Critical Two-Phase Flow in Pipes for Subcooled Stagnation States With a Cavity Flooding Incipient Flashing Model

1990 ◽  
Vol 112 (4) ◽  
pp. 1032-1040 ◽  
Author(s):  
S. Y. Lee ◽  
V. E. Schrock
Keyword(s):  
Nuclear Reactor ◽  
Safety Evaluation ◽  
Phase Region ◽  
Dominant Factor ◽  
Critical Flow ◽  
Primary System ◽  
Transient Heating ◽  
Two Phase ◽  
Flow Process ◽  
Sequence Of Events

Analysis of loss of coolant accident (LOCA) scenarios in nuclear reactor safety evaluation depends on knowledge of many complex phenomena. A primary phenomenon controlling the sequence of events, by determining the residual coolant mass inventory within the primary system, is the critical flow process. Critical flow of a flashing liquid is complicated by marked departure from thermal equilibrium. Several complex models have been proposed to represent the non-equilibrium effects, including six-equation two-fluid models. Amos and Schrock (1983) developed a model based on the premise that the two-phase region is homogeneous and that thermal nonequilibrium is the dominant factor causing the departure from the homogeneous equilibrium idealization. Flashing inception was represented by a modification of the Alamgir-Lienhard (1981) pressure undershoot. Exponential relaxation of the metastable liquid was formulated as suggested by Bauer et al. (1976) and the critical flow criterion used the sound speed formulation of Kroeger (1976). Lee and Schrock (1988) extended the Amos-Schrock work by developing an improved correlation for the pressure undershoot correction factor in terms of Reynolds number and subcooling Jakob number. Improvements were also made in the relaxation constant and in the application of Kroeger’s formulation. In the present paper a new cavity flooding model is used for the evaluation of pressure undershoot at flashing inception. This model is similar to the one developed by Fabic (1964) for the evaluation of liquid superheat required for boiling on a surface subjected to transient heating. The model contains an experimentally deduced factor, which is correlated against stagnation subcooling using the experimental data of Amos and Schrock (1983, 1984), Jeandey et al. (1981), and the Marviken tests (Anon., 1979). The model was then tested against seven additional data sets and shown to be very accurate in predicted mass flux (standard deviation of 10.9 percent for all data). The cavity flooding model is thought to represent the true physics more correctly than does the earlier model, which had its origin in molecular fluctuation theory.

Formation and Morphology of Kurnakov Type D022 Compound in Disordered fcc γ-(Ni, Fe) Matrix Alloys

2004 ◽  
Vol 842 ◽  
Author(s):  
Akane Suzuki ◽  
Masao Takeyama
Keyword(s):  
Lattice Misfit ◽  
Strain Ratio ◽  
Phase Region ◽  
Treatment Temperature ◽  
Austenitic Steels ◽  
Dominant Factor ◽  
Partial Replacement ◽  
Invariant Line ◽  
Two Phase ◽  
Model Case

ABSTRACTFormation and morphology of D022 compound Ni3V in γ-fcc alloys were investigated as a model case in order to understand fundamentals for microstructure control of new class of austenitic steels strengthened by Kurnakov-type GCP intermetallic compound. The formation process of the D022 phase in γ matrix varies, depending on the composition and heat treatment temperature, and precipitation of D022 takes place at temperature above T0 in the γ+D022 two phase region. The morphology of coherent precipitates of the D022 compound is sensitive to misfit strains against matrix and can be controlled by alloying addition. The habit planes between the two phases become irrational, parallel to both directions of the invariant line and an a-axis of D022, since the lattice misfit becomes negative along a-axis (δa) and positive along c-axis (δc) of the D022. The calculation based on the lattice invariant theory as well as experimental results clearly demonstrate that the misfit strain ratio δc/δa is a dominant factor to determine the habit plane. In addition, the shape of D022 phase, either prism or plate, depends strongly on the magnitude of |δa|. These findings will extend to Ni-Fe-Nb-V quaternary system, by partial replacement of Ni with Fe and that of V with Nb.

scholarly journals CRITICAL FLOW PREDICTION MODELS FOR THE COOLANT AT SUPERCRITICAL PARAMETERS

