Droplet entrainment correlation in vertical upward co-current annular two-phase flow

Upward annular two-phase flow in a vertical tube is characterized by the presence of liquid film on the tube wall and entrained droplet laden gas phase flowing through the tube core. Entrainment fraction in annular flow is defined as a fraction of the total liquid flow flowing in the form of droplets through the central gas core. Its prediction is important for the estimation of pressure drop and dryout in annular flow. In the following study, measurements of entrainment fraction have been obtained in vertical upward co-current air–water annular flow covering wide ranges of pressure and flow conditions. Comparison of the experimental data with the existing entrainment fraction prediction correlations revealed their inadequacies in simulating the trends observed under high flow and high pressure conditions. Furthermore, several correlations available in the literature are implicit and require iterative calculations.Analysis of the experimental data showed that the non-dimensional numbers, Weber number (We = ρ_gj_g²D/σ(Δρ/ρ_g)^1/4) and liquid phase Reynolds number (Re_f = ρ_fj_fD/μ_f), successfully collapse the data. In view of this, simple, explicit correlation was developed based on these non-dimensional numbers for the prediction of entrainment fraction. The new correlation successfully predicted the trends under the high flow and high pressure conditions observed in the current experimental data and the data available in open literature. However, in order to use the proposed correlation it is necessary to predict the maximum possible entrainment fraction (or limiting entrainment fraction). In the current analysis, an experimental data based correlation was used for this purpose. However, a better model or correlation is necessary for the maximum possible entrainment fraction. A theoretical discussion on the mechanism and modeling of the maximum possible entrainment fraction condition is presented.     

Natural convective flow between an array of vertical cylinders

The natural-convectioe flow of a viscous and heat-conducting fluid in systems of cylinders, arranged vertically in regular patterns, is studied. The aim of the study is to determine the conditions of stability of the fluid when heated from below and cooled from above. In particular, the influence of geometry and thermal properties of the system on the free stationary convection are studied. A new way of calculating the free convection threshold is proposed. The final results are analytical formulas for determining the critical Rayleigh numbers for the studied forms of flow and graphs, showing the dependency of these numbers on the geometrical parameters of arrays.     

Gas–liquid flow around an obstacle in a vertical pipe

This paper presents a novel technique to study the two-phase flow field around an asymmetric obstruction in a vertical pipe with a nominal diameter of DN200. Main feature of the experiments is the shifting of a half-moon shaped diaphragm causing the obstruction along the axis of the pipe. In this way, the 3D void field is scanned with a stationary wire-mesh sensor that supplies data with a spatial resolution of 3 mm over the cross-section and a measuring frequency of 2.5 kHz. Besides the measurement of time-averaged void fraction fields and bubble-size distributions, novel data evaluation methods were developed to extract estimated liquid velocity profiles as well as lateral components of bubble velocities from the wire-mesh sensor data. The combination of void fraction fields and velocity profiles offer the opportunity to analyse a two-phase flow in a geometry that owns a series of features characteristic for complex components of power and chemical plant equipment. Such characteristics are sharp edges with flow separation, recirculation areas, jet formation, stagnation points and curved stream-lines.

The tests were performed with an air–water flow at nearly ambient conditions and with a saturated steam–water mixture at 6.5 MPa. The superficial velocities of liquid and gas or, respectively, vapour were varied in a wide range.

The flow structure upstream and downstream of the obstacle is characterized in detail. Bubble size dependent effects of bubble accumulation and migration are discussed on basis of void-fraction profiles decomposed into bubble-size classes. A pronounced influence of the fluid parameters was found in the behaviour of bubbles at the boundary of the jet coming from the non-obstructed part of the cross-section. In case of an air–water flow, bubbles are restrained from entering the jet, a phenomenon which was not observed in high-pressure steam–water flow. A detailed uncertainty analyse of the velocity assessments finishes the presented paper. A blind pre-test calculation with CFX-10 based on the assumption of a mono-disperse bubbly flow has reproduced the overall void and velocity profiles. The results are used for the assessment of the influence of local accelerations on the liquid velocity measurement.     

