One-dimensional Two-fluid Model Research Articles

Steady-State Behavior of a Two-Phase Natural Circulation Loop With Thermodynamic Nonequilibrium

A model to predict the steady-state behavior of a rectangular two-phase natural circulation loop has been proposed. The analysis employs a one-dimensional two-fluid model to identify various system parameters, with particular emphasis on the subcooled boiling region. The onset of two-phase region and point of net vapor generation and associated liquid temperatures and vapor qualities have been estimated using a few widely recognized correlations. Predicted results demonstrate that the consideration of subcooled boiling may have significant effect on system behavior, particularly around the transition regions. The interaction of saturated bubbles and subcooled liquid and associated change in heat transfer and frictional forces has been discussed in detail. Fluid stream has been observed to have different combinations of flow stream conditions at boiler exit and condenser inlet. Five probable combinations have been identified and a generalized working-regime map has been proposed on Nsub−NZu plane. Attempts have been made to identify the influence of various control parameters. A favorable sink condition (higher coolant flow rate or lower coolant entry temperature) has been found to be of particular importance to attain a wider operating range of wall heat flux and better heat transfer characteristics. A design map has been proposed to identify favorable operating condition in terms of control parameters to ensure complete condensation.

混相流研究の進展 ４ 稠密格子サブチャンネル間のボイドドリフトに及ぼす表面張力低下の影響

Void drift between triangle tight lattice subchannels has been studied experimentally and analytically. In the experiment, a channel having two subchannels simplifying the triangle tight lattice subchannels was used. Experimental data were obtained for both air-water and air-water with a surfactant flows to know the effects of the reduced surface tension on flow and void redistributions due to the void drift. In the analysis, the experimental data were compared with the calculation by a subchannel analysis code based on a one-dimensional two-fluid model in which various constitutive equations of wall and interfacial friction forces were tested. The results of such experiment and test of analysis will be reported.

Pressure Drop in Two-Phase Swirling Flow in a Steam Separator

Pressure drop and liquid film thickness in air-water swirling flows in a one-fifth scale model of the steam separator are measured for a wide range of gas and liquid volume fluxes. Numerical simulations based on one-dimensional single-fluid and two-fluid models are also carried out to examine the feasibility of predicting the pressure drop and film thickness in swirling flows. The pressure drop in a single-phase swirling flow is about five times as large as that in a non-swirling flow due to the increase in the frictional pressure drop. The pressure gradient and liquid film thickness in a two-phase swirling annular flow at the inlet of the pick-off-ring of the separator are well evaluated by using a standard one-dimensional two-fluid model, provided that the interfacial and wall frictions in an ordinary two-phase annular flow are multiplied by appropriate constant values.

Void Fraction, Wall and Interfacial Friction Forces for Two-Phase Flow in Microchannel

The flow characteristics of the two-phase flows in a 100 µm circular horizontal microchannel have been investigated experimentally and analytically. In the experiments, nitrogen gas and one of four liquids (distilled water and 4.8, 49, 100 wt% ethanol in water) were injected through a T-junction type mixer to the microchannel, having smaller diameter than that of the mixer. Both quasi-homogeneous flow and quasi-separated flow was observed depending on gas and liquid flow conditions. Furthermore, the data on void faction, frictional pressure drop and interfacial friction force were found to be larger in the quasi-homogeneous flow than the quasi-separated one. In the analysis, empirical correlations of the liquid-wall friction force and the gas-liquid interfacial friction force were developed respectively for the quasi-homogeneous and the quasi-separated flows. By substituting these correlations into an analytical code based on a one-dimensional two-fluid model, we calculated the void fraction. The calculations reasonably agreed with the data irrespective of the quasi-homogeneous and the quasi-separated ones.