2021 ◽  
pp. 81-87
Author(s):  
D. Fedorov ◽  
V. Tuz ◽  
S. Klevtsov
Keyword(s):  
Prediction Models ◽  
Flow Characteristics ◽  
Physical Nature ◽  
Nuclear Industry ◽  
Fourth Generation ◽  
Critical Flow ◽  
Two Phase ◽  
Flow Process ◽  
Loss Of Coolant Accident ◽  
Supercritical Parameters

An interest of the problems of various thermophysical and hydrodynamic phenomena in the nuclear industry, determined by the real application in the field of analysis of the accident scenarios related to the loss of coolant accident. For the generic super critical water reactor the meaning of the problem at the initial stage of the critical flow process, is the existing of the uncertainty in the accepting boundary conditions to predict the flow characteristics. The article provides an analytical review of existing approaches for describing the critical flow phenomenon of the medium and to focus on the current predictive models. A description of the physical nature of such a phenomenon is provided. The scope of consideration includes information from the literature for single and two-phase flow, taking into account their physical basis and the assumptions made. The task of the work was to analyze the information found and to evaluate and update the data on the application of the models to obtain the critical characteristic. It was supposed to highlight the physical aspects and peculiarities of this phenomenon, as applied to the coolant at supercritical parameters. To formulate important requirements to the representative critical flow model for the possibility of its use in the system codes for evaluation of the nuclear safety problems of promising fourth generation nuclear reactors.

Phase Equilibria and Lattice Parameters of Fe2Nb Laves Phase in Fe-Ni-Nb Ternary System at Elevated Temperatures

2004 ◽  
Vol 842 ◽  
Author(s):  
Masao Takeyama ◽  
Nobuyuki Gomi ◽  
Sumio Morita ◽  
Takashi Matsuo
Keyword(s):  
Ternary System ◽  
Phase Equilibria ◽  
Elevated Temperatures ◽  
Phase Region ◽  
Lattice Parameters ◽  
Laves Phase ◽  
Austenitic Steels ◽  
Dominant Factor ◽  
Two Phase ◽  
Ni Content

ABSTRACTPhase equilibria in Fe-Ni-Nb ternary system at elevated temperatures have been examined, in order to identify the two-phase region of γ-Fe (austenite) and ε-Fe2Nb (C14). The ε single phase region exists in the range of 27.5 to 35.5 at.% Nb in the Fe-Nb binary system, and it extends toward the equi-niobium concentration direction up to 44 at.% Ni in the ternary system at 1473 K, indicating that more than half of the Fe atoms in Fe2Nb can be replaced with Ni. Thus, the γ+ε two-phase region exists extensively, and the solubility of Nb in γ phase increases from 1.5 to 6.0 at.% with increase in Ni content. The lattice parameters of a and c in the C14 Laves phase decrease with increasing Ni content. The change in a axis is in good agreement with calculation based on Vegard's law, whereas that of c axis is much larger than the calculated value. The result suggests that atomic size effect is responsible for a-axis change and the binding energy is dominant factor for the c-axis change. To extend these findings to development of new class of austenitic steels strengthened by Laves phase, an attempt has been made to control the c/a ratio by alloying. The addition of Cr is effective to make the c/a ratio close to the cubic symmetry value (1.633).

Core Ignition Prediction With Moving Two-Phase Zone Boundaries

2008 ◽  
Author(s):  
Dov Hasan ◽  
Yuri Nekhamkin ◽  
Eitan Wacholder ◽  
Ezra Elias
Keyword(s):  
Nuclear Reactor ◽  
Reactor Core ◽  
Phase Region ◽  
Transient Temperature ◽  
Phase Zone ◽  
Two Phase ◽  
Loss Of Coolant Accident ◽  
Hydraulic Behaviour ◽  
Nuclear Reactor Core ◽  
Accident Conditions

The interaction between a fuel rod metal clad and the surrounding steam in a nuclear reactor core under hypothetical accident conditions is considered using a thermal balance based model. This enables the calculation of the metal transient temperature and its rate of oxidation, which may possibly lead to ignition and rapid burning. The transient fluid thermal-hydraulic behaviour of the two phase region, as well as the propagation in space and time of its boundaries following a step change in the coolant inlet mass flow rate are solved using a one-dimensional, two-phase homogeneous flow model. The solution scheme consists of first solving the velocity field analytically followed by a numerical solution of the remaining balance equations for the density field. The transient location of the dry-zone region, as well as the other flow primary variables; i.e., vapour quality, and enthalpy are then directly obtained. Numerical results are illustrated based on input data of a partially uncovered AP600 type nuclear reactor core during a bottom-reflooding phase of a loss of coolant accident scenario.

