Hyperbolicity Analysis of a One-Dimensional Two-Fluid Two-Phase Flow Model for Stratified-Flow Pattern

2015 ◽  
Author(s):  
Carina N. Sondermann ◽  
Rodrigo A. C. Patrício ◽  
Aline B. Figueiredo ◽  
Renan M. Baptista ◽  
Felipe B. F. Rachid ◽  
...  
Keyword(s):  
Volume Fraction ◽  
Numerical Study ◽  
Fluid Model ◽  
Practical Importance ◽  
Stratified Flow ◽  
Hyperbolic Partial Differential Equations ◽  
Two Phase ◽  
One Dimensional ◽  
Flow Models ◽  
Two Fluid

Two-phase flows in pipelines occur in a variety of processes in the nuclear, petroleum and gas industries. Because of the practical importance of accurately predicting steady and unsteady flows along the line, one-dimensional two-fluid flow models have been extensively employed in numerical simulations. These models are usually written as a system of non-linear hyperbolic partial-differential equations, but some of the available formulations are physically inconsistent due to a loss of the hyperbolicity property. In these cases, the associated eigenvalues become complex numbers and the model loses physical meaning locally. This paper presents a numerical study of a one-dimensional single-pressure four-equation two-fluid model for an isothermal stratified flow that occurs in a horizontal pipeline. The diameter, pressure and volume fraction are kept constant, whereas the liquid and gas velocities are varied to cover the entire range of superficial velocities in the stratified region. For each point, the eigenvalues are numerically computed to verify whether they are real numbers and to assess their signs. The results show that hyperbolicity is lost near the boundaries of the stratified pattern and in a vast area of the region itself. Moreover, the eigenvalue signs alternate, which has implications on the prescription of numerical boundary conditions.

Numerical Study of Two-Phase Flow in a Horizontal Pipeline Using an Unconditionally Hyperbolic Two-Fluid Model

2018 ◽  
Author(s):  
Raphael V. N. de Freitas ◽  
Carina N. Sondermann ◽  
Rodrigo A. C. Patricio ◽  
Aline B. Figueiredo ◽  
Gustavo C. R. Bodstein ◽  
...  
Keyword(s):  
Volume Fraction ◽  
Numerical Study ◽  
Fluid Model ◽  
Momentum Conservation ◽  
Design Stage ◽  
Two Phase Flows ◽  
Two Phase ◽  
Efficient Manner ◽  
Two Fluid Model ◽  
Two Fluid

Numerical simulation is a very useful tool for the prediction of physical quantities in two-phase flows. One important application is the study of oil-gas flows in pipelines, which is necessary for the proper selection of the equipment connected to the line during the pipeline design stage and also during the pipeline operation stage. The understanding of the phenomena present in this type of flow is more crucial under the occurrence of undesired effects in the duct, such as hydrate formation, fluid leakage, PIG passage, and valve shutdown. An efficient manner to model two-phase flows in long pipelines regarding a compromise between numerical accuracy and cost is the use of a one-dimensional two-fluid model, discretized with an appropriate numerical method. A two-fluid model consists of a system of non-linear partial differential equations that represent the mass, momentum and energy conservation principles, written for each phase. Depending on the two-fluid model employed, the system of equations may lose hyperbolicity and render the initial-boundary-value problem illposed. This paper uses an unconditionally hyperbolic two-fluid model for solving two-phase flows in pipelines in order to guarantee that the solution presents physical consistency. The mathematical model here referred to as the 5E2P (five equations and two pressures) comprises two equations of continuity and two momentum conservation equations, one for each phase, and one equation for the transport of the volume fraction. A priori this model considers two distinct pressures, one for each phase, and correlates them through a pressure relaxation procedure. This paper presents simulation cases for stratified two-phase flows in horizontal pipelines solved with the 5E2P coupled with the flux corrected transport method. The objective is to evaluate the numerical model capacity to adequately describe the velocities, pressures and volume fraction distributions along the duct.

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.

An Upwind Numerical Method for a Hyperbolic One-Dimensional Two-Fluid Model

2011 ◽  
Author(s):  
Youn-Gyu Jung ◽  
Moon-Sun Chung ◽  
Sung-Jae Yi
Keyword(s):  
Numerical Method ◽  
Fluid Model ◽  
Equation System ◽  
Benchmark Problems ◽  
Two Phase ◽  
One Dimensional ◽  
Flow Problems ◽  
Complete Set ◽  
Two Fluid Model ◽  
Two Fluid

This study discusses on the implementation of an upwind method for a one-dimensional two-fluid model including the surface tension effect in the momentum equations. This model consists of a complete set of six equations including two-mass, two-momentum, and two-internal energy conservation equations having all real eigenvalues. Based on this equation system with upwind numerical method, the present authors first make a pilot code and then solve some benchmark problems to verify whether this model and numerical method is able to properly solve some fundamental one-dimensional two-phase flow problems or not.

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.

scholarly journals Computational investigation of liquid-solid slurry flow through an expansion in a rectangular duct

2014 ◽  
Vol 62 (3) ◽  
pp. 234-240 ◽  
Author(s):  
Gianandrea Vittorio Messa ◽  
Stefano Malavasi
Keyword(s):  
Volume Fraction ◽  
Particle Density ◽  
Fluid Model ◽  
Solid Volume Fraction ◽  
Solid Particles ◽  
Rectangular Duct ◽  
Two Phase ◽  
Horizontal Pipe ◽  
Two Fluid Model ◽  
Two Fluid

Abstract The flow of a mixture of liquid and solid particles at medium and high volume fraction through an expansion in a rectangular duct is considered. In order to improve the modelling of the phenomenon with respect to a previous investigation (Messa and Malavasi, 2013), use is made of a two-fluid model specifically derived for dense flows that we developed and implemented in the PHOENICS code via user-defined subroutines. Due to the lack of experimental data, the two-fluid model was validated in the horizontal pipe case, reporting good agreement with measurements from different authors for fully-suspended flows. A 3D system is simulated in order to account for the effect of side walls. A wider range of the parameters characterizing the mixture (particle size, particle density, and delivered solid volume fraction) is considered. A parametric analysis is performed to investigate the role played by the key physical mechanisms on the development of the two-phase flow for different compositions of the mixture. The main focuses are the distribution of the particles in the system and the pressure recovery

A NUMERICAL STUDY OF TWO-PHASE FLOW USING A TWO-DIMENSIONAL TWO-FLUID MODEL

2004 ◽  
Vol 45 (10) ◽  
pp. 1049-1066 ◽  
Author(s):  
Moon-Sun Chung ◽  
Seung-Kyung Pak ◽  
Keun-Shik Chang
Keyword(s):  
Two Phase Flow ◽  
Numerical Study ◽  
Fluid Model ◽  
Phase Flow ◽  
Two Dimensional ◽  
Two Phase ◽  
Two Fluid Model ◽  
Two Fluid

scholarly journals Prediction of Gas-Liquid Two-Phase Flow Performance of a Centrifugal Pump Using a One-Dimensional, Two-Fluid Model

1997 ◽  
Vol 63 (611) ◽  
pp. 2377-2385
Author(s):  
Kiyoshi MINEMURA ◽  
Tomomi UCHIYAMA ◽  
Katsuhiko KINOSHITA ◽  
Lin LYU ◽  
Shinji SYODA ◽  
...  
Keyword(s):  
Centrifugal Pump ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Phase Flow ◽  
Two Phase ◽  
One Dimensional ◽  
Two Fluid Model ◽  
Two Fluid
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