Longitudinal laminar flow in asymmetrical finite bundles of rods

Theoretical analysis is presented on the asymmetrical effects, i.e. peripheral displacement of rods or unequal rod diameters, on longitudinal laminar flow in a finite bundle of rods. Solution is by the method of superposition. Numerical results are obtained for shear stress and velocity distributions when only one rod is displaced in a seven rod cluster of equal-diameter rods.     

Study on flow characteristics in gas-molten metal mixture pool

As part of basic research on the flow characteristics of a two-phase mixture pool under severe accident of fast breeder reactor (FBR), visualization and measurement of nitrogen gas-molten lead/bismuth two-phase flow in a rectangular pool were performed by using the neutron radiography technique. Measurements of drag coefficient of a single bubble and bubble shape regime showed that the relationship between the shape, size and the rising velocity of a single isolated nitrogen bubble in the molten lead/bismuth was not much different from that for an ordinary one. Appropriate correlation for drift velocity and drag coefficient between phases were recommended based on the drift flux correlation of measured pool void fraction. One- and two-dimensional analyses were performed by using a next generation computational code for safety analysis of severe accident of FBRs, SIMMER-III with various drag coefficient models. It was revealed that Kataoka–Ishii’s equation was suitable basically for estimation of drift velocity, namely, drag force between phases.     

Experimental research on flow instability in vertical narrow annuli

A narrow annular test section of 1.5mm gap and 1800mm length was designed and manufactured, with good tightness and insulation. Experiments were carried out to investigate characteristics of flow instability of forced-convection in vertical narrow annuli. Using distilled water as work fluid, the experiments were conducted at pressures of 1.0～3.0 MPa, mass flow rates of 3.0～25 kg/h, heating power of 3.0～ 6.5kW and inlet fluid temperature of 20 ℃, 40 ℃ or 60℃. It was found that flow instability occured with fixed inlet condition and heating power when mass flow rate was below a special value. Effects of inlet subcooling, system pressure and mass flow rate on the system behavior were studied and the instability region was given.     

Effect of cluster eccentricity on longitudinal laminar flow in finite bundles of rods

Cluster eccentricity effects on longitudinal flow in finite bundles are analyzed theoretically by the method of superposition. Two displacements were studied: (1) along the line joining the centers of one peripheral rod and the cluster, and (2) along the line between two peripheral rods passing through the cluster center. The differences between the friction factors were negligible. Friction factors were obtained for five-, seven- and nine-rod clusters with various eccentricities, and were found to decrease steadily with eccentricity, while flow area and hydraulic diameter remained unchanged.     

Air-water multidimensional impingement flow on vertical flat wall

The emergency core cooling (ECC) water is supplied from the direct vessel injection (DVI) system in the Advanced Power Reactor 1400 MWe (APR1400) during a postulated large-break loss-of-coolant accident (LBLOCA). The velocity of ECC water exceeds 10 m/s in the early high pressure phase of LBLOCA and then is decreased to 2-3 m/s in the late phase of reflood. During the injection the flow behavior exhibits a complex mode involving impingement, bypass, entrainment, sweepout and condensation in the reactor downcomer. There is currently no model to accurately simulate the local and complicated flow behavior in the APR1400 downcomer during a LBLOCA. This study is aimed at developing models for the water film flow and deformation, both of which are expected to sizably affect the other multidimensional flow characteristics in the downcomer. Experimental studies are conducted to benchmark the predictive model by furnishing the boundary conditions for the analysis resorting to the Accelerated Liquid Phase Hydrodynamics Apparatus (ALPHA) and the Kinetic Aerodynamic Physics Parallelepiped Apparatus (KAPPA). The Poisson equation and potential theory are applied to formulate the behavior of the water film and air flow. In both the experimental and numerical studies, the temperature-dependent thermodynamic properties and the reactor vessel curvature are neglected to render the problem at hand tractable. The model is found to reasonably describe the downward film flow behavior. The water film is developed in proportion to the initial injection velocity of the ECC water. The downward velocity of water film is increased with the heights of injection. Regarding the film deformation the calculated results tend to deviate from the experimental data as the injected air velocity is increased. The disagreement is attributed to limitations inherent in the two-dimensional treatment and point source approach.     

