A remedy for the ill-posedness of the one-dimensional two-fluid model

2003 ◽  
Vol 222 (1) ◽  
pp. 40-53 ◽  
Author(s):  
Jin Ho Song
Keyword(s):  
Fluid Model ◽  
One Dimensional ◽  
Two Fluid Model ◽  
The One ◽  
Two Fluid

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.

Review of Applicability of the One-dimensional Two-fluid Model to the Prediction of Wave Growth and Slug Evolution in Horizontal Pipes

2010 ◽  
Author(s):  
Raad I. Issa ◽  
Liejin Guo ◽  
D. D. Joseph ◽  
Y. Matsumoto ◽  
Y. Sommerfeld ◽  
...  
Keyword(s):  
Fluid Model ◽  
Wave Growth ◽  
One Dimensional ◽  
Horizontal Pipes ◽  
Two Fluid Model ◽  
The One ◽  
Two Fluid

Proposed Use of the One-Dimensional Two-Fluid Model With Momentum Flux Parameters

2000 ◽  
Author(s):  
Jin Ho Song ◽  
H. D. Kim
Keyword(s):  
Differential Equations ◽  
Void Fraction ◽  
Momentum Flux ◽  
Fluid Model ◽  
Sufficient Conditions ◽  
Wave Number ◽  
One Dimensional ◽  
Two Fluid Model ◽  
The One ◽  
Two Fluid

Abstract The dynamic character of a system of the governing differential equations for the one-dimensional two-fluid model, where the appropriate momentum flux parameters are employed to consider the velocity and void fraction distribution in a flow channel, is analyzed. In response to a perturbation in the form of a traveling wave, a linear stability analysis is performed for the governing differential equations. The analytical expression for the growth factor as a function of wave number, void fraction, drag coefficient, and relative velocity is derived. It provides the necessary and sufficient conditions for the stability of the one-dimensional two-fluid model in terms of momentum flux parameters. It is analytically shown that the one-dimensional two-fluid model is mathematically well posed by use of appropriate momentum flux parameters, while the conventional two-fluid model makes the system unconditionally unstable. It is suggested that the velocity and void distributions should be properly accounted for in the one-dimensional two-fluid model by use of momentum flux parameters.

Numerical Solution of Wavy-Stratified Fluid-Fluid Flow With the One-Dimensional Two-Fluid Model: Stability, Boundedness, Convergence and Chaos

2014 ◽  
Author(s):  
William D. Fullmer ◽  
Alejandro Clausse ◽  
Avinash Vaidheeswaran ◽  
Martin A. Lopez de Bertodano
Keyword(s):  
Experimental Data ◽  
Fluid Flow ◽  
Chaotic Behavior ◽  
Fluid Model ◽  
Linear Instability ◽  
Energy Transfer Mechanism ◽  
One Dimensional ◽  
Two Fluid Model ◽  
The One ◽  
Two Fluid

In this paper the one-dimensional two-fluid model is used to dynamically simulate slightly inclined fluid-fluid flow in a rectangular channel. By that, it is specifically meant that the solutions exhibit a wavy pattern arising from the inherent instability of the model. The conditions and experimental data of Thorpe (1969) are used for comparison. The linear instability of the model is regularized, i.e., made well-posed, with surface tension and axial turbulent stress with a simple turbulent viscosity model. Nonlinear analysis in an infinite domain demonstrates for the first time one-dimensional two-fluid model chaotic behavior in addition to limit cycle behavior and asymptotic stability. The chaotic behavior is a consequence of the linear instability (the long wavelength energy source) the nonlinearity (the energy transfer mechanism) and the viscous dissipation (the short wavelength energy sink). Since the model is chaotic, solutions exhibit sensitive dependence on initial conditions which results in non-convergence of particular solutions with grid refinement. However, even chaotic problems have invariants and the ensemble averaged water void fraction amplitude spectrum is used to demonstrate convergence and make comparisons to the experimental data.

A Physically Based, One-Dimensional Two-Fluid Model for Direct Contact Condensation of Steam Jets Submerged in Subcooled Water

2015 ◽  
Vol 1 (2) ◽  
Author(s):  
David Heinze ◽  
Thomas Schulenberg ◽  
Lars Behnke
Keyword(s):  
Direct Contact ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Interfacial Area ◽  
Phase Flow ◽  
Two Phase ◽  
One Dimensional ◽  
Two Fluid Model ◽  
Contact Condensation ◽  
Two Fluid

A simulation model for the direct contact condensation of steam in subcooled water is presented that allows determination of major parameters of the process, such as the jet penetration length. Entrainment of water by the steam jet is modeled based on the Kelvin–Helmholtz and Rayleigh–Taylor instability theories. Primary atomization due to acceleration of interfacial waves and secondary atomization due to aerodynamic forces account for the initial size of entrained droplets. The resulting steam-water two-phase flow is simulated based on a one-dimensional two-fluid model. An interfacial area transport equation is used to track changes of the interfacial area density due to droplet entrainment and steam condensation. Interfacial heat and mass transfer rates during condensation are calculated using the two-resistance model. The resulting two-phase flow equations constitute a system of ordinary differential equations, which is solved by means of the explicit Runge–Kutta–Fehlberg algorithm. The simulation results are in good qualitative agreement with published experimental data over a wide range of pool temperatures and mass flow rates.

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