Two-phase Discharge Research Articles

Experimental investigation of two-phase discharge from a stratified region through a small branch mounted on an inclined wall

Experimental data are presented for the mass flow rate and quality of two-phase discharge through a small branch of diameter d (=6.35 mm) attached normally to an inclined flat plane. The flat plane was situated in a large tank containing a stratified mixture of air and water under pressure (316 kPa) and at room temperature. The plane was inclined through various angles ( θ) in increments of 30°, from the outlet-branch orientation being vertically upward through the horizontal to vertically downward. The bulk of the data correspond to seven inclination angles and two test-section-to-separator pressure differences (Δ P) of 11.0 and 115.5 kPa, and for each combination of θ and Δ P, the mass flow rate and quality were measured at different values of the interface level ( h) between the onsets of gas and liquid entrainment. Four additional data sets were generated for other values of Δ P in order to confirm certain trends. Influences of these independent variables on the mass flow rate and quality are discussed and normalized plots are presented showing that the data can be collapsed for a wide range of conditions. Comparisons are made between the present data and previous correlations/models and new empirical correlations are formulated and shown to be capable of predicting the present data with good accuracy.

Validation of two models for discharge rate

A substantial body of discharge rate data has been developed over the past half century applicable for validation of single and two-phase discharge models. This paper applies a wide range of test cases and compares predictions with test data for two types of discharge model: (a) the energy balance model, and (b) the non-equilibrium model of Diener and Schmidt. The latter enhances the original homogeneous equilibrium model of Leung. This exercise reveals possible inconsistency between experimental datasets as much as it provides confirmation of the accuracy of the models, but both models are shown to provide adequate predictions within a factor of two and generally better.

Influence of Wall Inclination Angles on the Onset of Gas Entrainment During Single and Dual Discharges From a Reservoir

A theoretical analysis was carried out to predict the influences of wall inclination angles of large reservoirs on the onset of gas entrainment during single and dual discharges from a stratified two-phase region. The findings reveal that when the wall inclination angle differs from zero, along with low values of Froude number, two distinct flow regimes occur: the gas-entrainment and no gas-entrainment regimes. A new criterion has been developed to predict the critical Froude number at the transition from the gas-entrainment to the no-gas-entrainment regime. The critical Froude number is defined as a function of the wall inclination angle for a single discharge. For dual discharge, the critical Froude number is found to be dependent on the wall inclination angle, the separating distance between the centerlines of the two branches, as well as the Froude number of the second branch. Furthermore, four different flow regions are mapped, representing the flow regime, as well as the two-phase flow for each branch. These maps serve to predict the flow regions, mass flow rates, and quality during single and dual two-phase discharges. For the gas-entrainment regime, the predicted values of the critical height at the onset of gas entrainment are compared with the experimental data reported in literatures. Comparisons showed good concurrence between the measured and predicted results. Furthermore, the influence of the wall inclination angle on the flow regions, the predicted critical height, and the location of the gas entrainment are presented and discussed at different values of independent variables.

Two-phase flow through pressure safety valves. Experimental investigation and model prediction

Due to the lack of experimental data regarding two-phase flow through safety relief valves, a number of different calculation methods are presently available in the literature for their sizing. All these models mainly refer to the flow through an ideal nozzle, so that, in order to match the measured values, a discharge coefficient is to be introduced in the calculation, the coefficient thus depending on the model adopted. Furthermore, most of the available data are referred to a few operating conditions. As a result, none of the available models is presently considered sufficiently accurate to be used in a wide range of operating conditions. In the present paper, new data are produced on a steam/water flashing system through a real valve with different values of the main operating parameters (vapour quality, inlet pressure, mass flow rate, and backpressure). The measurements are compared with the predictions of a commonly used homogeneous equilibrium model (HEM), the so-called ω method, and show that the model markedly underestimates the mass flow rate in the whole range of conditions investigated. This unexpectedly implies the introduction of a two-phase discharge coefficient much higher than the vapour coefficient. Finally, a new correlation for the discharge coefficient as a function of the main operating parameters is proposed.

Enhancement of the plasma chemistry process in a three-phase discharge reactor

The influence of solid packing on the chemical process involved in the solid–liquid–gas three-phase discharge plasma reactor, initiated by a bipolar pulsed power source was studied with indigo carmine (indigo-5,5′-disulfonic acid, IDS) as the probe. Dynamic scanning of the UV–Vis absorption spectrum was used as the analysis method. Experimental results show that addition of solid packing into the water–air two-phase discharge plasma reactor enhances the chemical processes in the reactor. The dielectric properties of the packing materials determine the degree of enhancement. Water treatment performance of the reactor with dielectric spheres is much better than that with conducting materials for the same experimental conditions. In addition, dielectric glass beads have a stronger influence on the chemical enhancement process than ceramic spheres. Decolourization of IDS in the plasma reactor with dielectric packing is a pseudo-first-order reaction. The total organic carbon in the solution decreases during the treatment process.