Mixed convective flow penetration in vertical channels

The primary purpose of the study is to investigate the factors relevant to the decay heat removal system in pool-type liquid metal reactors which are designed to remove decay heat in a passive way utilizing natural circulation. The reactor geometry is simulated by a vertical rod bundle channel connected to an upper plenum. Penetration of cold fluid from the upper plenum into the rod bundle channel is investigated experimentally and analytically with water as a working fluid. Three correlations to predict the onset of penetration, the penetration depth, and the ratio of penetrating to forced flowrate were developed. The correlations were found to agree well with experimental results for the range of Reynolds number in which experimental data were obtained.     

Transport processes in an inertial confinement fusion reactor

The quasi one-dimensional method previously developed for calculating a transient, compressible, viscous flow through a complex array of tubes or jets was extended to include heat and mass exchange between the fluid and the jets. The application was again the impulsive crossflow of a lithium plasma through a close-packed annular arrangement of liquid jets, a problem that arises in the deisgn of inertial confinement fusion reactors. It was found that the peak hoop stress in the first wall of the reactor may derive from the direct impact of the plasma, rather than from the subsequent impact of the jets or fragments thereof. Depending on conditions in the cavity, the peak wall stress was calculated to be up to 4 times less when heat and mass transfer were accounted for. The sensitivity of the design to key parameters was established.     

Heat transfer effects on flow past an impulsively started semi-infinite vertical plate with uniform heat flux

An implicit finite-difference technique is employed to derive a solution to the flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with uniform heat flux. Transient and steady-state velocity and temperature profiles, the local and average skin-friction and the Nusselt number are shown graphically. The velocity profiles at small values of time t are shown to agree with theoretical solution of the flow past an impulsively started infinite vertical plate with uniform heat flux. The effect of different parameters Pr (the Prandtl number) and Gr (the Grashof number) are studied. It is found that the number of time steps to reach steady-state depends strongly on Grashof number.     

Temperature distribution in mixed ThO2–UO2 fuel rods located in blanket of an inertial fusion energy breeder

Investigations of neutronic analysis and temperature distribution in fuel rods located in a blanket driven ICF (Inertial Confinement Fusion) have been performed for various mixed fuels and coolants under a first wall load of 5 MW/m². The fuel rods containing ThO₂ and UO₂ mixed by various mixing methods for achieving a flat fission power density are replaced in the blanket and cooled with different coolants; natural lithium, flibe, eutectic lithium and helium for the nuclear heat transfer. It is assumed that surface temperature of the fuel rod increases linearly from 500 °C (at top) to 700 °C (at bottom) during cooling fuel zone. Neutronic and temperature distribution calculations have been performed by MCNP4B Code and HEATING7, respectively. In the blanket fueled with pure UO₂ and cooled with helium, M (fusion energy multiplication ratio) increases to 3.9 due to uranium having higher fission cross-section than thorium. The high fission energy released in this blanket, therefore, causes proportionally increasing of temperature in the fuel rods to 823 °C. However, the M is 2.00 in the blanket fueled with pure ThO₂ and cooled with eutectic lithium because of more capture reaction than fission reaction. Maximum and minumum values of TBR (tritium breeding ratio) being one of main neutronic paremeters for a fusion reactor are 1.07 and 1.45 in the helium and the natural lithium coolant blanket, respectively. These consequences bring out that the investigated reactor can produce substantial electricity in situ during breeding fissile fuel and can be self-sufficient in the tritium required for the DT fusion driver in all cases of mixed fuels and coolant types. Quasi-constant fission power density profiles in FFB (fissile fuel breeding) zone are obtained by parabolically increasing mixture fraction of UO₂ in radial and axial directions for all coolant types. Such as, in the helium coolant blanket and the case of PMF (parabolically mixed fuel), Γ (peek-to-average fission power density ratio) of the blanket is reduced to 1.1, and the maximum temperatures of the fuel rods in radial direction of the FFB zone are also quasi-constant. At the same time, in the case of PMF, for all coolant types, the temperature profiles in the radial direction of the fuel rods rise proportionally with surface temperature from the top to the bottom of fuel rods in the axial direction. In other words, for each radial temperature profile in the axial direction, temperature differences between centerline and surface of the fuel rods are quasi-constant. According to the coolant types, these temperature diffences vary between 30 and 45 °C.     

