Freezing Flow in a Subcooled Permeable Medium

1992 ◽  
Vol 114 (4) ◽  
pp. 1036-1041 ◽  
Author(s):  
S. K. Griffiths ◽  
R. H. Nilson
Keyword(s):  
Freezing Point ◽  
Freezing Temperature ◽  
Similarity Solutions ◽  
Inlet Temperature ◽  
Governing Equations ◽  
Phase Zone ◽  
Two Phase ◽  
Liquid Zone ◽  
One Dimensional ◽  
Order Of Magnitude

Analytical similarity solutions are derived for the problem of transient one-dimensional flow and freezing of a liquid in an initially dry permeable half-space. The structure of the flow consists of three regions: a liquid zone in which the temperature decreases to the freezing temperature, a central two-phase zone where the temperature is at the freezing point, and a leading gas-filled region in which the temperature is nearly undisturbed. The propagation velocity of this intrusion is determined as a function of the subcooling, latent heat, and other process parameters. As the inlet temperature approaches the freezing temperature, the governing equations admit a pair of solutions having propagation velocities that sometimes differ by more than an order of magnitude.

scholarly journals On the Use of Asymptotic Solutions to Plane Ice—Water Problems

1969 ◽  
Vol 8 (53) ◽  
pp. 285-300 ◽  
Author(s):  
G. S. H. Lock
Keyword(s):  
Boundary Conditions ◽  
Asymptotic Solutions ◽  
Variable Properties ◽  
Governing Equations ◽  
Freezing And Thawing ◽  
One Dimensional ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Water Problems ◽  
Ice Water

The paper considers one-dimensional freezing and thawing of ice–water systems for the conditions first examined by Stefan. An order-of-magnitude analysis applied to the governing equations and boundary conditions quantifies the error resulting from the neglect of various factors. Principal among these are density difference, initial superheat and variable properties.Asymptotic solutions for the temperature distribution and interface history are developed for a wide range of boundary conditions: prescribed temperature or heat flux, prescribed convection and prescribed radiation. Comparison with known results reveals the general adequacy of the asymptotic solutions and an estimate of the error incurred.

Nonequilibrium Modeling of Two-Phase Critical Flows in Tubes

1987 ◽  
Vol 109 (3) ◽  
pp. 731-738 ◽  
Author(s):  
F. Dobran
Keyword(s):  
Two Phase Flow ◽  
Numerical Procedure ◽  
Phase Flow ◽  
Water Mixture ◽  
Governing Equations ◽  
Two Phase ◽  
One Dimensional ◽  
Variable Diameter ◽  
Variable Step ◽  
Tube Exit

A nonequilibrium two-phase flow model is described for the analysis of critical flows in variable diameter tubes. Modeling of the two-phase flow mixture in the tube is accomplished by utilizing a one-dimensional form of conservation and balance equations of two-phase flow which account for the relative velocity and temperature differences between the phases. Closure of the governing equations was performed with the constitutive equations which account for different flow regimes, and the solution of the nonlinear set of six differential equations was accomplished by a variable step numerical procedure. Computations were carried out for a steam-water mixture with varying degrees of liquid subcooling and stagnation pressures in the vessel upstream of the tube and for different tube lengths. The numerical results are compared with the experimental data involving critical flows with variable liquid subcoolings, stagnation pressures, and tube lengths, and it is shown that the nonequilibrium model predicts well the critical flow rate, pressure distribution along the tube, and the tube exit pressure.

Comparison of Boiling and Condensation Characteristics in the Porous Wick of a Flat Heat Pipe in Vertical and Horizontal Orientation

2014 ◽  
Vol 592-594 ◽  
pp. 1461-1465
Author(s):  
Rakesh Hari ◽  
Tom Jolly ◽  
C. Muraleedharan
Keyword(s):  
Phase Change ◽  
Heat Pipe ◽  
Temperature Drop ◽  
Similarity Solutions ◽  
Phase Zone ◽  
Two Phase ◽  
Water Steam ◽  
Pipe System ◽  
Porous Wick ◽  
Flat Heat Pipe

