Drift-flux Model Research Articles

Void fraction in a co-current two-phase flow through a prototypical PWR spent fuel assembly

The Fukushima accident has led in the last decade to numerous studies on the Spent Fuel Pools (SFP) accident phenomenology. In this context, the IRSN has launched an experimental project named DENOPI with the aim to study the behavior of spent fuel pools under loss of cooling and loss of coolant conditions. Within this project, the MEDEA facility is intended to study the thermal–hydraulics of a fully covered or uncovered spent fuel bundle. It consists in a hydraulic loop connected to an experimental test section in which a simulated one meter high PWR spent fuel bundle is located. The MEDEA-overflow experiments, presented in this study, consist in an adiabatic air/water flows in a fully covered unheated bundle. The pressure is measured all along the fuel bundle using several pressure transducers and the void fraction evolution is estimated and analyzed. Two different flow regimes are put in evidence in the MEDEA-overflow test series. Indeed, at low gas superficial velocities, a bubbly flow set up within the bundle whereas a transition to slug flow was obtained at larger ones. Finally, the results of several drift flux models are analyzed and compared to the experimental measurements.

Comparative evaluation of homogenous and drift-flux models for a three-phase downward flow in a pipe

The paper presents the comparative evaluation of the homogenous and the drift-flux flow modelling techniques employed in a three-phase downward flow in a vertical pipe. The study's objective is to analyse and compare the pressure drop of an experimental procedure of three-phase flow in a downward vertical pipe based on the two modelling techniques. The considered fluids include CO2 gas and the homogenous water and oil phases. The results show that the CO2 gas and the homogenous water and oil phases' velocities were obtained between 0.452 and 32.868 m/s and 0.008889 and 13.0734 m/s at 20, 50, 70 and 90% water cuts (WCs), respectively. On the other hand, the pressure drop (PD) ranged between 336.75≤PD≤4570.431 N/m3 and 27.741≤PD≤−2176.769 N/m3 for the homogenous and drift-flux models. A comparative evaluation between the two models established an excellent agreement with over-prediction. Additionally, at all WCs, the total PD shows an over-prediction of 8.685 % for the homogenous model and an under-prediction of 12.91% for the drift-flux. Hence, the homogenous modelling technique gave a higher efficiency and was recommended for the determination of the total pressure drop. Conversely, the drift-flux model was established to precisely determine the effect of single-phase flow properties on the total pressure drop of the flow process. The findings further provided a comprehensive understanding of introducing CO2 gas in a three-phase downward flow process to meet the demands of emerging technologies.

Simulation of Airborne Transport with a Simplified Drift-Flux Model

AbstractThe use of treated wastewater for irrigation is associated with the dispersion of fine droplets containing possibly pathogens. Their inhalation could expose workers and people in the surrou...

The WAF scheme for the isentropic drift-flux model of compressible two-phase flows

This paper focuses on the extension of the Weighted Average Flux (WAF) scheme for the numerical simulation of two-phase gas–liquid flow by imposing velocity equilibrium and without mechanical equilibrium of the transient drift-flux model. The model becomes a hyperbolic system of conservation laws with realistic closure relations where both phases are strongly coupled during their motion. Exploiting this, the drift-flux model discretization, simulation and investigation becomes very fast, simple and robust. The efficiency of the WAF scheme as being a second order in space and time without data reconstruction have been demonstrated in the published literature for compressible single-phase flows. However, the scheme is rarely applied to compressible two-phase flows. Based on a recent and complete exact Riemann solver for the drift-flux model, the model is numerically solved by the WAF scheme. The numerical algorithm accuracy and ability are validated through different published test cases. It is shown that the proposed scheme can be effectively employed to simulate two-phase flows involving discontinuities such as shocks and interfaces. The proposed WAF scheme is also compared with other numerical methods. Simulation results show appropriate agreement of WAF scheme even with the exact solutions. Comparisons of the presented simulations demonstrate that the behaviour of WAF scheme is encouraging, more accurate and fast than other numerical methods.

