Buoyantly-driven two-phase countercurrent flow in liquid discharge from a vessel with an unvented gas space

This paper details experiments and analyses regarding the phenomenon of liquid discharge into a gaseous atmosphere from the bottom of a vessel with an unvented, upper gas space. The primary goal is the development of a simple model that predicts the rate of liquid discharge under the prevailing unvented condition. A literature survey of previous work on this phenomenon yielded only simple experiments and analyses that were limited in scope. Experiments were subsequently undertaken with an air-water system, using a larger volume and a wide range of drain line diameters. In addition to flowrate data, visual information was acquired regarding the physical mechanism possibly governing the prevalent flow regimes. The governing physical mechanism is identified as the stability of a gas-liquid interface, perturbed by buoyancy, at the drain line entrance. G.I. Taylor's fundamental analysis of interfacial stability lead to the determination of criteria for flow regime transition among the three prevalent flow regimes, corresponding to so-called small, medium, and large diameters. Also, analysis of the growth of interfacial instabilities lead to the application of flooding models for drainage rates within each regime. The models for moderate and large diameters were then compared against data, which confirmed their success in predicting discharge rates under the unvented condition.The motivation for this effort, besides the basic scientific significance of studying such a fundamental phenomenon, was its numerous applications, one of which is commercial nuclear reactor systems. Specifically, the phenomenon prevails in liquid coolant discharge from a PWR pressurizer, with an unvented steam volume, into a steam atmosphere existing in the adjoining hot coolant leg. Such a phenomenon could occur as part of a transient, or severe accident, scenario, entailing saturated conditions and steam production in the normally subcooled primary heat transport loop. The developed model was implemented in the Modular Accident Analysis Program (MAAP), a computer code designed to predict reactor system behavior in response to postulated off-normal conditions, including severe accident scenarios.     

Effect of steam condensation on countercurrent flow limiting in nearly horizontal two-phase flow

An analytical model that includes the steam condensation effect has been derived and a parametric study has been performed. In addition, a series of experiments were performed and a total of 34 experimental data for the onset of countercurrent flow limiting (CCFL) in nearly horizontal countercurrent two-phase flow have been obtained for various flow rates of water. Comparisons of the present CCFL data with slug formation models show that the agreement between the present as well as the existing model and the data is about the same. However, the deviation between Taitel and Dukler’s model predictions and the data is the largest when j_f<0.04 m s⁻¹. A parametric study of the effect of condensation using the present model shows that, when all local conditions are similar, the model predicted local gas velocities that cause the onset of flooding are slightly lower when condensation occurred. Based on the visual observation and the evaluation of the present work, it has been concluded that the criterion derived for the onset of slug flow can be directly used to predict the onset of inner flooding in nearly horizontal two-phase flow within the experimental ranges of the present work.     

Analytical evaluation of two-phase natural circulation flow characteristics under external reactor vessel cooling

This work proposes an analytical method of evaluating the effects of design and operating parameters on the low-pressure two-phase natural circulation flow through the annular shaped gap at the reactor vessel exterior surface heated by corium (molten core) relocated to the reactor vessel lower plenum after loss of coolant accidents. A natural circulation flow velocity equation derived from steady-state mass, momentum, and energy conservation equations for homogeneous two-phase flow is numerically solved for the core melting conditions of the APR1400 reactor. The solution is compared with existing experiments which measured natural circulation flow through the annular gap slice model. Two kinds of parameters are considered for this analytical method. One is the thermal–hydraulic conditions such as thermal power of corium, pressure and inlet subcooling. The others are those for the thermal insulation system design for the purpose of providing natural circulation flow path outside the reactor vessel: inlet flow area, annular gap clearance and system resistance. A computer program NCIRC is developed for the numerical solution of the implicit flow velocity equation.     

Multidimensional two-phase flow regime distribution in a PWR downcomer during an LBLOCA refill phase

The multidimensional countercurrent two-phase flow regimes that occur in a pressurized-water reactor (PWR) vessel downcomer during the refill phase of a large-break loss-of-coolant accident are studied using a transparent 1/10 scale model of a PWR vessel. The various flow regimes and their distribution in the downcomer have been identified and mapped for a range of air-water flooding experiments. The two-phase flow patterns that are identified in the downcomer included various types of film flows, droplet flows, countercurrent churn flows and cocurrent flows depending on the flooding condition. Through observation of the two-phase flow dynamics it was deduced that the physical mechanisms associated with the flooding processes could be separated into a liquid entrainment process and a film flow reversal process. In addition to the above exercise, the effect of non-uniform injection of water into the downcomer via different combinations of cold leg was studied similarly by determining flooding curves and flow pattern maps. It was found that differences in the flooding characteristic were noticeable for various water inlet configurations when compared with the uniform injection case. The differences could be explained qualitatively in terms of the flooding mechanisms identified previously by examining the flow patterns in the downcomer for the non-uniform injection tests.     

