal, Annular flows to be applied in such applications where non-uniform heat flux occurs. In general, prediction methods in the literature totally ignore the influence of the non-uniformity in the Annular Film (thin at top while thick at bottom) on the heat transfer process whereas local measurements around the perimeter of horizontal tubes show a significant variation, up to a factor of four times or more in thickness and up to 25-30% or more in heat transfer from top to bottom. Therefore, starting with the original suite for symmetrical Annular flow models for convective boiling, condensation, entrainment, void fraction and two-phase pressure drops (Cioncolini and Thome (2009, 2011, 2012, 2012) [8-111) and their recent paper (Cioncolini and Thome (2013) [13]) for predicting the threshold between symmetric and asymmetric Annular flow, the new features added here are the predictions of the asymmetric Annular Film thickness and perimeter-wise heat transfer coefficients around the internal perimeter of horizontal tubes. To do this, a new set of 24 algebraic equations is proposed to provide the void fraction, liquid entrainment, pressure drop, liquid Film distribution and heat transfer around the perimeter with a simple calculation procedure. Predictions of the new model have been compared against experimental databases with a satisfactory agreement. (C) 2014 Elsevier Ltd. All rights reserved.

  • liquid Film circumferential asymmetry prediction in horizontal Annular two phase flow
    International Journal of Multiphase Flow, 2013
    Co-Authors: Andrea Cioncolini, John R Thome
    Abstract:

    Abstract This study considers the prediction of the degree of asymmetry in the circumferential distribution of the liquid Film in the tube cross section of horizontal Annular gas–liquid two-phase flow, endemic of the lower region of this flow regime near the stratified-wavy flow transition boundary. Focusing on disturbance waves as the predominant mechanism for transporting the liquid in the Annular Film from the bottom to the top of the tube to counterbalance the draining effect of gravity, a new prediction method for the degree of asymmetry in the Annular liquid Film is proposed that outperforms existing correlations. Flow pattern maps for horizontal gas–liquid two-phase flow of frequent use in the design of evaporators and condensers can thus be explicitly updated to account for both symmetric and asymmetric Annular flows. The underlying experimental database contains 184 measured liquid Film circumferential profiles, corresponding to 1276 local liquid Film thickness measurements collected from 15 different literature studies for tube diameters from 8.15 mm to 95.3 mm.

  • numerical modeling of laminar Annular Film condensation for different channel shapes
    International Journal of Heat and Mass Transfer, 2010
    Co-Authors: Stefano Nebuloni, John R Thome
    Abstract:

    This paper presents a theoretical and numerical model to predict Film condensation heat transfer in mini and micro-channels of different internal shapes. The model is based on a finite volume formulation of the Navier-Stokes and energy equations and it includes the contributions of the unsteady terms, surface tension, axial shear stresses, gravitational forces and wall conduction. Notably, interphase mass transfer and near-to-wall effects (disjoining pressure) are also included. Dimensional analysis and characteristic numbers of the process are proposed and simulation results are shown both in dimensionless and dimensional representations. Isothermal, iso-heat flux and variable heat flux external wall boundary conditions have been implemented and their effects on the distribution of the heat flux are shown and compared. The instantaneous local and perimeter-averaged heat transfer coefficients, the liquid condensate Film thickness distribution, the cross sectional void fraction and the mean vapor quality can be obtained for different channel shapes. Results obtained for steady state conditions are presented for circular, elliptical (with different eccentricities), flattened (with different aspect ratios) and flower shape cross sections for R-134a and ammonia, for hydraulic diameters between 10 pm and 3 mm. A time dependent simulation with variable heat flux is presented for a copper channel having a length of 4 cm and a rectangular cross section with a hydraulic diameter of 133 mu m and an aspect ratio of 2, showing the importance of axial conduction at this length scale. The model has been validated versus various benchmark cases and versus experimental data available in literature. (C) 2010 Elsevier Ltd. All rights reserved.