Flow regime and void fraction predictions in vertical rod bundle flow channels

This paper has studied the flow regimes and their transitions in upward gas-liquid two-phase flows in vertical rod bundle flow channels. The past experimental observations on the flow regimes have been extensively reviewed and analyzed. Various flow regimes with the observer-dependent names are re-classified into 5 flow regimes, namely, bubbly, finely dispersed bubbly, cap-bubbly, churn and annular flows according to their different flow characteristics in the vertical rod bundle flow channels. In view of the problems in the available flow regime transition criteria and the drift-flux correlations, this paper has proposed the mechanisms for the bubbly to cap-bubbly flow transition, the cap-bubbly to churn flow transition, the transition to annular flow and the transition to the finely dispersed bubbly flow and developed the corresponding flow regime transition criteria to predict the five flow regimes based on these mechanisms. This paper has further improved Han et al. correlations for the drift-flux parameters of the distribution parameter and the drift velocity to predict the void fractions in the 5 flow regimes, together the newly-developed transition criteria, in the vertical rod bundle flow channels. The newly-developed flow regime transition criteria and the improved Han et al. correlation for the drift-flux parameters of the distribution parameter and the drift velocity have been examined with the experimental data. The examination has concluded that the newly-developed flow regime transition criteria can correctly predict 82.9% of the 451 observed flow regime data in the vertical rod bundle flow channels and the drift-flux model using the improved Han et al. correlation and the newly-developed flow regime transition criteria can give satisfactory prediction for the 959 experimental data of the void fraction with the mean relative error of 0.0766.

Modeling of boiling flow in a channel under static along rolling and heaving motions

In this work, the analysis of thermal–hydraulic boiling flow in a vertical channel under static along rolling and heaving motions is investigated by using the drift-flux model. A code called DAFNO, based on the staggered finite volume technique to discretize governing equations in the drift-flux model is developed; Newton method is implemented to solve a non-linear system of equations and to prevent non-physical velocity and pressure results, fully implicit scheme is enforced for the temporal and spatial step of the equations. Various test problems are chosen to evaluate the performance of DAFNO; four experimental flow boiling channel data under static conditions are compared with DAFNO numerical results which show a very good agreement. Furthermore, void fraction, critical heat flux, and the drift velocity of vapor phase, under various rolling and heaving conditions are examined. It is observed that flow fluctuation modeling results are consistent with other complicated methods.

Derivation of a macroscopic mixture model for two-phase turbulent flows

This article addresses the issue of reduced models to describe turbulent two-phase flows in industrial applications. A spatially-averaged mixture or drift-flux model is derived theoretically from the local instantaneous Navier-Stokes description. Reynolds-averaging and space-averaging are applied successively. Between these two steps, a model reduction is achieved to account for the non-equilibrium between phases via algebraic relations. Applications of this work are not limited to porous media but also include macroscopic descriptions to model high-shear regions developing near the walls for internal flows. Thermal effects, heat transfer at the wall and phase-change are also considered and briefly discussed. The final model describes the evolution of mixture variables, including effects of both sub-filter spatial variations, turbulence, and local non-equilibrium in velocity, pressure and enthalpy. This analysis provides bridges between different approaches to model two-phase flows (local instantaneous description, two-fluid model, local drift-flux model and spatially-averaged drift-flux model). It clarifies the content of each model involved by defining them in terms of local instantaneous quantities. Turbulent fluctuations and phase intermittency are crucial mechanisms. Important effects to model also include void fraction dispersion and turbulent diffusion; then, it is necessary to model the relative velocity, including the drift velocity orthogonal to gravity induced by the complex interactions between turbulent velocity fluctuations and the interfacial momentum transfer.The final macroscopic (spatially-averaged) mixture formulation is open, in the sense that expressions to model the various terms representing the physics of the small scales are not provided; instead, the physical sense and the origin of these models are discussed. The paper is meant as a basis on which analyses on local imbalance assumptions or relative velocity closures can be assessed. CFD simulations can provide information to complement experiments in technically challenging physical conditions or on processes essential to the models yet difficult to access experimentally (such as interfacial transfers for instance). Different kinds of two-fluid models can be tested to analyse their consequences on the macroscopic spatially-averaged model. In addition, a new path to calibrate closure laws or propose new models is opened based on finer-scale descriptions. Guidelines to use fine simulations along with the open expressions to derive closure relations either for the local drift-flux or for the spatially-averaged models are presented. They concern the modelling of the local relative velocity, the spatial average of the diffusion of void fraction and of the pressure drop.

