One-dimensional Drift-flux Model Research Articles

Air-Lift Pumping System for Hybrid Mining of Rare-Earth Elements-Rich Mud and Polymetallic Nodules around Minamitorishima Island

REE-rich mud under the seabed at a 5500–5700 m water depth around Minamitorishima island and polymetallic nodules buried in the deep seabed are very promising and attractive to explore and develop. REEs are critical to develop due to the recent paradigm shift to renewable energies based on green technologies. Numerical analysis using a one-dimensional drift–flux model for gas–liquid–solid three-phase flow and gas–liquid two-phase flow was conducted to examine the characteristics of an air-lift pumping system for mining these mineral resources. Empirical equations of REE-rich mud and the physical properties of polymetallic nodules around Minamitorishima island were utilized in the analysis. As a result, the characteristics, i.e., the performance of the system, were clarified in three cases: REE-rich mud, polymetallic nodules, and both. The time transient, i.e., the unsteady characteristics of the system, was also shown, such as the start-up and feeding slurry with REE-rich mud and polymetallic nodules. The findings from the unsteady characteristics will be useful in considering the operation of a real project or a commercial system in the future.

One-dimensional drift-flux model for two-phase flow in NaCl solutions: The role of surface mobility

The presence of dissolved salts in water inhibits bubble coalescence, facilitating the generation of microbubbles, while also maintaining a tangentially mobile air-water surface. In this study, we investigated the variation of bubble size and gas holdup with gas velocity in NaCl solutions using a rectangular bubble column and interpreted the experimental data using the one-dimensional drift-flux model. For the generated bubbles at the size between 0.4 mm and 1 mm, we found that the Moore model assumes mobile air-water surfaces, rather than the Schiller and Naumann model, should be used to describe the bubble terminal velocity. The latter model, which assumes an immobile air-water surface, has been used successfully to predict two-phase flow in surfactant solutions but would overestimate the gas holdup by almost 100 % for NaCl solutions. This finding emphasizes the crucial role of surface mobility in determining gas holdup. Thus, we propose the use of a one-dimensional drift-flux model, incorporating the Moore model to describe bubble terminal velocity, for microbubble systems with a mobile air-water interface.

Stability Tests and Analysis of a Low-Pressure Natural Circulation Loop with Flashing Instability

Natural circulation is employed in new designs of light water reactors to enhance passive safety by maintaining flow and heat removal without pumps. Under low-pressure and low-flow-rate conditions, natural circulation is susceptible to two-phase instabilities leading to undesirable flow oscillations and operational difficulties. Flashing instability is one of the most widely reported low-pressure natural circulation instabilities, related to saturated vaporization triggered by a hydrostatic pressure drop in an adiabatic riser above a heated section. While existing studies have reported flashing instability experiments, modeling, and simulations including successes in matching numerical results and experimental data, solid yet clear analytical explanations for many of its qualitative features are still rare. To enhance the physical understanding beyond stability boundary prediction, the current work develops, validates, and analyzes a linear stability model of flashing instability. This model adopts a one-dimensional Drift-Flux Model simplified by physical assumptions and approximations, and it includes optional component models to match an actual facility for validation. Stability tests are performed on a 5-m-tall natural circulation loop, providing comprehensive benchmark data covering stability boundaries, one-dimensional transient signals, and periodic mean waveforms from local measurements. Validation confirms acceptable predictions of steady states, stability boundaries, and oscillation periods. The tractable model formulation leads to a closed-form characteristic function facilitating analytical manipulations and physical interpretations, based on which dominant pressure drop responses to inlet flow rate are extracted. The major instability mechanism is identified as a strong response of the two-phase driving force to the inlet flow rate that is delayed by enthalpy transportation through a long single-phase distance and can become an overwhelmingly destabilizing positive feedback under low-frequency perturbations. Experimentally reported qualitative features, including stability changes, timescale relations, and oscillation patterns, are analytically predicted and physically explained with clarity. In general, this study enriches experimental resources of flashing instability with a comprehensive dataset and provides a simple yet realistic analytical basis for physically understanding flashing instability beyond predicting stability boundaries.

