scholarly journals A Characteristic Analysis of One-Dimensional Two-Fluid Model with Interfacial Area Transport Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Xia Wang ◽  
Xiaodong Sun
Keyword(s):  
Transport Equation ◽  
Momentum Flux ◽  
Fluid Model ◽  
Interfacial Area ◽  
Characteristic Analysis ◽  
Interfacial Area Transport ◽  
One Dimensional ◽  
Interfacial Area Transport Equation ◽  
Two Fluid Model ◽  
Two Fluid

An interfacial area transport equation (IATE), proposed to dynamically describe the interfacial structure evolution of two-phase flows, could help improve the predictive capability of the two-fluid model. The present study aims to investigate the well-posedness issue of a one-dimensional two-fluid model with the IATE (named “two-fluid-IATE model” hereafter) using a characteristic analysis. The momentum flux parameters, which take into account the coupling of the volumetric fraction of phase and velocity distributions over the cross-section of a flow passage, are employed. A necessary condition for the system to achieve hyperbolicity under an adiabatic flow condition is identified. A case study is performed for an adiabatic liquid-liquid slug flow, which shows that the hyperbolicity of the two-fluid-IATE model is guaranteed if appropriate correlations of the momentum flux parameters are applied in the two-fluid-IATE model.

Hyperbolicity of One-Dimensional Two-Fluid Model With Interfacial Area Transport Equations

2009 ◽  
Author(s):  
Xia Wang ◽  
Xiaodong Sun
Keyword(s):  
Flow Regime ◽  
Momentum Flux ◽  
Fluid Model ◽  
Interfacial Area ◽  
Structure Evolution ◽  
Characteristic Analysis ◽  
Interfacial Area Transport ◽  
One Dimensional ◽  
Two Fluid Model ◽  
Two Fluid

Two-fluid model with an empirical flow regime concept is widely used for two-phase flow analyses but suffers from its static and often non-hyperbolic nature. Recently, an interfacial area transport equation (IATE) has been proposed within the framework of the two-fluid model to dynamically describe the interfacial structure evolution and model the interfacial area concentration with the ultimate goal of modeling flow regime transition dynamically. Studies showed that the two-fluid model with the IATE (termed “two-fluid-IATE model” hereafter) could provide a more accurate prediction of the phase distributions and therefore improve the predictive capability of the two-fluid model. The inclusion of the IATE in the two-fluid model, however, brings about a subject of concern, namely, the well-posedness of the model. The objective of the present study is to investigate the issue of the hyperbolicity of a one-dimensional two-fluid-IATE model by employing momentum flux parameters, which take into account the coupling of the void fraction (volumetric fraction of the dispersed phase) and radial velocity distributions over the cross section of a flow passage. A characteristic analysis of the partial differential equations of the one-dimensional two-fluid model and two-group IATEs for an adiabatic flow was performed to identify a necessary condition for the system to achieve hyperbolicty. A case study was performed for an adiabatic liquid-liquid slug flow and the analysis showed that the hyperbolicty of the two-fluid-IATE model was guaranteed if appropriate correlations of the momentum flux parameters were applied in the two-fluid-IATE model.

CFD Simulations of Cap-Bubbly Two-Phase Flows Using Two-Group Interfacial Area Transport Equation

2011 ◽  
Author(s):  
Xia Wang ◽  
Xiaodong Sun
Keyword(s):  
Transport Equation ◽  
Fluid Model ◽  
Interfacial Area ◽  
Phase Flow ◽  
Two Phase ◽  
Interfacial Area Transport ◽  
Interfacial Area Transport Equation ◽  
Proposed Model ◽  
Two Fluid Model ◽  
Two Fluid

Knowledge of cap-bubbly flows is of great interest due to its role in understanding of flow regime transition from bubbly to slug or churn-turbulent flow. One of the key characteristics of such flows is the existence of bubbles in different sizes and shapes associated with their distinctive dynamic natures. This important feature is, however, generally not well captured by available two-phase flow models. In view of this, a modified two-fluid model, namely a three-field two-fluid model, is proposed. In this model, bubbles are categorized into two groups, i.e., spherical/distorted bubbles as Group-1 while cap/churn-turbulent bubbles as Group-2. A two-group interfacial area transport equation (IATE) is implemented to describe the dynamic changes of interfacial structure in each group, resulting from intra- and inter-group interactions and phase changes due to evaporation and condensation. Attention is also paid to the appropriate constitutive relations of the interfacial transfers due to mechanical and thermal non-equilibrium between different fields. The proposed three-field two-fluid model is used to predict the phase distributions of adiabatic air-water flows in a narrow rectangular duct. Good agreement between the simulation results from the proposed model and relevant experimental data indicates that the proposed model may be used as a reliable computational tool for two-phase flow simulations in narrow rectangular flow geometry.

