Two-phase Steam Flow Research Articles

Numerical study of non-equilibrium condensing supersonic steam flow in a jet-pump based on supersaturation theory

Condensation process in high velocity flowing steam inside jet-pumps and ejectors significantly affect the performance of these devices. The formation of droplets in the steam passed through the primary nozzle of a jet-pump, releases an amount of latent heat and numerous tiny particles which change the flow properties. Conventional CFD approaches of investigating ejectors consider steam as an ideal gas with a single-phase flow. In the present study, a robust mathematical model was developed to take into account the droplet formation phenomena in the flowing steam, wherein a large number of droplets are formed in the subcooled vapor through a non-equilibrium supersaturation phenomenon. Separately, the mathematical method was used to model the operating performance of a pilot-scale ejector and to investigate the deviation of the entrainment ratio and the compression ratio from the corresponding ideal-gas values. It was found that the error of the entrainment ratio substantially reduced from 10.0% for a single-phase steam to 1.69% for a two-phase steam, and the error of the compression ratio reduced from 7.3% to 3.52%, respectively. Moreover, effects of variations of the suction flow pressure and temperature on the two-phase steam flow velocity, density, pressure and temperature was investigated and thoroughly discussed. In addition, flow Mach number was introduced as a major characteristic to compare shock-wave patterns of supersonic flow in both steam assumptions. Finally, it was shown that the pressure-rise through the normal shock-wave in the two-phase flow simulation is considerably higher than that of the single-phase flow simulation.

Effect of friction work on key parameters of steam at different state in toe-point injection horizontal wellbores

When modeling of steam flow in wellbores, the effect of friction work on temperature/steam quality of both fluid in wellbores and reservoir should be considered. A model that can describe the energy re-distribution in the system should be built.In this paper, new energy balance equations for steam flow in inner tubing (IT) and annuli are developed with consideration of the effect of frction work on the energy re-distribution process in the system. The heat energy caused by shear stress has an obvious influence on the increase of steam quality or superheated steam temperature, especially under high injection speed condition.Firstly, a model for steam flow is developed in wellbores based on the energy and momentum balance equations. The energy balance equation controlls the predicted values of steam quality or superheated steam temperature, and the momentum balance equation controlls mainly the steam pressure. Secondly, coupled with the seepage model in oil layer, a comprehensive mathematical model is establiehed for single, two-phase flow of steam in horizontal wells with toe-point injection technique.Results show that: (a) when the effect of friction work was neglected, the predicted steam quality or superheated steam temperature were obviously smaller than field data. (b) While seam quality decreases with distance when wet steam flows in wellbores, superheated steam temperature in annuli has an increase at the heel-point in annuli. This is because the fluid with lower temperature in annuli absorbs heat from steam with higher temperature in IT. (c). In order to obtain a satisfactory oil recovery ratio, field engineers are suggested to increase the injection pressure to a reasonable level based on the rock fracture pressure experiment.

MEASUREMENT AND MODELING OF FLOW PATTERN TRANSITIONS IN GAS-LIQUID SYSTEMS

This paper gives a comprehensive interpretation on the flow patterns occurring in gas-liquid horizontal, inclined and vertical pipeline flows and investigates various effects on their transitions. The postulated theoretical models for prediction of flow pattern transitions in systems without mass transfer are presented in detail. For horizontal pipe flows with boiling and condensation, a modified mechanistic theory is suggested; the predicted transitions are in good agreement with the experimental data. Finally, the approaches developed by Venkateswarar et al. (1982) to modelling the flow pattern transition for two-phase flows of steam and water in vertical rod bundles are presented.