Effects of Surface Tension on Two-Phase Void Drift Between Triangle Tight Lattice Subchannels

In this study, void drift phenomena, which are one of three components of the intersubchannel fluid transfer, have been investigated experimentally and analytically. In the experiments, data on flow and void redistributions were obtained for hydraulically nonequilibrium flows in a multiple channel consisting of two subchannels simplifying a triangle tight lattice rod bundle. In order to know the effects of the reduced surface tension on the void drift, water and water with a surfactant were used as test liquids. In addition, data on the void diffusion coefficient, D̃, needed in a void drift model, have been obtained from the redistribution data. In the analysis, the flow and the void redistributions were predicted by a subchannel analysis code based on a one-dimensional two-fluid model. From a comparison between the experiment and the code prediction, the present analysis code was found to be valid against the present data if newly developed constitutive equations of wall and interfacial friction were incorporated in to the model to account for the reduced surface tension effects.

Drag coefficient in one-dimensional two-group two-fluid model

Recently, the concept of the interfacial area transport equation has been proposed to predict the dynamic change of interfacial structure in transient and developing flows. In this approach, bubbles are categorized into two groups (group 1: spherical/distorted bubbles; group 2: cap/slug/churn-turbulent bubbles) due to the considerable difference in their transport characteristics. In this paper, the equations for calculating drag coefficients of both groups under developing flow conditions are derived based on the momentum equations in the one-dimensional two-group two-fluid model. It is found that void fraction of both groups should be taken into account in determining drag coefficient of each group. The shape factor is important for group 2 bubbles even though it can be approximated to be unity for group 1 bubbles. Experimental data of air–water upward bubbly flows in various sizes of pipes are used to examine the existing drag coefficient model of group 1 bubbles. It is shown that the Ishii and Chawla’s models for spherical and distorted bubbles can predict the experimental data in the forced convective flow systems satisfactorily, which confirms their applicability to bubbly flow systems.

Void Fraction, Wall and Interfacial Friction Forces for Two-Phase Flow in Microchannel

The flow characteristics of the two-phase flows in a 100μm circular horizontal microchannel have been investigated experimentally and analytically. In the experiments, nitrogen gas and one of four liquids (distilled water and 4.8, 49, 100 wt% ethanol in water) were injected through a T-junction type mixer to the microchannel, having smaller diameter than that of the mixer. Both quasi-homogeneous flow and quasi-separated flow was observed depending on gas and liquid flow conditions. Furthermore, the data on void faction, frictional pressure drop and interfacial friction force were found to be larger in the quasi-homogeneous flow than the quasi-separated one. In the analysis, empirical correlations of the liquid-wall friction force and the gas-liquid interfacial friction force were developed respectively for the quasi-homogeneous and the quasi-separated flows. By substituting these correlations into an analytical code based on a one-dimensional two-fluid model, we calculated the void fraction. The calculations reasonably agreed with the data irrespective of the quasi-homogeneous and the quasi-separated ones.

Stability of Stratified Gas-Liquid Flow in Horizontal and Near Horizontal Pipes

A viscous Kelvin-Helmholtz criterion of the interfacial wave instability is proposed in this paper based on the linear stability analysis of a transient one-dimensional two-fluid model. In this model, the pressure is evaluated using the local momentum balance rather than the hydrostatic approximation. The criterion predicts well the stability limit of stratified flow in horizontal and nearly horizontal pipes. The experimental and theoretical investigation on the effect of pipe inclination on the interfacial instability are carried out. It is found that the critical liquid height at the onset of interfacial wave instability is insensitive to the pipe inclination. However, the pipe inclination significantly affects critical superficial liquid velocity and wave velocity especially for low gas velocities.

Parametric study of a model for determining the liquid flow-rates from the pressure drop and water hold-up in oil–water flows

