On the one-dimensional two-phase inverse Stefan problems

1993 ◽  
Vol 45 (8) ◽  
pp. 1178-1185 ◽  
Author(s):  
Yu. V. Zhernovoi
Keyword(s):  
Two Phase ◽  
One Dimensional ◽  
Stefan Problems ◽  
The One

Modeling of Wall Friction for Multispecies Solid-Gas Flows

1986 ◽  
Vol 108 (4) ◽  
pp. 486-488 ◽  
Author(s):  
E. D. Doss ◽  
M. G. Srinivasan
Keyword(s):  
Shear Stress ◽  
Flow Model ◽  
Flow Characteristics ◽  
Wall Friction ◽  
Gas Flows ◽  
Two Phase ◽  
One Dimensional ◽  
Friction Models ◽  
Wall Interaction ◽  
The One

The empirical expressions for the equivalent friction factor to simulate the effect of particle-wall interaction with a single solid species have been extended to model the wall shear stress for multispecies solid-gas flows. Expressions representing the equivalent shear stress for solid-gas flows obtained from these wall friction models are included in the one-dimensional two-phase flow model and it can be used to study the effect of particle-wall interaction on the flow characteristics.

A Linear Stability Analysis for an Improved One-Dimensional Two-Fluid Model

2003 ◽  
Vol 125 (2) ◽  
pp. 387-389 ◽  
Author(s):  
Jin Ho Song
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Fluid Model ◽  
Two Phase ◽  
One Dimensional ◽  
Proposed Model ◽  
Two Fluid Model ◽  
The One ◽  
Two Fluid

A linear stability analysis is performed for a two-phase flow in a channel to demonstrate the feasibility of using momentum flux parameters to improve the one-dimensional two-fluid model. It is shown that the proposed model is stable within a practical range of pressure and void fraction for a bubbly and a slug flow.

Verification of a One-Dimensional Two-Phase Flow Model of the Frontal Gap in Electrochemical Machining

1976 ◽  
Vol 98 (2) ◽  
pp. 431-437 ◽  
Author(s):  
F. Fluerenbrock ◽  
R. D. Zerkle ◽  
J. F. Thorpe
Keyword(s):  
Flow Model ◽  
Radial Flow ◽  
Electrochemical Machining ◽  
Equilibrium Conditions ◽  
Two Phase ◽  
One Dimensional ◽  
Supply Pressure ◽  
Theoretical Predictions ◽  
The One ◽  
Experimental Pressure

A set of six equations, which are based on the ECM model developed by Thorpe and Zerkle, can be solved numerically to yield the one-dimensional distributions of pressure, temperature, gas density, gap thickness, void fraction, and electrolyte velocity in the rectilinear ECM frontal gap under equilibrium conditions. The validity of the model, which also applies to radial flow geometries, is confirmed by comparing experimental pressure and gap profiles with theoretical predictions. It is shown that for a given set of operating parameters there is a minimum supply pressure below which no machining is possible. When machining steel with an aqueous NaCl electrolyte the deposition of a black smut (Fe(OH)2) occurs beyond a certain smut-free entrance length, which was experimentally found to be proportional to the inlet gap thickness.

Novel Dynamic Numerical Microchannel Evaporator Model to Investigate Parallel Channel Instabilities

2015 ◽  
Author(s):  
Tom Saenen ◽  
John R. Thome
Keyword(s):  
Three Dimensional ◽  
Parallel Channel ◽  
Two Phase ◽  
One Dimensional ◽  
Pressure Losses ◽  
Initial Validation ◽  
Numerical Solver ◽  
The One ◽  
Flow Conservation ◽  
Stability Results

A novel fully dynamic model of a microchannel evaporator is presented. The aim of the model is to study the highly dynamic parallel channel instabilities that occur in these evaporators in more detail. The numerical solver for the model is custom-built and the majority of the paper is focused on detailing the various aspects of this solver. The one-dimensional homogeneous two-phase flow conservation equations are solved to simulate the flow. The full three-dimensional conduction domain of the evaporator is also dynamically resolved. This allows for the correct simulation of the complex hydraulic and thermal interactions between the microchannels that give rise to the parallel channel instabilities. The model uses state-of-the-art correlations to calculate the frictional pressure losses and heat transfer in the microchannels. In addition, a model for inlet restrictions is also included to simulate the stabilizing effect of these components. In the final part of the paper, initial validation results of the model are presented, in which stability results of the model are compared to existing experimental data from literature. Finally, some representative dynamic results are also given to demonstrate some of the unique capabilities of the model.