A theory on the discharge coefficient for safety relief valve

Abstract Comparing the flow through an SRV to that through an orifice, a simple theory is proposed to relate the discharge coefficient in two-phase compressible flow to the value in liquid incompressible flow. This approach made use of the author’s omega method applicable for both flashing discharge and non-flashing discharge. The two-phase discharge coefficient is shown to be a smooth function of the omega parameter. For non-flashing two-phase discharge, the discharge coefficient is shown to lie between the liquid coefficient and the gas coefficient. For flashing two-phase discharge, the discharge coefficient is higher than the gas coefficient. Comparison with recently published SRV data seems to support the present recommendation.

Effect of depressurization on reactor vessel inventory in the absence of ECCS injection

A series of tests were performed to evaluate inventory depletion as a reactor vessel undergoes depressurization in the absence of any emergency core coolant system injection (ECCS). These tests were carried out in a scaled representation of a reactor vessel which was initially filled with saturated water up to the elevation of the hot legs. Depressurization valves installed on take-off lines from the hot legs were opened and level swell ensued in the reactor vessel initiating a two-phase blowdown. This was followed by subsequent single-phase discharge transient which in some cases led to core uncovery. A combined model encompassing the two-phase and single-phase discharge portions of the transient is proposed. The inventory-versus-pressure traces obtained from the model compare well with the experimental results. These traces are discussed as bounding trajectories for a large class of small break loss of coolant accident (LOCA) transients which otherwise must be considered individually.

Two-Phase Flow From a Stratified Region Through a Small Side Branch

Experimental data are presented for the mass flow rate and quality of two-phase (air-water) discharge through a small branch (6.35 mm i.d.) located on the side of a large reservoir under stratified conditions. These data correspond to different values of the interface level between the onsets of gas and liquid entrainments for test-section pressures ranging from 316 to 517 kPa, test-section-to-separator pressure differences ranging from 40 to 235 kPa, and different hydraulic resistances of the line connecting the test section and separator. Influences of these independent variables on the mass flow rate and quality are discussed and normalized plots are presented showing that the data can be collapsed for a wide range of conditions. Comparisons are made with previous investigations and new empirical correlations are formulated and shown to be capable of predicting the present data with good accuracy.

Discharge from a smooth stratified two-phase region through two horizontal side branches located in the same vertical plane

Experimental data are presented for the mass flow rate and quality of two-phase (air-water) discharge from a stratified region through two side branches (6.35 mm W.) with their parallel centrelines located in a vertical plane. These data correspond to different values of the interface level between the onset of gas entrainment at the upper branch to the onset of liquid entrainment at the lower branch for test-section pressures of 316 and 517 kPa, test-section-to-separators pressure difference ranging from 40 to 235 kPa, branch separating distance to diameter ratio ranging from 1.5 to 8 and different hydraulic resistances of the lines connecting the test section to the separators. Normalized plots are shown to be capable of absorbing the effects of some independent variables within the tested range of operating conditions. Empirical relations were developed for the prediction of the two-phase mass flow rate and quality in terms of normalized parameters. These relations represent the data with a high degree of correlation.

Single and two-phase discharge from a pressurized vessel

The objective of this work was to establish models for the blowdown process of partially filled pressure liquefied vessels and to validate the models by comparison with experimental pressure measurements. On the basis of experiments using small 400 mL steel pressure vessels with creep and knife induced cracks, a crack opening model was developed using the Crack Opening Displacement theory and plastic displacement assumptions. For a single-phase discharge, an expression for the unsteady compressible choked flow through openings of varying areas was developed. The results of this blowdown model were compared with experimental pressure measurements obtained for nine small vessels filled with argon and water - at different fill levels (70, 80 and 90%) with different initial pressures. The influence of the speed of crack propagation and discharge coefficient were evaluated. The simulations of the single-phase model were found to be in reasonable agreement with the experiments. The work also presents a comparison of several available two-phase blowdown models applicable to the discharge of a pressure liquefied gas (simulated here by refrigerants R11, R22 and R123). Some modifications to these models were also examined. The two-phase models did not seem to adequately describe the experimental results even when the model parameters were adjusted to suit the experiments.

Experimental investigation of the two-phase discharge from a stratified region through two side branches oriented horizontally

Experimental data are presented for the mass flow rate and quality of two-phase (air-water) discharge from a stratified region through two side branches (6.35 mm I.D.) with their parallel centerlines located in a horizontal plane. These data correspond to different values of the interface level between the onset of gas entrainment and that of liquid entrainment for test section pressures of 316 and 517 kPa, test section-separator pressure difference 40–235 kPa, branch separating-distance-to-diameter ratio 1.5–8, and different hydraulic resistances of the lines connecting the test section to the separators. The influences of these independent variables on the deviation between the present results (of mass flow rate and quality) and those corresponding to a single discharge are presented and discussed. Normalized plots are presented showing that the present data of dual discharge and those of a single discharge can be collapsed for the whole test range when specific definitions are used for the dimensionless height of the interface and mass flow rate. Excellent agreement is demonstrated between single-discharge correlations and the present data using these dimensionless quantities.