A flow-pattern-dependent model, traditionally used for calculation of pressure drop and water hold-up, is accustomed for calculation of the liquid production rates in oil–water horizontal flow, based on the known pressure drop and water hold-up. The area-averaged steady-state one-dimensional two-fluid model is used for stratified flow, while the homogeneous model is employed for dispersed flow. The prediction errors appear to be larger when the production rates are calculated instead of pressure drop and water hold-up. The difference in the calculation accuracies between the direct and inverse calculation is most probably caused by the different uncertainties in the measured values of the input variables and a high sensitivity of the calculated phase flow-rates on even small change of the water hold-up for certain flow regimes. In order to locate the source of error in the standard two-fluid model formulation, several parametric studies are performed. In the first parametric study, we investigate under which conditions the momentum equations are satisfied when the measured pressure drop and water hold-up are imposed. The second and third parametric studies address the influence of the interfacial waves and drop entrainment on the model accuracy, respectively. These studies show that both interfacial waves and drop entrainment can be responsible for the augmentation of the wall-shear stress in oil–water flow. In addition, consideration of the interfacial waves offers an explanation for some important phenomena of the oil–water flow, such as the wall-shear stress reduction.

The WAHA Code : a numerical tool for water hammer in two-phase flow – some simulations of experiments

The WAHA computer code has been developed during the WAHALoads project in the frame of the 5th European Program. The main purpose of the WAHA code is to predict various mechanisms of single- and two-phase water hammer transients in piping systems. The WAHA code can simulate thermal-hydraulic transients with one-dimensional six-equation two-fluid model approximations and calculate the hydraulic forces on the piping system due to water hammers in two-phase flow. In the first part of the present paper, the main features of the WAHA code and its capabilities are presented : basic equations, specific closures laws, numerical scheme, possible boundary conditions, some basic results of water hammers induced by a rapid valve closure. In the second part of the paper, a description of the UMSICHT test facility PPP which has been used for water hammer tests inducing bubble condensation is given. The installation has been equipped with a new measurement technology including new wire mesh sensors with thermocouples for the measurement of condensation heat transfer and other innovative transient measurement techniques. From the UMSICHT data bank,some basic data have been chosen as reference case for validating the WAHA code. The third part deals with the simulation of several test cases using the WAHA code : Edwards pipe - Discharge of a hot liquid from a horizontal pipe. PPP water hammer tests – Depressurisation inducing cavitation water hammer initiated by a fast valve closure. Super Moby Dick experiment – Critical two-phase flow through a long nozzle. The results of these simulations are systematically compared with the experimental data, when available. It is concluded that the WAHA code has the abilitity to correctly predict various mechanisms of transients flows occurring in piping systems.

Stability of stratified flow and slugging in horizontal gas-liquid flow*

Abstract A transient one-dimensional two-fluid model is proposed to investigate numerically the interfacial instability and the onset of slugging for liquid-gas flow in a horizontal duct. In the present model, the effects of surface tension and transverse variations in dynamic pressure are taken into account. The evolution of interfacial disturbances in displayed and compared with the linear viscous Kelvin-Helmholtz stability analyses. It shows that interfacial wave is more instable due to the non-linear effect. The model predicts well the stability limit of stratified flow in comprison with the experimental data, and also automatically tracks the onset of slugging. The results show that the initiation of hydrodynamic slugging is related to local interfacial instability. Based on the cycle of slugging, a model for slug frequency is presented, which predicts the trends of slug frequencies with gas/liquid flow rate well in comparison with the available data. The effects of physical properties on slugging ha...

Simulation of SBLOCA based on an Improved Choked Flow Model for RELAP5/MOD3 Code

This paper is a continuation of the present author’s previous publication dealing with a new choked flow model for two-phase flow. The model based on a hyperbolic one-dimensional two-fluid model, where in the momentum equations the terms representing the interfacial pressure difference has been included in lieu of the virtual mass force terms. The new choked flow model is an improvement upon the choked flow model of the current RELAP5/MOD3 code, which itself is based on the Trapp–Ransom method. The author compares the predictions of this improved model with Trapp–Ransom model and Henry–Fauske model, for an assumed flow in a vertical pipe. The author simulates a typical PWR system with a hypothetical SBLOCA as well, and compares the system behaviors predicted by RELAP5/MOD3, based on the aforementioned choked flow models. He shows that the improved choked flow model leads to better predictions.