The two-phase flow through porous media is an important topic which spans a broad spectrum of engineering disciplines especially in porous heat pipes. Heat pipe is a thermodynamic device that transports heat energy from one location to another with a negligible temperature drop. The aim of the present work is to investigate the phase change mechanisms, namely boiling and condensation, in the flat heat pipe system with different orientation. Governing equations used for the formulation are continuity, mixture momentum, liquid conservation and energy equations. These equations are converted into three ordinary differential equations using similarity transformation and two-phase similarity solutions are obtained for both boiling and condensing flows. In each case, a two phase zone where the liquid and vapour can coexist appears adjacent to the wall. As the heat transfer at the wall gradually enhances, the liquid saturation at the wall approaches to the limiting value, zero, for boiling and unity for condensation. The present work is an attempt to predict numerically the liquid wall saturation, non-dimensional temperature, non-dimensional temperature gradient and effect of Sherwood number during the phase change of water-steam system in the heat pipe for horizontal and vertical cases. Nomenclature

scholarly journals On the Use of Asymptotic Solutions to Plane Ice—Water Problems

1969 ◽  
Vol 8 (53) ◽  
pp. 285-300
Author(s):  
G. S. H. Lock
Keyword(s):  
Boundary Conditions ◽  
Asymptotic Solutions ◽  
Variable Properties ◽  
Governing Equations ◽  
Freezing And Thawing ◽  
One Dimensional ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Water Problems ◽  
Ice Water

The paper considers one-dimensional freezing and thawing of ice–water systems for the conditions first examined by Stefan. An order-of-magnitude analysis applied to the governing equations and boundary conditions quantifies the error resulting from the neglect of various factors. Principal among these are density difference, initial superheat and variable properties.Asymptotic solutions for the temperature distribution and interface history are developed for a wide range of boundary conditions: prescribed temperature or heat flux, prescribed convection and prescribed radiation. Comparison with known results reveals the general adequacy of the asymptotic solutions and an estimate of the error incurred.

Exact Solution for Freezing in Cylindrical Symmetry with Extended Freezing Temperature Range

1979 ◽  
Vol 101 (2) ◽  
pp. 331-334 ◽  
Author(s):  
M. N. O¨zis¸ik ◽  
J. C. Uzzell
Keyword(s):  
Solid Solution ◽  
Solid Fraction ◽  
Freezing Temperature ◽  
Cylindrical Symmetry ◽  
Infinite Medium ◽  
The Other ◽  
Phase Zone ◽  
Two Phase ◽  
Temperature Range ◽  
Liquidus Temperatures

The problem of solidification by a line heat sink in an infinite medium with cylindrical symmetry for a substance having an extended freezing temperature range between the solidus and liquidus temperatures is solved exactly for two different cases characterizing the distribution of the solid fraction within the two-phase zone. In one of the models, the solid fraction is assumed to vary linearly with the temperature and in the other solidification within the two-phase zone is assumed to have a linear relationship with the distance. The analysis is applicable for both eutectic and solid solution alloys.

Similarity Analysis of Condensing Flow in a Fluid-Driven Fracture

1988 ◽  
Vol 110 (3) ◽  
pp. 754-762 ◽  
Author(s):  
S. K. Griffiths ◽  
R. H. Nilson
Keyword(s):  
Single Phase ◽  
Dimensionless Parameter ◽  
Nuclear Explosion ◽  
Similarity Solutions ◽  
Pure Substance ◽  
Underground Nuclear Explosion ◽  
Governing Equations ◽  
Opening Displacement ◽  
One Dimensional ◽  
Fracture Length

Similarity solutions are derived for some fundamental problems of condensing flow in a hydraulically driven fracture. The governing equations describe one-dimensional homogeneous turbulent flow along a wedge-shaped hydraulic fracture in an elastic medium. The instantaneous fracture speed is determined as an analytical function of fracture length, material properties, process parameters, and a single eigenvalue, which is calculated by solving a system of ordinary differential equations for the variation of pressure, energy, velocity, and opening displacement along the fracture. Results are presented for abrupt condensation of a pure substance and for gradual condensation of air/water mixtures. The rate of condensation is controlled by the rate of heat transfer to the fracture wall, which depends upon a single dimensionless parameter. For small and large values of this parameter the present multiphase solutions are in agreement with previous solutions for single-phase flows of vapors and liquids. Although most of the results are presented in dimensionless form, some numerical examples are given for steam-driven fractures emanating from the cavity resulting from an underground nuclear explosion.