Development of preconditioners for numerical simulation of two-phase flow using Krylov subspace methods

In general, Newton-Krylov methods alone are not effective for solving non-symmetric matrices arising from the simulation of one-dimensional subcooled flow boiling inside a vertical tube with upward flow using the Drift-Flux Model (DFM); and, appropriate preconditioning is required. Because the key to the success of Newton-Krylov methods is the application of efficient and robust preconditioners, it is necessary to study the performance of the various Newton-Krylov methods preconditioned with different preconditioners. Therefore, the performance of three different preconditioners combined with four different Newton-Krylov methods, along with their implementation process, has been investigated. The results show that the preconditioning technique effectively reduces the number of iterations and the CPU time. Also, it is found that among the proposed preconditioners, the semi-implicit physics-based preconditioning (SI-PBP) has the best performance in terms of reducing the number of iterations and CPU time. Therefore, it can be used for simulation of other engineering problems.

Holdup Measurements of Aqueous Foam Flows and Flow Regime Characterization through Image Processing

Summary One of the most critical issues in the oil and gas industry is the dewatering of the pipelines used for natural gas transportation, and foam injection seems to be a prominent solution. This work has two goals: The main one concerns the development of an optical tool to measure the liquid holdup in foamy flows and perform the flow regime characterization, whereas the secondary goal is to quantify the effectiveness of surfactant injection in reducing the liquid loading. In this paper, we present the results of an experimental campaign aimed at the characterization of gas-liquid-foam flows in a horizontal pipe. Initially, liquid loading measurements for gas and liquid superficial velocities, ranging from 0.41 to 2.30 m/s and from 0.03 to 0.06 m/s, respectively, were performed by means of a specifically developed optical method. For each liquid superficial velocity, the minimum liquid holdup was found to lie in the proximity of the boundary between plug and stratified flow regime, with a superficial gas velocity between 0.44 and 0.90 m/s. Hence, the plug flow region corresponds to the best operating condition to perform the pipeline dewatering procedure. Moreover, the drift-flux model usually adopted for ordinary two-phase gas-liquid flows seems to fit well with the measured values of void fraction.

Thermal prediction of transient two-phase flow in cryogenic transportation based on drift-flux model

Accurate prediction as well as effective thermal management of transient cryogenic transportation is of great importance to the safe and high-efficiency utilization of cryogenic fluids. To predict the unstable cryogenic transportation process, a one-dimensional model coupling two-phase flow with transient heat conduction of solid tube is developed in this study. The transient two-phase flow is described by a drift-flux model, and a finite volume method (FVM) with staggered grid mesh is adopted for numerical calculation. Verified by a lot of experimental data, the proposed model shows its applicability in a wide range of conditions. Then, thermal performance and pressure surge phenomenon are investigated in detail. The intermittent chill-down strategy is recommended to take full use of the sensible energy of fluid from the perspective of energy saving. Besides, the pressure surge is verified as a special physical phenomenon in cryogenic fluids transportation process, which brings higher challenges to the storage, handling and transport of cryogenic fuels.

Void Fraction Prediction Method in Gas–Liquid Flow through Channel Packed with Open-Cell Metal Foams

This paper reports the results of a study concerned with air–water and air–oil two-phase flow in channels packed with open-cell metal foams. The research was conducted in horizontal channel with an internal diameter of 0.02 m and length of 2.61 m. The analysis applied three metal foams with pore density 20, 30, and 40 PPI and porosity typical for industrial applications, changing in the range of 92–94%. The experimental data were used to develop a new method for predicting void fraction in two-phase gas–liquid flow in channels packed with metal foams. A new gas void fraction calculating method based on drift-flux model was developed. This model gives a correct representation of changes in the gas void fraction value and good prediction accuracy. The average relative error in calculating the air void fraction in two-phase flow is less than 13%, and 86% of experimental points is characterized by an error less than 20%.

Experimental and numerical investigation of gas-liquid metal two-phase flow pumping

Adapting an efficient method for pumping gas-liquid metal two-phase flow can make liquid metal magnetohydrodynamics (LMMHD) power generation systems economically feasible. An experimental facility was developed using a dual injection gas-lift pump to provide the circulation needed for the liquid metal in the LMMHD system. Also, a numerical simulation was performed in order to understand the behaviour of the two-phase flow through the gas-lift pump and be able to optimize the pump design for the best operational condition of the LMMHD system. In addition, the data were compared to a 1-D drift flux model that predicted the performance of the pump within the loop. The numerical results were found to be in an agreement with the experiments within ±25% which is considered adequate for optimization and design purposes of a two-phase flow system. The dual injection design was evaluated, and the axial injection mode was found to be more efficient in providing the required pumping than radial mode. Moreover, the flow visualization of the two-phase flow patterns seen in the pump riser was captured both experimentally and numerically indicating a swirl-like motion that can potentially be used to enhance heat transfer in the actual operational setting. Also, the optimum condition for pumping was found to occur at a slug-like flow structure in the riser.