PREMATURE SHUT OFF POSSIBILITY PREDICTION FOR AUTOMOTIVE FUEL TANK SYSTEM

Prediction of the possibility of a vehicle fuel tank supply process prematureshut off is of main concern for the automotive industry. The main objectiveof this work is to show that premature shut off can be explained by the absenceof a steady state after the initial transient in the fuel supply process. Thevehicle fuel tank considered in this work is composed only of a rectilinearpipe inclined with respect to the horizontal and connected to the top of arectangular tank. The counter-current two-phase flow in the pipe is modeledusing the one-dimensional drift flux model and the tankis modeled as a control volume where mass conservation for each phase isconsidered. Linear stability analysis of the two-phase flow model shows theabsence of the steady state phase for a range of liquid flow rates before theflooding condition is achieved as a function of tube inclination and length.This fact suggests that premature shut off occurs due to the absence of asteady state regime phase during the fuel supply process.

Experimental investigation on local/global void distribution of air-water two-phase flow in a 3 × 3 rod bundle channel under low-flow conditions

In this study, the vertical upward air–water two-phase flow tests have been carried out to investigate the distribution of local and global void fractions in a rod bundle channel under low-flow conditions. The height of the rod bundle channel is about 5 m, and the channel cross section is comprised of a 52 × 52 mm rectangular casing and 3 × 3 circular rods. The rods with a diameter of 11.5 mm and a pitch of 15.4 mm were set as a rectangular array. Four sets of non-intrusive conductivity sensors were built to measure the local and global void fractions of various gaps within the rod bundle channel. The tests were operated at low flow conditions: jg= 0.016–0.92 m/s and jf = 0.02–0.05 m/s, which covered the possible flow regimes of bubbly, cap-bubbly and cap-turbulent flows. The measured global void fraction were benchmarked with existing one-dimensional drift-flux model, and the local void fractions have been summed up by regions and compared with the global void fraction for validation. The dynamic characteristics of local/global void fractions have been analyzed with probability density function (PDF) and fast Fourier transform (FFT), and the distributions and variations of averaged void fraction against test conditions have been presented. Furthermore, the empirical correlations for estimating the local void fractions have been proposed, which can successfully estimate the local void distribution from global void fraction with limited errors. The present results and correlations can be a reference for future development and modification of detailed two-phase flow models in the rod bundle geometry.

Application of the one-dimensional drift-flux model for numerical simulation of gas–liquid isothermal flows in vertical pipes: a mechanistic approach based on the flow pattern

The multiphase flow prediction becomes necessary for the technical–economical feasibility of several transportation processes in the petroleum industry, among others. Depending on the flow rates, phases’ physical properties, and pipe characteristics, gas–liquid flows can assume three flow patterns: dispersed, separated, and intermittent. The drift-flux model is adopted in various commercial simulators and allows all flow patterns simulation provided that the constitutive equations are suitable for each flow pattern. The interfacial terms, the well-posedness, and the reduced number of transport equations are the main advantages of the drift-flux model in comparison with other models, such as the two-fluid model. But the constitutive laws for predicting the wall shear force are its weak point and depend on the arrangement of each flow pattern, unlike relative motion that can be determined by correlations that are flow pattern-independent or not. This work aims to perform the steady-state numerical simulation of gas–liquid flows in vertical pipes, applying a one-dimensional mechanistic approach dependent on the flow pattern, for the closing of the constitutive equations, solved in a single running algorithm. The results obtained by this approach are compared against two sets of experimental data for the pressure gradient of upward air–water vertical isothermal flow cases, presenting satisfactory results, thus demonstrating the accuracy of the approach employed.

One-dimensional drift-flux model and a new approach to calculate drift velocity and gas holdup in bubble columns

In view of the practical importance of the drift-flux model and the variety of industrial applications of large-diameter columns, the model coefficients, including the distribution parameter (C0) and drift velocity (C1), have been investigated for the upward two-phase flow in large- and small-diameter columns. The distribution parameter and drift velocity reflect the non-uniformity in the flow and the local relative motion between two phases, respectively. As the formation of cap bubbles and occurrence of liquid recirculation are two of the most important characteristics in a large-diameter column, the distribution parameter and drift velocity in such a column are rather different from those in a small-diameter column. In this study, the local flow parameters measured by other researchers were collected, and C0 and C1 were calculated based on their definitions. The experimental values in small- and large-diameter columns were compared, and the performances of various existing constitutive equations for the drift-flux model were re-evaluated. Two semi-empirical correlations for the drift velocity and gas holdup were developed, and their performances were verified against experimental data for various two-phase flow conditions.