  • a theoretical model for the prediction of the critical heat flux in heated microchannels
    International Journal of Heat and Mass Transfer, 2008
    Co-Authors: Remi Revellin, John R Thome
    Abstract:

    Abstract A theoretical model for the prediction of the critical heat flux of refrigerants flowing in heated, round microchannels has been developed and presented here. The model is based on the two-phase conservation equations and includes the effect of the height of the interfacial waves of the Annular Film. Validation has been carried out by comparing the model, a numerical solution of a non-linear system of five differential equations, with a critical heat flux (CHF) database including three different refrigerants from two different laboratories. More than 96% of the data are predicted within a ±20% error band and a mean absolute error of 8%. Furthermore, it is also possible to predict CHF data from a third laboratory for water and R-113 flowing in rectangular (using the width of the channel as the characteristic dimension) and circular microchannel heat sinks with multiple channels. All together, 90% of the entire database, including four different fluids and different geometries, are predicted by the model within a ±20% error band and a mean absolute error of 9.3% for channels from 0.215 to 3.15 mm in size, mass fluxes from 29 to 1600 kg/m2 s, heated lengths from 10 to 126 mm and subcoolings from 2 to 77 °C.

S Nogueira - One of the best experts on this subject based on the ideXlab platform.

  • flow in the nose region and Annular Film around a taylor bubble rising through vertical columns of stagnant and flowing newtonian liquids
    Chemical Engineering Science, 2006
    Co-Authors: S Nogueira, M L Riethmuler, J B L M Campos, A M F R Pinto
    Abstract:

    The flow in the nose region and in the Annular Film around individual Taylor bubbles rising through stagnant and co-current vertical columns of liquid were studied, employing particle image velocimetry (PIV) and pulsed shadowgraphy techniques (PST) at the same time. The combined techniques enabled simultaneous determination of the bubble shape and the velocity profiles in the liquid Film. Experiments were performed with water and aqueous glycerol solutions in a wide range of viscosities (1 × 10 −3 Pa s < � < 1. 5P a s), in an acrylic column of 32 mm ID. Values for the distance ahead of the nose in which the flow is disturbed by the presence of the bubble are presented for the conditions studied. The bubble shapes in the nose region are compared with Dumitrescu’s shape for potential flow. The velocity profiles show that after the nose region the liquid begins to accelerate downwards, and at a certain distance from the bubble nose the velocity profile and the liquid Film thickness stabilise. The liquid Film acquires characteristics of a free-falling Film. Values of the developing length and Film thickness are reported for the experimental conditions studied. Average velocity profiles in the fully developed Film are also presented. A critical Reynolds number of around 80 (based on the mean absolute velocity in the liquid Film and on the Film thickness) is reported for the transition from laminar to turbulent regime. Shear stress profiles (in the fully developed Film) are also provided. The data reported are relevant for the validation of numerical codes in slug flow. 2005 Elsevier Ltd. All rights reserved.

T J Pedley - One of the best experts on this subject based on the ideXlab platform.

  • the nonlinear growth of surface tension driven instabilities of a thin Annular Film
    Journal of Fluid Mechanics, 1991
    Co-Authors: Mark Johnson, Roger D Kamm, Lee Wing Ho, Ascher H Shapiro, T J Pedley
    Abstract:

    The stability and initial growth rate of disturbances on an Annular Film lining a cylindrical tube have been the focus of several previous works. The further development of these disturbances as they grow to form stable unduloids or liquid bridges is investigated by means of a thin-Film integral model. The model is compared both with perturbation theories for early times, and a numerical solution of the exact equations (NEKTON) for later times. The thin-Film model gave results that were in good agreement with solutions of the exact equations. The results show that linear perturbation theory can be used to give good estimates of the times for unduloid and liquid bridge formation. The success of the model derives from the dominant influence of narrow draining regions that feed into the growing unduloid, and these regions remain essentially one-dimensional throughout the growth of the instability. The model is used to analyse the evolution of the liquid layer lining the small airways of the lung during a single breath. The timescales for formation of unduloids and liquid bridges are found to be short enough for the liquid layer to be in a virtually quasi-equilibrium state throughout the breathing cycle. This conclusion is only tentative, however, because the model assumes that the surface tension of the airway liquid lining does not change with changes in interfacial area despite the known presence of pulmonary surfactant.