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.

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.

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.

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.

The Interfacial Area Weighted Area-Averaged Gas Velocity Model for the Interfacial Area Transport Equation in the System Analysis Code

2021 ◽  
Author(s):  
Mengsi Shen ◽  
Meng Lin
Keyword(s):  
Experimental Data ◽  
Transport Equation ◽  
Interfacial Area ◽  
Theory Model ◽  
Gas Velocity ◽  
Two Phase ◽  
Interfacial Area Concentration ◽  
Interfacial Area Transport ◽  
Drift Flux Model ◽  
Interfacial Area Transport Equation

Abstract The interfacial area transport equation is a more accurate and stable way to compute the interfacial area concentration than the traditional empirical correlation in the two-phase two-fluid model. And among the parameters in the two-group interfacial area transport equation, the interfacial area concentration weighted area-averaged gas velocity is an important parameter to close the two-group area-averaged interfacial area transport equation in the system analysis code. However, there has been no theory model to compute the interfacial area concentration weighted area-averaged gas velocity until now. So this study established the theory model for two-group interfacial area concentration weighted area-averaged gas velocity based on the drift-flux model for the two-phase dispersed bubble flow. The experimental data were selected from the published literature, which include the detailed two-phase interfacial structure experimental data for the slug bubble flow. The interfacial area concentration weighted area-averaged gas velocity model predicted the selected experimental data well, which validated the developed model. Moreover, the difference between the interfacial area concentration weighted area-averaged gas velocity and the void weighted area-averaged gas velocity is clarified quantitatively for the first time. The theory model developed in this study can be improved and then be used to compute the interfacial area weighted area-averaged gas velocity because it includes the empirical parameter of conventional drift-flux model.

Numerical Modeling of Two-Phase Flows Using Advanced Two Fluid Systems

2002 ◽  
Author(s):  
Anela Kumbaro ◽  
Imad Toumi ◽  
Vincent Seignole
Keyword(s):  
Fluid Model ◽  
Interfacial Area ◽  
Group Model ◽  
Two Phase Flows ◽  
State Equations ◽  
Two Phase ◽  
Interfacial Area Concentration ◽  
Void Fractions ◽  
Two Fluid Model ◽  
Two Fluid

The purpose of this paper is to report on the development and assessment of approximate Riemann solver methods for the discretization of non-linear non-conservative systems arising in the simulation of two-phase flows. These methods are able to treat general two-phase flow systems with realistic state equations and are flexible enough to be applied on any mesh type, structured as well as unstructured. We will detail models that go from the basic 6 equation two-fluid model to the coupling of this system with one or more transport equations, for instance on volumetric interfacial area concentration, or on partial void fractions of groups of bubbles (MUlti-Size-Group model). This kind of transport equation is useful to predict at a finer level the interfacial patterns or bubble size distribution and takes account of coalescence or breakup rates of inclusions. We make a glimpse at the choices made regarding this aspect. Different physico-numerical benchmarks are provided in order to illustrate the numerical and physical modeling. Confrontation with experimental or analytical reference data are performed whenever possible. Computer simulations are performed using OVAP, a new multidimensional CFD code.

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.

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.

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