Modeling Gas-Liquid Head Performance of Electrical Submersible Pumps

This study presents a new gas-liquid model to predict electrical submersible pumps head performance. The newly derived approach based on gas-liquid momentum equations along pump channels has improved the Sachdeva model (Sachdeva, R., Doty, D. R., and Schmidt, Z., 1988, “Two-Phase Flow through Electrical Submersible Pumps,” Ph.D. dissertation, The University of Tulsa, Oklahoma; 1994, “Performance of Electric Submersible Pumps in Gassy Wells,” SPE Prod. Facil., 9, pp. 55–60) in the petroleum industry and generalized the Minemura model (Minemura, K., Uchiyama, T., Shoda, S. and Kazuyuki, E., 1998, “Prediction of Air-Water Two-Phase Flow Performance of a Centrifugal Pump Based on One-Dimensional Two-Fluid Model,” ASME J. Fluids. Eng., 120, pp. 327–334) in the nuclear industry. The new two-phase model includes novel approaches for wall frictional losses for each phase using a gas-liquid stratified assumption and existing correlations, a new shock loss model incorporating rotational speeds, a new correlation for drag coefficient and interfacial characteristic length effects by fitting the model results with experimental data, and an algorithm to solve the model equations. The model can predict pressure and void fraction distributions along impellers and diffusers in addition to the pump head performance curve under different fluid properties, pump intake conditions, and rotational speeds.

Onset of pulsing in gas–liquid trickle bed filtration

When liquid suspensions containing low concentration of fine solids are treated in catalytic packed bed gas–liquid–solid reactors, which are operated in trickle flow or near the transition between trickle and pulse flow, plugging develops and increases the resistance to two-phase flow. Also due to obstruction, such accumulation of fines in the catalyst bed shifts progressively the flow pattern from trickling to pulsing flow. The progressive onset of pulsing flow along the packed bed was estimated using a sequential approach based on combining a “large time-scale” unsteady-state filtration solution of two-phase flow with a “short time-scale” solution of a linear stability analysis of two-phase flow. Space–time evolution and two-phase flow of the deposition of fines in trickle bed reactors under trickle flow regime was described using a one-dimensional two-fluid model based on the volume-average mass and momentum balance equations and volume-average species balance equation for the fines. The model hypothesized that plugging occurred via deep-bed filtration and incorporated physical effects of porosity and effective specific surface area changes due to the capture of fines, inertial effects of phases, and coupling effects between the fines filter rate equation and the interfacial momentum exchange force terms. The transition between trickle flow and pulse flow regimes was described from a stability analysis of the solution of the transient two-fluid model around an equilibrium state of trickle flow under pseudo steady state conditions. The impact of liquid superficial velocity, viscosity and surface tension, gas superficial velocity and density, feed fines concentration, and fines diameter on the transition between trickle and pulse flows in the presence of fines deposition was analyzed.

1178. 急拡大を伴う鉛直円管内空気―水系気泡流に対する1次元2流体モデルの適用性

Experiment and numerical calculation were made on the multi-dimensional behavior of upward gas-liquid bubbly flow in a vertical pipe with an axisymmetric sudden expansion. The variation of the void fraction distribution in the sudden expansion was measured at the different axial and radial positions using a point-electrode resistivity probe for various gas and liquid flow conditions. Based on the measured void fraction distribution in the sudden expansion, the axial profiles for the phase distribution parameters were evaluated in the sudden expansion. Numerical calculations were carried out to predict the cross-sectional averaged void fractions along the flow direction by using the one-dimensional two-fluid model considering the phase distribution parameter to verify the applicability of the computations. From these results, it concretely pointed out that some multi-dimensional modeling or modifications for numerical simulation would be needed and the distribution parameter was one of the most important parameters for one-dimensional two-fluid model to evaluate accurately the void fraction distriblltions affected by the multi-dimensional channel geometry.