CHARACTERISTICS OF THE STEAM FLOW IN THE END SEALS OF HIGH PRESSURE CYLINDERS IN THE STATE OF VACUUM AUGMENTATION

The algorithm was developed to determine steam parameters in the front and back end seals in the mode of vacuum augmentation based on A. Stodol approach that allows us to take into account the steam leakage from the chambers with drainages and determine flow characteristics in each chamber. The steam flow behavior was determined for each section of the end seals of high pressure cylinder (HPC) of the turbine К-325-23.5 at the stage of the preparation for the hot and cold starting. Steam flow characteristics were determined taking into consideration hydraulic resistance of the steam pipelines of drainage system in the time interval of turbine heating of 0 to 2 hours. Forty minutes before the rotor push the steam is injected through the exhaust pipeline at a pressure of 0.6–1.0 MPa and a temperature of 290 to 350 °С. This steam enters the unheated rotor sections of HPC in the region of end seals. Pressure distributions and steam flow consumptions in the section of front and back end seals are indicative of the irrational circuit of rotor heating and the possibility of formation of high thermal stresses. The data analysis shows that a more rational circuit is required for the rotor heating in the region of the front end seal. Using calculated steam parameters heat emission coefficients were calculated for single-phase and two-phase steam flows on the HPC rotor surface in the region of end seals for subsequent thermal strength analysis. // o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o

Parametric studies influencing condensation evolution in compressible steam flow

In this paper, the effect of operational and geometrical parameters on the location of condensation onset and the rate of condensations are considered. These parameters are expansion rate of different geometry, inlet stagnation condition and the waves. To do so, a numerical method is presented to solve the two-dimensional two-phase steam flow over a series of geometries (such as nozzles, expansion corners and steam turbine blade-to-blade passages) by means of equilibrium thermodynamics model.

Evaluation of simultaneous effects of inlet stagnation pressure and heat transfer on condensing water-vapor flow in a supersonic Laval nozzle

In supersonic two-phase flows of steam, under the influence of rapid expansion, the vapor becomes supersaturated. Following this condition, nucleation happens during the vapor phase; formed tiny droplets grow along the passage and, therefore, the condensation phenomenon occurs. The effects of the condensation phenomenon in power steam turbines include efficiency drop and mechanical damage. In the previous work of the authors, volumetric heating was introduced as an approach towards reducing the mentioned damage and loss. However, further investigations revealed that heating decreases the mass flow rate, which can be increased by adjusting the inlet stagnation pressure. In this paper, using a semi-analytical and a one-dimensional modeling approach, the simultaneous effects of volumetric heat transfer and inlet stagnation pressure variation are investigated in order to remedy the mass flow rate reduction. The results show that increasing the inlet stagnation pressure up to 5% can fix the mass flow rate of the non-adiabatic flow, compared to the adiabatic flow under the same conditions.

Theoretical investigation of effects of local cooling of a nozzle divergent section for controlling condensation shock in a supersonic two-phase flow of steam

In supersonic adiabatic two-phase flows of steam, under the influence of supersonic acceleration, the fluid loses its equilibrium conditions and becomes supersaturated. Following this condition and to restore the fluid to equilibrium, micro droplets of water form in the absence of any surface or foreign particles. This phenomenon is called homogeneous nucleation and the formed minute small droplets grow along the fluid flow path. The formation of these droplets and their growth causes the release of the latent heat of evaporation to the gas phase particularly in the nucleation region, and results in an increase in the flow pressure which is called the condensation shock. In this paper, and in continuation of the series of papers by the authors, in addition to analytically solving the adiabatic gas-liquid supersonic flow of steam in a convergent-divergent channel, a novel solution to controlling the undesired effects of this pressure rise (condensation shock) is presented. In the proposed method, with the help of cooling the divergent section of the nozzle, the analytical model for the 1D non-adiabatic two-phase steam flows is further developed which shows considerable decrease in the intensity of the formed condensation shock. Also the growth rate of the formed droplets due to the cooling of the steam flow has higher importance than the nucleation itself.

Effective Technology of Preventive Measures against Piping Damage on Steam Lines in Nuclear Power Plants

Nuclear power plants are required to have especially high reliability and increasingly longer service life. As a contribution to the solution of these issues, an analysis was conducted on steam field-related troubles and their causes based on a data from an online database that tracks troubles at nuclear power plants and the authors' experience. As a result, the reality of piping damage attributed to the two-phase flow of steam and condensate characteristic of nuclear power plants was elucidated. This note introduces preventive measures against piping damage to steam and condensate lines that has been proven effective through actual use in various industries under the following topics: 1) technology for the separation of steam/condensate in steam piping, 2) technology for the discharge of condensate from steam piping, and 3) technology for the measurement, inspection or monitoring of steam and condensate lines.

