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Annular Film

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John Tsamopoulos – 1st expert 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.

Kostas D Housiadas – 2nd expert 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.

John R Thome – 3rd expert 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.