Flow Visualization of Submerged Steam Jet in Subcooled Water

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
Fang Yuan ◽  
Quanbin Zhao ◽  
Daotong Chong ◽  
Weixiong Chen
Keyword(s):  
Nuclear Reactor ◽  
Bubble Diameter ◽  
Flow Region ◽  
Pressure Oscillation ◽  
Transfer Characteristic ◽  
Dominant Frequency ◽  
Phase Region ◽  
Two Phase ◽  
Penetration Length ◽  
Subcooled Water

Steam discharged into subcooled water is investigated experimentally to demonstrate the direct contact condensation phenomena in nuclear reactor safety system and underwater propulsion apparatus. The steam jet condenses to various shapes at different thermal hydraulic conditions. A condensation regime diagram is drawn to classify the regime for different flow patterns, among which there are three typical shapes of steam plume characterizing the chugging, condensation oscillation, stable condensation regime (Figure 1). The flow region can be separated into three parts—vapor, water and two-phase regions, and the white patch in the image indicating the two-phase region is a mixture of condensed vapor and subcooled water. Three typical stages of bubble motions—growth (subimage 1 to 6, Figure 2), necking (subimage 7 to 10, Figure 2), and detachment (subimage 11 to 13, Figure 2)—are demonstrated. The bubble diameter reaches the maximum at the necking stage and remains approximately invariant with the connecting neck prolonging for a period. A series of sequent photos exhibits shape transformations at the stable condensation regime, implying that the steam plume grows and shortens periodically due to comprehensive effects of injection, viscosity damping and condensation (Figure 3). The dimensionless penetration length, defined as the ratio of penetration length to nozzle diameter, is in the range of 8.23–11.67 in the Figure 3. The majority of previous literatures present the average dimensionless penetration length which is closely related with time-averaged heat transfer characteristic. However, variations of steam plume are proven to account for pressure oscillation phenomena by the transient visualization investigations, in which the first dominant frequency acquired from the FFT domain graph of pressure signal is consistent with the period of steam plume variations. The second dominant frequency is verified to be caused by oscillations of detached bubbles (subimage 8 and 9, Figure 3) in the research.

The Critical and Two-Phase Flow of Steam

1961 ◽  
Vol 83 (2) ◽  
pp. 145-154 ◽  
Author(s):  
William G. Steltz
Keyword(s):  
Digital Computer ◽  
Critical Pressure ◽  
Single Phase ◽  
Unit Area ◽  
Pressure Ratio ◽  
Phase Region ◽  
Critical Flow ◽  
Two Phase ◽  
Analytic Expressions ◽  
Inlet Conditions

The results of a digital computer and analytic study of the critical flow of a compressible fluid are presented in this paper. The expanding flow of a fluid in a single-phase region as well as the expansion of a fluid to a two-phase region is considered and described by analytic expressions relating choking velocity, critical pressure ratio, and flow per unit area characteristics. A comparison is made of the analytic results which assume a constant value of the isentropic expansion exponent, with the digital computer results using the actual properties of steam. All analyses assume the fluid to be in thermodynamic equilibrium. A skeleton Mollier diagram is presented for steam showing the exponent in the wet and superheated regions. The choking velocity is presented in plot form as a function of the inlet conditions as well as state point conditions; critical pressure ratio is presented as a function of inlet conditions. The critical flow per unit area is presented in the form of a factor K plotted versus inlet conditions; this factor K when multiplied by inlet pressure produces the desired value of critical flow.