Reducing entropy generation by volumetric heat transfer in a supersonic two-phase steam flow in a Laval nozzle

In a supersonic flow of pure vapour in adiabatic diffusers, under some circumstances, nucleation phenomenon occurs and consequently vapour condensation is observed. In this process, the resulted pressure rise is called the condensation shock, which causes the entropy generation. The innovation of this research is analytically modelling the volumetric heat addition to the steam flow in a 1D convergent?divergent supersonic nozzle. The analysis of the results shows that an appropriate volumetric heat addition to the convergent section of a convergent?divergent supersonic nozzle can reduce the degree of supercooling and subsequently reduce the nucleation rates significantly. The condensation reduction declines the irreversible internal heat transfer, which improves the efficiency of the steam flow.

Experimental Investigations of Two-Phase Steam Flows in Horizontal Channels of Small Diameter

This article describes experimental investigations of two-phase flow regimes for steam–water flowing in horizontal ducts of small diameters. In this respect two-phase flow patterns are determined on a test stand based on visualization of real flows. Measurements were performed for a round tube with an internal diameter of 2.8 mm under mass flux ranging from 160 kg/s-m2 to 1600 kg/s-m2 at saturation temperatures between 373 K and 403 K. Registered steam quality varied from 0.02 to 0.27. Experimental setup, methodology, and recorded two-phase flow patterns referenced to annular, intermittent, and transient flows are presented. The results obtained have been compared with annular to wavy transition criteria described on the flow map by Soliman.

A numerical investigation of two-phase steam flow around a 2-D turbine's rotor tip

In flow of steam during the divergence nozzles, expansion and decreasing the enthalpy, brings the flow near the saturation conditions. After supercooling, nucleation forms in the flow and the second phase appears. This phenomenon occurs specially during the last stages of steam turbines as low-pressure case and nuclear reactors as high-pressure. In this research, a numerical scheme for transonic two-phase flow within the passages of 2-D rotor-tip section with various backpressures is applied and an Eulerian–Eulerian reference frame is employed for both phases. A classical homogenous nucleation model applied for the mass transfer in the transonic conditions. Five deferent cases have been tested and through the results, pressure profiles around the blades are compared with the experimental data and good agreement is observed. Results show that the most condensation is on the suction surface of blade and it grows by decreasing the downstream pressure.

Correction for Bakhtar et al. , Instability in two-phase flows of steam

Correction for ‘Instability in two-phase flows of steam’ by F. Bakhtar, S. R. Otto, M. Y. Zamri and M. Sarkies (Proc. R. Soc. A 464 , 537–553. (doi: 10.1098/rspa.2007.0087 )). The following equation contains typographical errors that has no consequence for any other equation or result in the above paper.

Instability in two-phase flows of steam

In two-phase flows of steam, when the velocity is between the equilibrium and frozen speeds of sound, the system is fundamentally unstable. Because any disturbance of the system, e.g. imposition of a small supercooling on the fluid, will cause condensation, the resulting heat release will accelerate the flow and increase the supercooling and thus move the system further from thermodynamic equilibrium. But in high-speed flows of a two-phase mixture, dynamic changes affect the thermodynamic equilibrium within the fluid, leading to phase change, and the heat release resulting from condensation disturbs the flow further and can also cause the disturbances to be amplified at other Mach numbers. To investigate the existence of instabilities in such flows, the behaviour of small perturbations of the system has been examined using stability theory. It is found that, although the amplification rate is highest between the equilibrium and frozen speeds of sound, such flows are temporally unstable at all Mach numbers.

A comparative study of treatment of two-dimensional two-phase flows of steam by a Runge-Kutta and by Denton's methods

This paper describes a comparative study of the treatment of two-dimensional nucleating flows of steam using two different time-marching numerical schemes. A treatment based on Denton's scheme but a refined grid has been available from earlier work. To compare with this a treatment based on the Runge-Kutta scheme has been developed, which is described. Solutions using this scheme and a simple mesh are compared with experimental results and with solutions using the earlier treatment. The agreement obtained between the two schemes and with the experimental results is satisfactory. Oscillating flows in a convergent-divergent nozzle are also examined and excellent agreement obtained with experimental measurements.