Influences of physical properties of two-phase mixture on voidfraction in an annular vessel

To keep the void fraction of two-phase hydrogen in the moderator cell of the cold neutron source (CNS) of China Advanced Research Reactor (CARR) to a specified range, an annular vessel with the same size as the actual moderator cell was used as test section. Deionized water and alcohol, sucrose, and sodium chloride solutions with different concentrations were used as working fluid to find out influences of physical properties, such as density, viscosity and surface tension, of the two-phase mixture on void fraction. The tests proved that the ratio of surface tension to density of liquid phase has great influence on void fraction: the larger the ratio, the smaller the void fraction. Since the ratio of surface tension to density of Freon 113 is lower than that of liquid hydrogen, Freon 113 can be used as a working fluid to study the void fraction in the two-phase hydrogen thermosiphon loop in the CNS of CARR and the results will be conservative.     

Review of two-phase flow instability

Boiling flow in a water-cooled reactor, an evaporator, or an electronic cooling system is susceptible to thermal-hydrodynamic instabilities, which may cause flow oscillations of constant amplitude or diverging amplitude. These oscillations could induce boiling crisis, disturb control systems, or cause mechanical damage. This paper identifies the causes and mechanisms of these instabilities. Based on their mechanisms, various types of instabilities are classified and tabulated. The parametric effects on flow instability, observed experimentally, are systematically presented. Various analytical techniques for predicting the instability threshold are reviewed in terms of their applicability and accuracy.     

Experimental investigation of local two-phase flow parameters of a subcooled boiling flow in an annulus

As a series of subcooling boiling flow tests, local two-phase flow parameters were obtained at SUBO (subcooled boiling) test facility under steam–water flow conditions. The test section is a vertical annulus of which the axial length is 4.165 m with a heater rod at the center of a channel. The inner and outer diameters of the test section and the heater rod are 35.5 mm and 9.98 mm, respectively. The test was performed by a two-stage approach. Stage-I for the measurement of local bubble parameters has been already done (Yun et al., 2009). The present work focused on the stage-II test for the measurement of local liquid parameters such as a local liquid velocity and a liquid temperature for a given flow condition of stage-I. A total of six test cases were chosen by following the test matrix of stage-I. The flow conditions are in the range of the heat flux of 370–563 kW/m², mass flux of 1110–2100 kg/(m² s) and inlet subcooling of 19–31 °C at pressure condition of 0.15–0.2 MPa. From the test, local liquid parameters were measured at 6 elevations along the test section and 11 radial locations of each elevation in addition to the previously obtained local void fraction, interfacial area concentration, Sauter mean diameter and bubble velocity. The present subcooled boiling (SUBO) data completes a data set for use as a benchmark, validation and model development of the Computational Fluid Dynamics (CFD) codes or existing safety analysis codes.     

Flooding and flow reversal of two-phase annular flow

The flooding and flow reversal conditions of two-phase annular flow are mathematically defined in terms of a characteristic function representing a force balance. Sufficiently below the flooding point in counter-current flow, the interface is smooth and the characteristic equation reduces to the Nusselt relationship. Just below the flooding point and above the flow reversal point in cocurrent flow, the interface is “wavy”, so that the interfacial shear effect plays an important role. The theoretical analysis is compared with experimental results by others. It is suggested that the various length effects which have been experimentally observed may be accounted for by the spatial variation of the droplet entrainment.     

Linear analysis of flow instabilities in an open two-phase natural circulation loop

This paper describes the instability maps for the excursive and the density wave instabilities which may occur in an open two-phase natural circulation loop. Criteria for the excursive and the density wave instability were obtained from the steady loopwise momentum equation and the characteristic equation, respectively. A simple, one-dimensional two-phase homogeneous equilibrium flow was assumed. Heat flux, inlet subcooling, inlet- and exit-line restrictions, condenser liquid level, loop height and the heater section length were taken as parameters. The results were summarized on the instability map in the plane of N_pch(Fr)^1/2 vs. N_sub. The stable region appears at the lower left part of the map, bounded by two boundaries; the excursive instability region appears at the upper right part of the map. From the map, it can be readily confirmed that the dynamic stability criterion automatically satisfies the excursive stability criterion. Effects of parameters on the stability of the system were also discussed in this paper. The upper boundary of the stable region was compared with the experimental results reported previously.     