Effects of Surface Tension on Film Condensation in a Porous Medium

1990 ◽  
Vol 112 (3) ◽  
pp. 751-757 ◽  
Author(s):  
A. Majumdar ◽  
C. L. Tien
Keyword(s):  
Boundary Layer ◽  
Surface Tension ◽  
Porous Medium ◽  
Film Condensation ◽  
Phase Zone ◽  
Two Phase ◽  
Liquid Zone ◽  
Darcy Velocity ◽  
Characteristic Boundary ◽  
Surface Tension Forces

In the process of film condensation in a porous medium, the thermodynamics of phase equilibria requires the existence of a two-phase zone lying between the liquid and the vapor regions. In the two-phase zone, solutions of the conservation equations indicate a boundary-layer profile for the capillary pressure. The liquid zone is analyzed using three models, which assume either slip or no slip at the wall and Darcy velocity or no shear at the interface with the two-phase zone. The results show that the condition of no slip at the wall must be satisfied in all cases except where the thickness of the liquid zone is much larger than the characteristic boundary layer in the porous medium. At the interface with the two-phase zone, the assumption of no shear is more realistic than that of an imposed Darcy velocity, in conjunction with no-slip condition at the wall. Comparisons with experiments suggest that the drag on the liquid film due to surface tension is significant for permeabilities lower than 10−7 m2. A dimensionless group, characterizing viscous flow due to surface tension forces, is introduced in this study.

scholarly journals One-Dimensional Modelling of a Trilateral Flash Cycle System with Two-Phase Twin-Screw Expanders for Industrial Low-Grade Heat to Power Conversion

Designs ◽  
2019 ◽  
Vol 3 (3) ◽  
pp. 41 ◽  
Author(s):  
Giuseppe Bianchi ◽  
Matteo Marchionni ◽  
Stuart Kennedy ◽  
Jeremy Miller ◽  
Savvas Tassou
Keyword(s):  
Power Conversion ◽  
Operating Conditions ◽  
Staggered Grid ◽  
Inlet Temperature ◽  
Low Grade ◽  
Two Phase ◽  
One Dimensional ◽  
Twin Screw ◽  
Low Grade Heat ◽  
The Impact

This paper provides an overview of a one-dimensional modelling methodology for equipment and systems for heat to power conversion based on a staggered grid space discretization and implemented in the commercial software GT-SUITE®. Particular attention is given to a newly developed modelling procedure for twin-screw machines that is based on a chamber modelling approach and considers leakage paths between cells and with the casing. This methodology is then applied to a low-grade heat to power conversion system based on a Trilateral Flash Cycle (TFC) equipped with two parallel two-phase twin-screw expanders and a control valve upstream of the machines to adapt the fluid quality for an optimal expander operation. The standalone expander model is used to generate performance maps of the machine, which serve as inputs for the TFC system model. Parametric analyses are eventually carried out to assess the impact of several operating parameters of the TFC unit on the recovered power and cycle thermal efficiency. The study shows that the most influencing factors on the TFC system’s performance are the inlet temperature of the heat source and the expander speed. While the first depends on the topping industrial process, the expander speed can be used to optimize and control the TFC system operation also in transient or off-design operating conditions.

A ONE-DIMENSIONAL TWO-PHASE FLOW MODEL AND EXPERIMENTAL VALIDATION FOR A FLASHING VISCOUS LIQUID IN A SPLASH PLATE NOZZLE

2015 ◽  
Vol 25 (9) ◽  
pp. 795-817 ◽  
Author(s):  
Mika P. Jarvinen ◽  
A. E. P. Kankkunen ◽  
R. Virtanen ◽  
P. H. Miikkulainen ◽  
V. P. Heikkila
Keyword(s):  
Viscous Liquid ◽  
Experimental Validation ◽  
Flow Model ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
One Dimensional
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