GENERALIZATION OF AN ANALYTICAL TWO-PHASE STEAM FLOW CALCULATOR TO HIGH-PRESSURE CASES

Extension of a recently developed analytical two-phase steam flow calculator to high pressure cases is performed in this paper. The initial solution, obtained in earlier study was developed for low pressure cases. In low pressure cases, the vapor portion of the two-phase mixture reliably obeys the ideal gas Equation of State (EOS). In the present high pressure study, real gas effects are included using the more suitable EOS of “Lee-Kesler”. The model similar to the low pressure model assumes local equilibrium between the phases, in which condensation onsets as soon as the saturation line is closed. Before the condensation onset, the stagnation properties echo those at the inflow. However, beyond the condensation onset, the transfer of latent heat toward the vapor portion of the two-phase mixture rises its stagnation temperature. To evaluate this rise in the vapor portion stagnation temperature, a non dimensional parameter ζ is defined. Comparison for low- and high-pressure cases between the present analytical solution and the published experimental values in the literature show very good agreement.

DEVELOPMENT OF AN ANALYTICAL SOLUTION FOR COMPRESSIBLE TWO-PHASE STEAM FLOW

An analytical solution for the isentropic expansion of subsonic-supersonic two-phase steam flow is provided in this paper. The results are supported by our earlier numerical computations, and available experimental values of others (1973). The two-phase mixture is assumed to undergo an isentropic expansion. However the entropy of the vapor portion of the two-phase mixture increases as the released latent heat of the condensate, reversibly moves toward the vapor, and enhances its entropy, as well as the so called “local stagnation” temperature of the vapor. The mass flow rate of the vapor portion of the two-phase mixture is obtained based on the “local stagnation” conditions, and then corrected to give the mixture mass flow rate. Most of the attempts have been made to develop the solution in a manner similar to those of the ideal gases.

Nucleating unsteady flows in low-pressure steam turbine stages

The present paper deals with the detailed numerical investigation of transonic, turbulent, unsteady two-phase steam flows with internal heat addition after partial condensation of the working fluid. The observed phenomena include homogeneously, homogeneously-heterogeneously and heterogeneously dominated condensation effects. The results concerning the different condensation mechanisms are initially discussed in terms of the turbulent, transonic flow through Laval nozzles. Further, an interesting phenomenon of nucleation and droplet growth inside turbulent boundary layers is presented. Application to transonic turbine flows in the rotor cascade VKI-1 shows the influence of homogeneous nucleation on the turbulent shock-boundary layer interaction. Finally, the different types of condensation models were compared to investigate the two-dimensional transonic two-phase flow in an entire turbine stage including high-frequency rotor-stator interactions.

Steady Adiabatic, Two-Phase Flow of Steam and Water Through Porous Media

Summary Reliable steam/water relative permeability curves that have not been previously reported were obtained under conditions of near-adiabatic, two-phase, steady flow in an unconsolidated Ottawa sandpack. Comparison of higher-temperature steam/water relative permeability curves to those for nitrogen/water at room temperature indicate that the two types of flows are essentially identical.

FLOW PATTERN TRANSITIONS IN GAS-LIQUID SYSTEMS: MEASUREMENT AND MODELING

This paper gives a comprehensive interpretation on the flow patterns occurring in gas-liquid horizontal, inclined and vertical pipeline flows and investigates various effects on their transitions. The postulated theoretical models for prediction of flow pattern transitions in systems without mass transfer are presented in detail. For horizontal pipe flows with boiling and condensation, a modified mechanistic theory is suggested; the predicted transitions are in good agreement with the experimental data. Finally, the approaches developed by Venkateswarar et al. (1982) to modelling the flow pattern transition for two-phase flows of steam and water in vertical rod bundles are presented.

An investigation of two-dimensional flows of nucleating and wet steam by the time-marching method

A numerical method for the solution of two-dimensional two-phase flows of steam is described. Comparisons are with two sets of experimental results in nozzles and the agreement obtained is satisfactoryy. Some predictions of two-phase effects in blade cascades are also presented.