A model for simulating gas bubble entrainment in two-phase horizontal slug flow

In an earlier paper it was shown that the basic one-dimensional transient two-fluid model is capable of capturing horizontal and near-horizontal slug flow automatically. However, that work did not account for the effect of gas entrainment into the liquid slug body which is deemed to be an important phenomenon. In this paper, a mathematical model to account for the entrainment of gas bubbles into liquid slugs is proposed, implemented and validated. The model is cast in the framework of the existing two-fluid model and is incorporated in a computational procedure, which is applied to the prediction of slug flow in horizontal and slightly inclined pipes. The model entails the introduction of a scalar equation for the transport of the dispersed gas bubbles within the liquid. The rate of entrainment of gas at the slug front is supplied as a closure relation, the expression for which is obtained from existing correlations. The model is validated against experimental data and the comparison shows satisfactory agreement. However, the inclusion of the aeration model appears to yield marginal differences when compared to predictions which ignore entrainment in the horizontal pipe flow cases studied. More significant differences are obtained in the case of the flow in a V-section pipeline.

On the simulation of three-phase slug flow in nearly horizontal pipes using the multi-fluid model

The article presents a mathematical model to simulate three-phase (liquid/liquid/gas) stratified and slug flows. The approach is based on the one-dimensional transient two-fluid model in which the two-phases consist of the gas and the mixture of the two liquids, with the motion of the liquid phases relative to each other being modelled via a drift–flux model. In order to close the model, a scalar transport equation for the conservation of mass for one of the liquid phases is introduced. Other closure models incorporated relate to the liquid–liquid flow pattern (stratified or fully dispersed), the phase inversion point (when the continuous liquid phase becomes dispersed in the other and vice-versa), the slip between the liquid phases and the mixture viscosity (which changes abruptly when phase inversion occurs). The equations are solved numerically using a previously developed finite volume methodology that had been applied to the prediction of two-phase slug flow and by which liquid slugs are automatically captured as an outcome of the numerical integration. The new method is applied to the study of the flow of oil, water and air in horizontal pipes. The method is shown to be able to predict locally whether the two liquids form a dispersion (of either oil droplets in water continuous flow (O/W) or water droplets in oil continuous flow (W/O)) or flow in stratified layers. It is demonstrated that the developed model is capable of correctly predicting slugging, and is moreover able to reproduce successfully observed experimental trends for the major slug properties, such as pressure gradient, slug frequency, and total liquid hold-up. The study revealed that the slip between the two liquid phases plays a major role in determining the slug characteristics in three-phase flow.

Critical Heat Flux Prediction Method Based on Two-Phase Turbulence Model

In this paper, we present an analytical methodology to predict forced convective CHF (Critical Heat Flux) for DNB (Departure from Nucleate Boiling) type boiling transition that occurs inside of uniformly heated round tubes. Axial directional two-phase flow analysis was conducted based on one-dimensional two-fluid model and typical constitutive models. At the same time, the radial directional distribution of void fraction at any axial location was calculated based on the bubble diffusion model, which was coupled with two-phase turbulence model for boiling bubbly flow. The calculated void fraction showed the wall peak distribution, and was compared with experimental data, which was derived from subcool boiling experiments. IPNVG (Incipient Point of Net Vapor Generation), which means the starting point of two-phase flow analysis, was also investigated well, since it was revealed that IPNVG had a significant influence on CHF prediction. By using this methodology for calculating radial directional void fraction distribution, we carried out CHF prediction for water on the assumption that DNB would occur when the local void fraction near the heated wall exceeds a critical value. The predicted CHF agreed well with experimental data, and the accuracy was within about 20%.

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

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.

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

A one-dimensional two-fluid model with explicit momentum flux parameters is proposed as a remedy for the mathematical ill-posedness of the standard one-dimensional two-fluid model. By constructing a simplified two-phase flow using existing correlations for the distribution parameter C o and velocity profile, the momentum flux parameter is determined as a function of void fraction and density ratio for the whole range of flow regime. By performing a linear stability analysis for a two-phase flow in a channel described by the proposed model, an analytical expression for the growth factor is derived as a function of wave number, void fraction, drag coefficient, and relative velocity. From the analytical expression for the growth factor, the stability criteria are derived as a function of void faction, density ratio, and momentum flux parameters. It is shown that the two-phase flow in a channel described by the proposed model is stable in the whole range of flow regime.