Experimental observations on flow characteristics in an open two-phase natural circulation loop

The flow behavior in an open two-phase natural circulation loop was studied experimentally using Freon-113. The heat flux, inlet- and exit-restrictions, liquid charging level and inlet subcooling were taken as parameters. As a result, three basic circulation modes were observed with variation of the heat flux: periodic circulation (A), continuous circulation, and periodic circulation (B). Of these modes, only the continuous circulation mode was stable and the maximum circulation rate appeared with this mode. An increase in the inlet-restriction and/or decrease in the exit-restriction broadened the range of the continuous circulation mode and stabilized the system. When the liquid charging level was lowered or the inlet subcooling was decreased, the continuous circulation mode started at a lower heat flux and the system became stable. The results are summarized on instability maps in the plane of heat flux vs. inlet subcooling.     

Satisfying flow criteria in the reactor vessel of an atomic power plant

Special Design Office for Machinery, Institute of Machine Science. Translated from Atomnaya Énergiya, Vol. 71, No. 3, pp. 214–220, September, 1991.     

Study of incident water hammer in an engineering loop under two-phase flow experiment

Water hammer can occur in case of an inflow of sub-cooled water into pipes or other parts of the equipment filled with steam or steam-water mixture. The shock loading due to dynamic pressure during water hammer induces high stresses in the walls of piping especially in the bends. A study was carried out to analyze real life incident of water hammer wherein an attempt was made to recreate water hammer involving steam-water interaction in an instrumented engineering loop to capture pressure, temperature, flow rate and fluid levels in the loop. The arrival time of multiple shocks and the time lag between them is examined in the paper with the support of energy balance equation for variable flow processes.     

Identification of flow patterns of two-phase flow by mathematical modelling

In this paper a steady state mathematical model is proposed to identify two-phase flow patterns. Model calculation results are compared with recorded flow pattern maps and data with satisfactory results. The method can be extended to wider parameter ranges and various duct contours as well as unsteady or transient conditions.     

A study of critical two-phase flow models

The existing computer codes use different boundary conditions in the calculation of critical two-phase flow. In the present study these boundary conditions are compared. It is shown that the boundary condition should be determined from the hydraulic model used in the computer code. The use of a correlation, which is not based on the hydraulic model used, leads often to bad results. Usually a good agreement with data is obtained in the calculation as far as the critical mass flux is concerned, but the agreement is not so good in the pressure profiles. The reason is suggested to be mainly in inadequate modeling of non-equilibrium effects.     

Characteristics of two-phase one-component flow with slip

All loss-of-coolant-accident analysis codes solve the one-dimensional hydraulic conservation equations for a two-phase compressible fluid. Some codes allow slip between the phases, this slip being specified by a slip model. In this paper the characteristics of these conservation equations with well-known slip models (Jones, Moody, Fauske, Smith and CISE) are evaluated as a function of pressure, quality and mass velocity. Regions in which two of the characteristics are complex are shown on contour maps. The significance of these regions is discussed.     

Effect of flow-induced vibration on local flow parameters of two-phase flow

A preliminary study was conducted experimentally in order to investigate the effect of flow-induced vibration on flow structure in two-phase flow. Two kinds of experiments were performed, namely ‘reference’ (no vibration) and ‘vibration’ experiments. In the reference experiment, an experimental loop was fixed tightly by three structural supports, whereas the supports were loosen a little in the vibration experiment. In the vibration experiment vibration was induced by flowing two-phase mixture in the loop. For relatively low superficial liquid velocity, flow-induced vibration promoted the bubble coalescence but liquid turbulence energy enhanced by the vibration might not be enough to break up the bubble. This leaded to the marked increase of Sauter mean diameter, and the marked decrease of interfacial area concentration. Accordingly, flow-induced vibration changed the void fraction profile from ‘wall peak’ to ‘core peak’ or ‘transition’, which increased distribution parameter in the drift-flux model. For high superficial liquid velocity, shear-induced liquid turbulence generated by two-phase flow itself might be dominant for liquid turbulence enhanced by flow-induced vibration. Therefore, the effect of flow-induced vibration on local flow parameters was not marked as compared with that for low superficial liquid velocity. Since it is anticipated that flow structure change due to flow-induced vibration would affect the interfacial area concentration, namely interfacial transfer term, further study may be needed under the condition of controlled flow-induced vibration.