Down flow of water-air mixtures in vertical columns

Published data and data obtained by the present authors on gas-liquid (water-air) down flows are examined. Down flows are investigated for the conditions of the cooling loop of the RBMK control-and-protection system and the system ejecting gas in the safety-and-control system channels with film cooling. A criterial analysis is performed of the main parameters characterizing down flows in regimes of companion motion of the phases and hovering of the gas phase.     

Two-phase slug flow in vertical and inclined tubes

Gas-liquid slug flow is investigated experimentally in vertical and inclined tubes.The non-invasive measuremnts of the gas-liquid slug flow are taken by using the EKTAPRO 1000 High Speed Motion Analyzer.The information on the velocity of the Talyor bubble,the size distribution of the dispersed bubbles in the liquid slugs and some characteristics of the liquid film around the Taylor bubble are obtained.The experimental results are in good agreement with the available data.     

Hydromagnetic free convection effects on the oscillatory flow of an electrically conducting rarefied gas past an infinite vertical porous plate

Unsteady two-dimensional free convection flow of an electrically conducting, viscous, incompressible rarefied gas, past an infinite vertical porous plate in the presence of a transverse magnetic field is studied. The freestream velocity oscillates in time about a constant mean, while the suction velocity, normal to the porous plate, is constant. The magnetic Reynolds number of the flow is not taken to be small enough, so that the induced magnetic field is not negligible. The plate temperature is constant and the difference between the temperature of the plate and the freestream is moderately large causing the free convection currents. The flow field is described by a nonlinear coupled system of equations subjected to the first-order velocity slip and temperature jump boundary conditions. With viscous dissipative heat and Joule heating taken into account, approximate solutions of the problem are obtained for the velocity, temperature and induced magnetic field, as well as, for the related to them quantities of the skin friction, rate of the heat transfer and electric current density.     

Heat transfer in turbulent longitudinal flow through unbaffled assemblies of fuel rods

A numerical analysis of heat transfer in turbulent longitudinal flow through assemblies of unbaffled fuel rods is presented. The solution applies to triangular or rectangular arrays of fuel rods with fully developed velocity and temperature profiles, for fluids with Prandtl number 1 and « 1. In the case of liquid metals, the thermal resistance of the cladding and bond are considered, but the turbulent heat transport component is neglected. For common liquids the circumferential turbulent heat transfer is considered. Results are compared in the range of dimensionless rod spacing of 1.0–1.6. Theoretical predictions and experimental results of other authors dealing with the problem show relatively good agreement.     

Growth of uranium rods in an aggressive gaseous medium

This article describes the growth (increase in length) of uranium specimens which takes place when heated specimens are exposed to air, nitrogen, and carbon dioxide. The dependence of this growth on temperature, pressure of the medium, the rod diameter, and on the degree of initial uranium surface oxidation was determined. Also the growth of copper wire specimens was detected. A possible mechanism of the growth of uranium rods is suggested.In conclusion, the authors extend their gratitude to P. A. Petrov for his guidance in the work.     

Study on intermittent flow behavior in a vertical channel under low-pressure condition

The intermittent flow behavior in a vertical annulus under a low-pressure condition was experimentally studied using a scaling experiment facility. The temperature and pressure variations in the channel had been obtained under the heat load ranging from 0 to 2.0 kW, initial subcooled water temperature ranging from 50 to 90 °C and length–diameter ratio ranging from 1.6 to 50. The effects of the heat load and length–diameter ratio of channel on the flow characteristics were investigated in detail. The experimental results showed that the steam bubbles erupted more frequently and regularly at a high heat load. The intermittent flow period decreased with increase of the heat load and aspect ratio. Based on the mechanism analysis, an empirical model considering the steam oscillation and the vapor–liquid interface rupture based on the experimental data was proposed. It was found that the accumulated steam basically increased linearly. The oscillation of the pressure and velocity decreased gradually with continuous steam accumulation. The Reynolds number of the liquid within the rising section was very small at the stagnation state since there was no forced circulation flow. Finally, a blockage was engendered in the pipeline with the steam accumulated.