Air-water two-phase flow regime and transition criteria in vertical upward narrow rectangular channels

Upward two-phase flow in two different vertical narrow gaps was investigated experimentally. For better understanding the characteristics of air-water flow in rectangular channels, the visual images were captured through high-speed cameras and the void fraction results were obtained through three impedance void meters. The flow pattern was identified through ReliefF-FCM clustering algorithm to avoid the subjectivity of human observation. The flow regime maps were plotted in two different forms, superficial velocities and void fraction and compared with the previous model in the open literature. Through the analysis of the experimental results, the air-water flow in narrow rectangular channels is characterized by the limitation of bubble distribution, coalescence and movement. The probability of bubble coalescence in narrow rectangular channels is increased compared with those in conventional channels due to the restriction of the narrower side walls. New transition criteria was obtained according to the drift-flux model and the force balance analysis which shows satisfactory agreements with existing experimental data for gaps of 1–6 mm.

Accuracy and efficient solution of helical coiled once-through steam generator model using JFNK method

The Helical coiled tube Once-Through Steam Generator (H-OTSG) is key equipment in the High-Temperature Gas-cooled Reactor (HTGR) system, where the fission energy is transferred from the helium side to the water side, together with the complicated heat transfer and phase change phenomenon. In detail, the water is heated to the water-steam two-phase flow by the hot helium and further to the superheated steam. As a result, the H-OTSG is a multi-phases, multi-physics, and multi-domain highly nonlinear system due to the complex constitutive equations in the two-phase flow model. The accuracy and efficient solution of this highly nonlinear system is a key point for the successful simulation of the H-OTSG. In this work, the advanced Jacobian-Free Newton Krylov (JFNK) method is used instead of the traditional semi-implicit iteration method to pursue high computational performance. An efficient physical-based preconditioner is proposed, which is derived from the original semi-implicit based method. Moreover, the numerical technologies of the phase generation/disappearance and the global convergence algorithms of JFNK method are implemented and discussed. The two-phase drift-flux model is used to describe the two-phase flow in the waterside and the second-order accuracy temporal and spatial numerical scheme is employed to discrete the conservation equations. A new H-OTSG simulation code based on JFNK method is developed in this work and applied to analyze the steady and transient state behavior of the H-OTSG in the 10 MW high-temperature gas-cooled reactor (HTR-10). The simulation results show that the accuracy of the newly developed H-OTSG simulation code agrees well with the design data under different operating conditions. Furthermore, the computational performance of the JFNK method with the physical-based preconditioner is the best compared with the traditional Picard iteration method, Newton–Krylov method and JFNK method without preconditioner.

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.

Liquid holdup optical measurements for horizontal stratified flows with an opaque fluid layer

This study presents a method to measure the void fraction in presence of a stratified three-phase flow with an opaque fluid like foam. The commonly used resistive probes, which were successfully applied for air-water flows, fail in detecting the liquid/foam interface due to the variable conductivity of foam. To overcome this problem, a new optical method was developed. A probe consisting of a steel rod covered in red vinyl plastic with a black measuring scale having 1 mm resolution was introduced radially into the flow; the foam layer, being opaque, can be easily identified against the measuring scale in a side view of the flow. The behavior over time of the liquid-foam interface was thus recorded through a video camera. A couple of small LED lamps provided the lighting to record the scene. The videos were then processed to count the measuring scale marks below the foam layer in order to get the instantaneous values of liquid layer depth. Measurements were performed at different pipe sections. The results were compared to those obtained for air-water flows at the same superficial velocities, with the latter ranging from 0.76 to 2.30 m/s for air and 0.03 to 0.06 m/s for water respectively. A liquid loading reduction up to 41 % was detected at the lowest gas superficial velocity, i.e. 1 m/s, while when the gas superficial velocity increases the difference in the liquid holdup lowers and becomes negligible at 2.30 m/s, regardless the value of the liquid superficial velocity. Since no specific model exists for foamy flows, as a first attempt the Zuber and Findlay drift-flux model was finally adopted to correlate the data.