One-dimensional drift-flux model of gas holdup in fine-bubble jet reactor

A one-dimensional drift flux model of the gas holdup in the fine-bubble jet reactor (for short FJR) was developed and experimentally verified. The model consists of three key sub-models (bubble Sauter mean diameter, bubble average rising velocity and energy dissipation rate). Effects of downcomer length, liquid dynamic viscosity and surface tension on the bubble Sauter mean diameter, energy dissipation rate, and gas holdup were discussed theoretically. Furthermore, three kinds of systems (air-tap water, air-aqueous ethanol, and air-aqueous glycerol) were chosen to validate the model under different conditions including liquid flow rate, nozzle diameter, downcomer length, and temperature. Theoretical results indicated that the energy dissipation rate in the downcomer of FJR was the critical factor influencing gas holdup in the column of FJR. It is also found that gas holdups predicted by the model were roughly identical to experimental results and errors were within ±15%.

Effect of wall wettability condition on drift-flux parameters in lead–bismuth two-phase flow in circular and annular bubble columns

ABSTRACT Lead–bismuth two-phase flow in a cylindrical vessel and annulus was experimentally investigated by varying the surface wettability of the vessel wall. The test section used in this study was a cylindrical stainless vessel with/without inner sleeve to change the hydraulic diameter. Volume-averaged void fraction was measured by varying the surface wettability of the test section, which was enhanced by using a soldering flux. Measured void fraction was compared with existing two-phase flow correlations and with one-dimensional theoretical simulations assuming one-dimensional drift-flux model. From experimental results, measured distribution parameters of the lead–bismuth two-phase flow are much larger than that of ordinary two-phase flow regardless of the surface wettability. In the present work, the one-dimensional analysis was carried out for the cylindrical vessel to reproduce the distribution parameter. From the simulation results, predicted value for the cylindrical vessel showed good agreement with experimental results. However, in annulus, the distribution parameters in annulus were underestimated by the present model. It was suggested that, in case of annulus, steeper void fraction profile might be formed near the inner surface for poor wettability condition.

Differential-Algebraic numerical approach to the one-dimensional Drift-Flux Model applied to a multicomponent hydrocarbon two-phase flow

Abstract This paper presents a numerical investigation of the solution of the steady-state one-dimensional Drift-Flux Model. It is proposed that these simulations, though often based on finite-volume discretizations and iterative sequential procedures, are preferably performed using established numerical methods specifically devised for Differential-Algebraic Equations (DAE) systems. Both strategies were implemented in a computer code developed for simulations of multicomponent hydrocarbon two-phase flows. The SIMPLER semi-implicit algorithm was employed in the solution of the finite-volume discretized model in order to provide comparison grounds with the adaptive BDF-implementation of DAE integration package DASSLC. Based on test simulations of a naphtha two-phase flow under varying heat-transfer conditions, the DAE approach was proved highly advantageous in terms of computational requirements and accuracy of results, both in the absence and presence of flow-pattern transitions. Numerical difficulties arising from the latter were successfully worked around by continuously switching regime-specific constitutive correlations using adjustable steep regularization functions.

JFNK method with a physics-based preconditioner for the fully implicit solution of one-dimensional drift-flux model in boiling two-phase flow

The Jacobian-free Newton-Krylov (JFNK) method with an efficient physics-based preconditioner is applied for the numerical solution of the one-dimensional drift-flux model with the closure constitutive equations. Additional closure correlations, including the flow pattern dependent heat transfer correlations and the flow pattern independent kinematic constitutive correlation, are used to close the governing equations of one-dimensional drift-flux model. The governing equations have been discretized using the first-order upwind method for spatial discretization and the fully implicit method for temporal discretization. An efficient physics-based preconditioner derived from the semi-implicit solution of governing equations is used in the JFNK method to improve the efficiency and numerical stability. The numerical verification and code validation have been performed for subcooled boiling two-phase flow in a vertical tube. By comparing with the other methods (JFNK method without preconditioner, the Broyden method and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method), the preconditioning JFNK method shows the robustness and a good computational efficiency. Moreover, by comparing the numerical simulation results with the experimental results, it is found that the JFNK method with a physics-based preconditioner shows the good accuracy for the numerical simulation for one-dimensional boiling two-phase flow.