Thermal Hydraulic and Two-Phase Phenomena in Reflooding of Nuclear Reactor Cores

1984 ◽  
Vol 106 (4) ◽  
pp. 477-485 ◽  
Author(s):  
S. M. Ghiaasiaan ◽  
I. Catton ◽  
R. B. Duffey
Keyword(s):  
Nuclear Reactor ◽  
Phase Region ◽  
Hydraulic Analysis ◽  
Level Variation ◽  
Slab Geometry ◽  
Two Phase ◽  
The Core ◽  
Power Profile ◽  
Implicit Expressions ◽  
Thermal Hydraulic Analysis

A quasi-steady, two-dimensional thermal hydraulic analysis of the two-phase region formed ahead of a quench front during reflooding of a slab or cylindrical core is carried out, and the results for slab geometry are compared with the experiment. It is shown that the two-phase level variation in the core is due to the transverse heat flux power profile, and is sensitive to the assumed pressure-drop boundary condition for the bundle, while the effects of crossflow and axial friction are small. Implicit expressions are given for predicting the quasi-steady two-phase level variation across slab and cylindrical cores.

Solution Properties and Phase Behavior of Ammonium Hexylene Octyl Succinate in Water and Water-Oil System

1970 ◽  
Vol 3 (1) ◽  
Author(s):  
Md. Hamidul Kabir ◽  
Ravshan Makhkamov ◽  
Shaila Kabir
Keyword(s):  
Critical Micelle Concentration ◽  
Phase Behavior ◽  
Liquid Crystalline ◽  
Carbon Number ◽  
Phase Region ◽  
Solution Properties ◽  
Middle Phase ◽  
Two Phase ◽  
Lamellar Liquid Crystal ◽  
Drug Ingredient

The solution properties and phase behavior of ammonium hexylene octyl succinate (HOS) was investigated in water and water-oil system. The critical micelle concentration (CMC) of HOS is lower than that of anionic surfactants having same carbon number in the lipophilic part. The phase diagrams of a water/ HOS system and water/ HOS/ C10EO8/ dodecane system were also constructed. Above critical micelle concentration, the surfactant forms a normal micellar solution (Wm) at a low surfactant concentration whereas a lamellar liquid crystalline phase (La) dominates over a wide region through the formation of a two-phase region (La+W) in the binary system. The lamellar phase is arranged in the form of a biocompatible vesicle which is very significant for the drug delivery system. The surfactant tends to be hydrophilic when it is mixed with C10EO8 and a middle-phase microemulsion (D) is appeared in the water-surfactant-dodecane system where both the water and oil soluble drug ingredient can be incorporated in the form of a dispersion. Hence, mixing can tune the hydrophile-lipophile properties of the surfactant. Key words: Ammonium hexylene octyl succinate, mixed surfactant, lamellar liquid crystal, middle-phase microemulsion. Dhaka Univ. J. Pharm. Sci. Vol.3(1-2) 2004 The full text is of this article is available at the Dhaka Univ. J. Pharm. Sci. website

Gas-Water Flow Behaviour During Mutual Displacement in Porous Media

2017 ◽  
Vol 10 (1) ◽  
pp. 13-22
Author(s):  
Renyi Cao ◽  
Junjie Xu ◽  
Xiaoping Yang ◽  
Renkai Jiang ◽  
Changchao Chen
Keyword(s):  
Porous Media ◽  
Relative Permeability ◽  
Gas Storage ◽  
Fluid Distribution ◽  
Water Displacement ◽  
Phase Zone ◽  
Two Phase ◽  
Flow Process ◽  
Single Well ◽  
Mutual Displacement

During oilfield development, there exist multi-cycle gas–water mutual displacement processes. This means that a cycling process such as water driving gas–gas driving water–water driving gas is used for the operation of injection and production in a single well (such as foam huff and puff in single well or water-bearing gas storage). In this paper, by using core- and micro-pore scales model, we study the distribution of gas and water and the flow process of gas-water mutual displacement. We find that gas and water are easier to disperse in the porous media and do not flow in continuous gas and water phases. The Jamin effect of the gas or bubble becomes more severe and makes the flow mechanism of multi-cycle gas–water displacement different from the conventional water driving gas or gas driving water processes. Based on experiments of gas–water mutual displacement, the changing mechanism of gas–water displacement is determined. The results indicate that (1) after gas–water mutual displacement, the residual gas saturation of a gas–water coexistence zone becomes larger and the two-phase zone becomes narrower, (2) increasing the number of injection and production cycles causes the relative permeability of gas to increase and relative permeability for water to decrease, (3) it becomes easier for gas to intrude and the invaded water becomes more difficult to drive out and (4) the microcosmic fluid distribution of each stage have a great difference, which caused the two-phase region becomes narrower and effective volume of gas storage becomes narrower.

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