TOWARD A NONINVASIVE MEASUREMENT METHOD OF CO2 ARTERIAL PRESSURE

Until now, the measurement of carbon dioxide blood pressure is done ex vivo, using an invasive process. This paper describes a first step toward a novel noninvasive process for in vivo measurement of this pressure. As first approximation, the blood solution is modeled as a simple aqueous solution of carbon dioxide in a cylindrical rigid canalization. The drift flux model and the Young–Laplace equation are employed to describe the fluid behavior. The numerical model relates the carbon dioxide pressure through the mixture pressure and velocity. The spatial distributions of these parameters are implemented to create linear mathematical relations between the mean mixture pressure and the radial velocity variation. As long as we are interested in a noninvasive measuring of the carbon dioxide pressure, a response model is proposed to describe the ultrasound signal backscattered by the considered solution. The linear relations are applied to deduce the carbon dioxide pressure through the measured radial velocity difference, using two computing methods of ultrasound signal. A comparative study is made between them showing the more appropriate process to compute the carbon dioxide pressure.

Flow Characteristics of Air-Water Two-Phase Flows in a Serpentine Tube

Experiments on air-water two-phase flows in a serpentine tube consisting of vertical U-bends and circular straight pipes were carried out to discuss the flow characteristics based on the high-speed video images of the flows at various gas and liquid superficial velocities. The pipe diameter, D, and the bend radius of curvature, R, were 20 mm, i.e. the bend ratio, R/D, was unity, and the length of the straight pipe was 1500 mm. The void fraction in each section was measured by using a quick-closing valve method. As a result, the following conclusions were obtained: (1) the top and bottom U-bends cause coalescence of large bubbles and liquid slug formation, respectively, which results in enhancement of flow pattern transition between the slug and annular flows, (2) the void fraction in the downward flow is larger than that in the upward flow due to acceleration of the liquid phase and the buoyancy acting on bubbles in the downward flow, and (3) void correlations based on the drift-flux model for fully-developed flows are applicable to the void fractions in the straight pipe sections under the present experimental conditions.

Experimental investigation of two-phase flow evolution in a tight lattice bundle using wire-mesh sensor

Tight lattice fuel assemblies have significant advantages in power density and conversion ratios. However, the dynamic characteristics of two-phase flow in tight lattice bundles, which is very important to safety analysis, are still not clarified. This study presents an experimental investigation of two-phase flow evolution in a double sub-channels tight lattice bundle. The experimental channel was up-scaled (1:2.7) compared with the prototype fuel. Phase distributions at four different axial positions, z/Dh = 28.95, 57.90, 86.86, and 115.8, are measured with a high spatiotemporal resolution by a 16 × 32 wire-mesh sensor. The flow regime includes bubbly flow, cap-bubbly flow, and slug flow. In the bubbly flow, the large-scale pulsations across the gap of two sub-channels were observed, as same as the single-phase flow in a tight lattice bundle. The time-averaged void fraction shows a gap region peak in bubbly flow. In the cap-bubbly flow, the cap bubbles are confined to a single sub-channel due to the small gap. The cap bubbles are alternated arrangements in the two sub-channels and the large-scale pulsations across the gap are caused due to this special flow configuration. The time-averaged void fraction shows a core peak profile in a cap-bubbly flow. In the slug flow, the slug bubbles can across the small gap to span the two sub-channels and the time-averaged void fraction shows a core peak profile. Even though the time-averaged void fraction almost coincides at different axial positions, the phase interface structure shows a significantly different according to the virtual side view of void fraction. The accuracy of the drift-flux models has been evaluated with the experimental data. The Bestion's model underestimated the void fraction in the channel while the Chexal's model overestimated it. Clark's model gets the best prediction with an error of 10.1%.

Port-Hamiltonian formulation of two-phase flow models

Abstract Two-phase flows are frequently modelled and simulated using the Two-Fluid Model (TFM) and the Drift Flux Model (DFM). This paper proposes Stokes–Dirac structures with respect to which port-Hamiltonian representations for such two-phase flow models can be obtained. We introduce a non-quadratic candidate Hamiltonian function and present dissipative Hamiltonian representations for both models. We then use the structure of the corresponding formally skew-adjoint operator to derive a Stokes–Dirac structure for the two variants of multi-phase flow models. Moreover, we discuss the difficulties in deriving a port-Hamiltonian formulation of the DFM with general slip conditions, and argue why this model may not be energy-consistent.