Axial and radial void fraction measurements in convective boiling flows

This work is inspired by the need to have measurements and predictive capability on vertical saturated boiling flows, which are of importance in boiling water nuclear reactors. In these systems, sub-cooled water flows upwards in vertical tubes which contain a multiplicity of nuclear fuel rods, and the heat is taken away from these rods by natural convection boiling. A close analog of this situation exists when the liquid is in forced flow, and the heat flux from the vertical rods is quenched by forced convection boiling of the upward liquid water flux.In this work, we present experimental data has for axial, and radial vapor void fraction distributions in an annular boiling channel for low mass-flux forced the flow of water at high inlet sub-cooling. A single centrally placed electrical rod, designed to mimic the nuclear fuel rod has been used. The void fraction measurement is made using gamma ray densitometry technique. Axial and radial vapor void fractions have been reported, as a function of inlet liquid flux and inlet liquid temperature. The experimental data has been rationalized using a simple one-dimensional drift flux model adapted to the conditions of the experiment.

Comparative analysis of wall shear stress models to the drift-flux model applied to slug flow regime

Abstract The one-dimensional drift-flux model efficiently predicts gas–liquid flows dominated by gravity force. The advantages of the drift-flux model applied to pipe flows are the absence of interfacial terms, well posedness and the reduced number of transport equations, but its weakness lays on the constitutive laws to predict the wall shear force of a gas–liquid mixture. Its success on upward vertical slug flows is, in part, due to the fact that for gravity dominated flows the friction contribution to the pressure gradient is usually small. In these applications the accuracy of the wall shear force model is not dominant. A challenging aspect is the application of the drift-flux model to the horizontal slug flows where the pressure gradient is due to friction force. The objective of this work is to develop a comparative analysis among wall shear stress models applied to the one-dimensional, steady state drift-flux approach applied to gas–liquid mixture flowing in the slug regime. Effective viscosity models based on the homogeneous and also on empirical propositions are employed. Additionally it is also introduced a mechanistic wall shear stress model. The effect of the use of distinct wall shear models into the drift-flux model is assessed by comparing the estimated pressure gradients against experimental data.

Assessment of TAPINS code for application to thermal-hydraulic analysis of an integral reactor, REX-10

The thermal-hydraulic analysis program for integral reactor system (TAPINS) is a thermal-hydraulic system code developed by Seoul National University for transient analysis of an integral reactor, REX-10. Specialized for a fully passive integral pressurized water reactor, TAPINS adopts a one-dimensional four-equation drift-flux model for two-phase flows. It also consists of component models for the core, the helical-coil steam generator, and the steam-gas pressurizer. This paper presents the developmental assessment of TAPINS to validate its applicability to the thermal-hydraulic analysis of REX-10. Assessment problems are determined by taking into account thermal-hydraulic phenomena expected during design basis accidents of REX-10, including the loss-of-feedwater accident and the small-break loss-of-coolant accident. To confirm the predictive capability of TAPINS for these phenomena, the TAPINS model is validated against four sets of separate effects problems, including the pressurizer insurge test, the subcooled boiling experiment, the critical flow test, and the Edwards pipe problem. In addition, the calculation results of TAPINS are compared with the experimental data obtained from a series of integral effects tests using a scaled apparatus of REX-10. From the validation results, it is demonstrated that TAPINS can provide the reasonable prediction on the thermal-hydraulic responses of REX-10 during the transient and accident conditions.

One-dimensional drift-flux model for two-phase flow in pool rod bundle systems

A one-dimensional drift-flux model was developed and benchmarked with existing models in the present study. Different from existing empirical correlations, this newly developed 1-D drift-flux model started from the variations of two-phase flow distribution parameter C 0 for non-dimensional superficial gas velocity 〈 j g + 〉 from low to high, which represents the variation of phase distribution patterns. Due to a combination of small-scale sub-channel effect and large-scale casing effect in a rod bundle, the Hibiki–Ishii’s drift velocity V gj + was introduced to describe the relative motion between two phases. A clear boundary of distribution parameter, C 0, can be found when the non-dimensional superficial gas velocity 〈 j g + 〉 is closed to 0.5. A linearly increasing trend and an exponentially decreasing trend of C 0 were found in the lower and higher gas sides divided by this boundary, respectively. Through the present model, one dimensional area-averaged gas velocity and void fraction can be determined for rod bundles in pool conditions. The prediction results were compared with several existing models and experimental data. The present model shows a good agreement with the existing experimental data and can be applied to both boiling and adiabatic air–water two-phase flows. In order to explain the peak values of C 0 in low superficial gas velocity conditions, several possible superficial velocity and void fraction profiles were examined by considering the recirculation flow/void distributions.