Method of the integral error functions for the solution of the one- and two-phase Stefan problems and its application

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1017-1029 ◽  
Author(s):  
Merey Sarsengeldin ◽  
Stanislav Kharina
Keyword(s):  
A Priori ◽  
Linear Combinations ◽  
Two Phase ◽  
Electrical Arc ◽  
Error Functions ◽  
Stefan Problems ◽  
Finite Sums ◽  
Integral Error ◽  
Faà Di Bruno Formula ◽  
The One

The analytical solutions of the one- and two-phase Stefan problems are found in the form of series containing linear combinations of the integral error functions which satisfy a priori the heat equation. The unknown coefficients are defined from the initial and boundary conditions by the comparison of the like power terms of the series using the Faa di Bruno formula. The convergence of the series for the temperature and for the free boundary is proved. The approximate solution is found using the replacement of series by the corresponding finite sums and the collocation method. The presented test examples confirm a good approximation of such approach. This method is applied for the solution of the Stefan problem describing the dynamics of the interaction of the electrical arc with electrodes and corresponding erosion.

Simulation of Copolymer Phase Separation in One-Dimensional Thin Liquid Films

2012 ◽  
Vol 2 (1) ◽  
pp. 33-46
Author(s):  
Hidenori Yasuda
Keyword(s):  
Phase Separation ◽  
Shallow Water Equations ◽  
Microphase Separation ◽  
Liquid Films ◽  
Thin Liquid Films ◽  
Two Phase ◽  
One Dimensional ◽  
Positive Volume ◽  
Spurious Oscillations ◽  
The One

AbstractThis paper discusses the development of an invariant finite difference scheme to simulate the microphase separation of copolymers in one-dimensional thin liquid films. The film phenomena are modelled using two-phase shallow water equations and the Ohta-Kawasaki potential, which governs the phase separation of the copolymer. Non-positive volume fractions and spurious oscillations are eventually eliminated, in simulating the one-dimensional phase separation lamellar pattern.

Numerical Solutions of the Equations for One-Dimensional Multi-Phase Flow in Porous Media

1966 ◽  
Vol 6 (01) ◽  
pp. 62-72 ◽  
Author(s):  
Byron S. Gottfried ◽  
W.H. Guilinger ◽  
R.W. Snyder
Keyword(s):  
Porous Media ◽  
Numerical Methods ◽  
Numerical Solutions ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Two Phase ◽  
One Dimensional ◽  
Three Phase ◽  
Three Phase Flow ◽  
The One

Abstract Two numerical methods are presented for solving the equations for one-dimensional, multiphase flow in porous media. The case of variable physical properties is included in the formulation, although gravity and capillarity are ignored. Both methods are analyzed mathematically, resulting in upper and lower bounds for the ratio of time step to mesh spacing. The methods are applied to two- and three-phase waterflooding problems in laboratory-size cores, and resulting saturation and pressure distributions and production histories are presented graphically. Results of the two-phase flow problem are in agreement with the predictions of the Buckley-Leverett theory. Several three-phase flow problems are presented which consider variations in the water injection rate and changes in the initial oil- and water-saturation distributions. The results are different physically from the two-phase case; however, it is shown that the Buckley-Leverett theory can accurately predict fluid interface velocities and displacing-fluid frontal saturations for three-phase flow, providing the correct assumptions are made. The above solutions are used as a basis for evaluating the numerical methods with respect to machine time requirements and allowable time step for a fixed mesh spacing. Introduction Considerable progress has been made in recent years in obtaining numerical solutions of the equations for two-phase flow in porous media. Douglas, Blair and Wagner2 and McEwen11 present different methods for solving the one-dimensional case for incompressible fluids with capillarity (the former using finite differences, the latter with an approach based upon characteristics). Fayers and Sheldon4 and Hovanesian and Fayers8 have extended these studies to include the effects of gravity. West, Garvin and Sheldon,14 in a pioneer paper, treat linear and radial systems with both capillarity and gravity and they also include the effects of compressibility. Douglas, Peaceman and Rachford3 consider two-dimensional, two-phase, incompressible flow with gravity and capillarity and Blair and Peaceman1 have extended this method to allow for compressible fluids. No one, however, has examined the case of three-phase flow, even for the relatively simple case of one-dimensional flow of incompressible fluids in the absence of gravity and capillarity. In obtaining a numerical technique for simulating forward in situ combustion laboratory experiments, Gottfried5 has developed a method for solving the one-dimensional, compressible flow equations with any number of flowing phases. Gravity and capillarity are not included in the formulation. The method has been used successfully, however, for two- and three-phase problems in a variable-temperature field with sources and sinks. This paper examines the algorithm of Gottfried more critically. Two numerical methods are presented for solving the one-dimensional, multi-phase flow equations with variable physical properties. Both methods are analyzed mathematically, and are used to simulate two- and three-phase waterflooding problems. The numerical solutions are then taken as a basis for comparing the utility of the methods. Problem Statement Consider a one-dimensional system in which capillarity, gravity and molecular diffusion are negligible. If n immiscible phases are present, n 2, the equation describing the flow of the ith phase is:12Equation 1 where all terms can vary with x and t.

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