Interfacial Area Transport Equation and Implementation Into Two-Fluid Model

2009 ◽  
Vol 1 (1) ◽  
Author(s):  
Mamoru Ishii ◽  
Seungjin Kim ◽  
Xiaodong Sun ◽  
Takashi Hibiki
Keyword(s):  
Transport Equation ◽  
Fluid Model ◽  
Interfacial Area ◽  
Flow Conditions ◽  
Two Phase ◽  
Interfacial Area Concentration ◽  
Interfacial Area Transport ◽  
Interfacial Area Transport Equation ◽  
Two Fluid Model ◽  
Two Fluid

A dynamic treatment of interfacial area concentration has been studied over the last decade by employing the interfacial area transport equation. When coupled with the two-fluid model, the interfacial area transport equation replaces the flow regime dependent correlations for interfacial area concentration and eliminates potential artificial bifurcation or numerical oscillations stemming from these static correlations. An extensive database has been established to evaluate the model under various two-phase flow conditions. These include adiabatic and heated conditions, vertical and horizontal flow orientations, round, rectangular, annulus, and 8×8 rod-bundle channel geometries, and normal-gravity and reduced-gravity conditions. Currently, a two-group interfacial area transport equation is available and applicable to comprehensive two-phase flow conditions spanning from bubbly to churn-turbulent flow regimes. A framework to couple the two-group interfacial area transport equation with the modified two-fluid model is established in view of multiphase computational fluid dynamics code applications as well as reactor system analysis code applications. The present study reviews the current state-of-the-art in the development of the interfacial area transport equation, available experimental databases, and the analytical methods to incorporate the interfacial area transport equation into the two-fluid model.

Two-Fluid CFD Model of Adiabatic Air-Water Upward Bubbly Flow Through a Vertical Pipe With a One-Group Interfacial Area Transport Equation

2009 ◽  
Author(s):  
Deoras Prabhudharwadkar ◽  
Chris Bailey ◽  
Martin Lopez de Bertodano ◽  
John R. Buchanan
Keyword(s):  
Experimental Data ◽  
Transport Equation ◽  
Bubbly Flow ◽  
Interfacial Area ◽  
Correct Prediction ◽  
Interfacial Area Transport ◽  
One Dimensional ◽  
Interfacial Area Transport Equation ◽  
The One ◽  
Two Fluid

This paper describes in detail the assessment of the CFD code CFX to predict adiabatic liquid-gas two-phase bubbly flow. This study has been divided into two parts. In the first exercise, the effect of Lift Force, Wall Force and the Turbulent Diffusion Force have been assessed using experimental data from the literature for air-water upward bubbly flows through a pipe. The data used here had a characteristic near wall void peaking which was largely influenced by the joint action of the three forces mentioned above. The simulations were performed with constant bubble diameter assuming no bubble interactions. This exercise resulted in selection of the most appropriate closure form and closure coefficients for the above mentioned forces for the range of flow conditions chosen. In the second exercise, the One-Group Interfacial Area Transport equation was introduced in the two-fluid model of CFX. The interfacial area density plays important role in the correct prediction of interfacial mass, momentum and energy transfer and is affected by bubble breakup and coalescence processes in adiabatic flows. The One-Group Interfacial Area Transport Equation (IATE) has been developed and implemented for one-dimensional models and validated using cross-sectional area averaged experimental data over the last decade by various researchers. The original one-dimensional model has been extended to multidimensional flow predictions in this study and the results are presented in this paper. The paper also discusses constraints posed by the commercial CFD code CFX and the solutions worked out to obtain the most accurate implementation of the model.

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.

Prediction of interfacial area transport in a coupled two-fluid model computation

2016 ◽  
Vol 54 (1) ◽  
pp. 58-73 ◽  
Author(s):  
Joshua P. Schlegel ◽  
Takashi Hibiki ◽  
Xiuzhong Shen ◽  
Santosh Appathurai ◽  
Hariprasad Subramani
Keyword(s):  
Fluid Model ◽  
Interfacial Area ◽  
Model Computation ◽  
Interfacial Area Transport ◽  
Two Fluid Model ◽  
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.

Study on Drag Coefficients for Two Groups of Bubbles

2004 ◽  
Author(s):  
Xiaodong Sun ◽  
Yang Liu ◽  
Basar Ozar ◽  
Mamoru Ishii ◽  
Joseph M. Kelly
Keyword(s):  
Gas Phase ◽  
Fluid Model ◽  
Interfacial Area ◽  
Current Approach ◽  
Two Phase ◽  
Drag Coefficients ◽  
Interfacial Area Transport ◽  
Wide Range ◽  
Two Fluid Model ◽  
Two Fluid

To apply the two-fluid model to a wide range of flow regimes in gas-liquid two-phase flows, the gas phase is categorized into two groups: small spherical/distorted bubbles as Group 1 and large cap/slug/churn-turbulent bubbles as Group 2 in the modeling of interfacial area transport. The interfacial transfer terms of momentum and energy for the gas phase are then divided into two groups accordingly in the implementation of the two-group interfacial area transport equation to the two-fluid model. Thus, the drag coefficients and the interfacial heat transfer for each group bubbles need to be developed. An approach has been sought for evaluating the drag coefficients of each bubble group based on a comprehensive experimental data base obtained in air-water upward flows in various size round pipes. Comparisons have been made with the theory of the drag coefficients and it was found that the agreement is not very satisfactory although the general trends can be predicted by the current approach.

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