One-Dimensional Drift-Flux Model at Reduced Gravity Conditions

The drift-flux model is of practical importance for two-phase flow analyses at reduced gravity conditions. In view of this, the drift-flux model, which takes the gravity effect into account, is studied in detail. The constitutive equation of the distribution parameter for bubbly flow, which takes the gravity effect into account, has been proposed, and the constitutive equations for slug, churn, and annular flows, which can be applicable to reduced gravity conditions, are recommended based on existing experimental and analytical studies. The previously derived constitutive equations of the drift velocity in various two-phase flow regimes, which takes the frictional pressure loss into account, are adopted in this study. A comparison of the model with various experimental data over various flow regimes and a wide range of flow parameters taken at microgravity conditions shows a satisfactory agreement. The drift-flux model has been applied to reduced gravity conditions such as 1.62 and 3.71 m/s 2 , which correspond to the lunar and Martian surface gravities, respectively, and the effect of the gravity on the void fraction in two-phase flow systems has been discussed.

Laser-induced fluorescence (LIF) studies of liquid–liquid flows. Part I: Flow structures and phase inversion

A non-intrusive dye tracing technique, laser-induced fluorescence (LIF), has been applied to investigate the co-current flow of two immiscible organic–aqueous liquid flows in a vertical pipe. This technique allowed detailed visualization of the dynamic evolution of the flows. Flow structures in liquid–liquid flows at high dispersed phase fraction were revealed which had not been seen before. In pipe flow, an unstable range was found in the flow pattern map in which oil-in-water (o/w) and water-in-oil (w/o) dispersions could co-exist. Secondary dispersions (o/w/o and w/o/w) were observed for most volume fractions and velocities, especially in the unstable range. It was observed that, when the flow is in the unstable region, both w/o/w and o/w/o secondary dispersions could appear in the same set of experiments. It was found that this unstable range in the pipe flow, in spite of the similar appearance, was different to the ambivalent range seen in agitated systems. The one-dimensional drift flux model of Wallis (1969) for dispersed flow and a laminar model for co-current downward annular flow, were also applied to predict the in situ oil holdup; good agreement was obtained.

Structure of vertical downward bubbly flow

In view of the great importance to two-fluid model, structure of downward bubbly flows in vertical pipes has been discussed intensively based on available data sets of local flow parameters including extensive air–water data sets recently measured by the authors. In this study, an approximate radial phase distribution pattern map has been proposed based on available data sets, and radial profiles of local flow parameters such as void fraction, interfacial area concentration, interfacial velocity, and bubble Sauter mean diameter have been discussed in detail. The one-dimensional drift-flux model for a downward two-phase flow and the correlation of the interfacial area concentration have been compared with the downward flow data. The correlations applicable to the predictions of one-dimensional void fraction and interfacial area concentration for a downward bubbly flow have been recommended by the comparison.

One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes

In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the kinematic constitutive equation for the drift velocity has been studied for various two-phase flow regimes. The constitutive equations that specify the relative motion between phases in the drift-flux model has been derived by taking into account the interfacial geometry, the body-force field, the shear stresses, the interfacial momentum transfer and the wall friction, since these macroscopic effects govern the relative velocity between phases. A comparison of the models with existing experimental data shows a satisfactory agreement.

Minimum superficial gas velocity for onset of foaming

This paper is concerned with semi-batch foams generated by injecting gas bubbles in a vertical column containing a liquid phase at rest. Its aim is to better understand the physical mechanisms responsible for foam formation at the liquid free surface and to predict the superficial gas velocity for onset of foaming. The model for predicting the onset of foaming is derived from the one-dimensional drift-flux model for gravity driven flow in the absence of wall shear. The analysis is based on experimental data reported in the literature and covers a wide range of physico-chemical properties, bubble sizes and shapes, and flow regimes. It identifies the inhibition of coalescence between rising bubbles and bubbles at rest at the free surface as a key mechanism responsible for the onset of foaming. A semi-empirical correlation for high viscosity fluids has been developed and good agreement with experimental data is found.