Numerical Study of Two-Dimensional Structure in Critical Steam-Water Two-Phase Flow

High pressure two-phase discharge flow from a vessel through a short pipe into an open space at atmospheric pressure was numerically analyzed using one-and two-dimensional non-equilibrium two-fluid models, in order to investigate effects of two-dimensional flow structure on thermal hydraulic phenomena in critical two-phase flows. Two-dimensional calculations revealed that flow contraction at the pipe inlet caused a liquid core in the central region of the pipe cross section, while void fraction in the vicinity of the pipe inner wall was large. This uneven phase distribution, which cannot be treated with one-dimensional calculations, seemed to result in larger discharge flow rate predictions because of phase slip promotion in two- dimensional calculations than that in one-dimensional calculations. Barrel-shaped shock waves, which are commonly observed in critical gas flow, did not appear in the calculated two-phase jets because large volumetric expansion due to flashing prevented the discharged two-phase mixture from over-depressurization.

The design of disposal systems for runaway chemical reactor relief

Abstract Options for the treatment or disposal of the two-phase discharge from a runaway reactor following emergency venting are discussed. Methods are given for the design of separation vessels and quench tanks. Different types of separation vessel and various design methods are compared. Examples are given for the different methods and systems.

Small-scale evaluation of dump tank sizing methods

Abstract Methods are given for the design of dump tanks to separate the liquid and vapour/gas phases from a two-phase emergency relief discharge from a runaway chemical reactor. A small-scale test apparatus is described which has been used to evaluate the design methods. Results and analysis are given for reacting and non-reacting systems, which give good agreement with the predictions from the design methods for water depressurization and a ‘vapour-pressure’ system. Results for a hybrid system indicate the problems associated with deciding whether the major component of the relief stream is the gas or the vapour.

Numerical Study of Two-Dimensional Structure in Critical Steam-Water Two-Phase Flow.

High pressure two-phase discharge flow from a vessel through a short pipe into an open space at atmospheric pressure was numerically analyzed using one- and two-dimensional non-equilibrium two-fluid models, in order to investigate effects of two-dimensional flow structure on thermal hydraulic phenomena in critical two-phase flows. Two-dimensional calculations revealed that flow contraction at the pipe inlet caused a liquid core in the central region of the pipe cross section, while void fraction in the vicinity of the pipe inner wall was large. This uneven phase distribution, which cannot be treated with one-dimensional calculations, seemed to result in larger discharge flow rate predictions because of phase slip promotion in two-dimensional calculations than that in one-dimensional calculations. Barrel-shaped shock waves, which are commonly observed in critical gas flow, did not appear in the calculated two-phase jets because large volumetric expansion due to flashing prevented the discharged two-phase mixture from over-depressurization.

Expansion zone modeling of two-phase and gas discharges

An expansion zone model couples a discharge rate model with a high momentum jet dispersion model for sonic or choked flow. Conventional expansion zone modeling, as based on an overall force balance, predicts large increases in the expansion zone diameter and only moderate increases in the expansion zone velocity at a range of low superheat. Alternately, it is shown that any analytic solution for a discharge model can be used also as an expansion zone model. In particular, the homogeneous equilibrium model (HEM) for two-phase discharge and the model for isentropic discharge of an ideal gas are used to exemplify expansion zone modeling. The new approach predicts, in contrast to the conventional approach, large increases in velocity and only moderate increases in expansion zone diameter. Experimental data are needed to decide which model is more nearly correct.

Reaction Forces During Two-Phase Discharges

Reaction Forces During Two-Phase Discharges

Two-phase flow discharge in nozzles and pipes — a unified approach

Abstract This paper presents a unified treatment on homogeneous two-phase discharge through short nozzles and long pipes. The resulting generalized solutions, cast in terms of a limited number of dimensionless variables, can adequately account for liquid properties, inlet conditions, effect due to pipe friction, gravitational change, inlet subcooling and presence of non-condensable gases. The results are also presented in the form of design charts, for practising engineers.

On the prevention of two-phase fluid venting during safety valve action

Abstract Pressure vessels containing liquefied gases such as propane or chlorine are protected against overpressures by safety valves which are located in the vapour space of the vessel and are designed to vent vapour. When the safety valve opens, liquid or a liquid-vapour mixture may be discharged, depending upon the rate of depressurization. This paper relates the initial vapour space volumes and the valve throat areas to the depressurization rates and to the formation of superheated liquid due to boiling delay. A sudden rise of the liquid-vapour interface (the so-called liquid swell) results, and may lead to undesirable two-phase fluid discharge.

Practical containment concepts in connection with short duration high rate two-phase discharges

Practical containment concepts in connection with short duration high rate two-phase discharges