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.

The Two-Phase Critical Flow of One-Component Mixtures in Nozzles, Orifices, and Short Tubes

1971 ◽  
Vol 93 (2) ◽  
pp. 179-187 ◽  
Author(s):  
Robert E. Henry ◽  
Hans K. Fauske
Keyword(s):  
Critical Pressure ◽  
Single Phase ◽  
Pressure Ratio ◽  
Stagnation Pressure ◽  
Experimental Results ◽  
Critical Flow ◽  
Two Phase ◽  
Transfer Rates ◽  
Critical Flow Rate ◽  
Flow Through

The critical flow of one-component, two-phase mixtures through convergent nozzles is investigated and discussed including considerations of the interphase heat, mass, and momentum transfer rates. Based on the experimental results of previous investigators, credible assumptions are made to approximate these interphase processes which lead to a transcendental expression for the critical pressure ratio as a function of the stagnation pressure and quality. A solution to this expression also yields a prediction for the critical flow rate. Based on the experimental results of single-phase compressible flow through orifices and short tubes, the two-phase model is extended to include such geometries. The models are compared with steam-water, cryogenic, and alkali-metal experimental data.

Analysis of two-phase ejectors with Fabri choking

2002 ◽  
Vol 216 (5) ◽  
pp. 607-621 ◽  
Author(s):  
W E Lear ◽  
G M Parker ◽  
S A Sherif
Keyword(s):  
Single Phase ◽  
Phase Region ◽  
Working Fluid ◽  
Two Phase ◽  
Cross Sectional ◽  
Flow Phenomena ◽  
Mass Flowrate ◽  
Inlet Conditions ◽  
R 134A ◽  
Phase Fluid

A one-dimensional mathematical model was developed using the equations governing the flow and thermodynamics within a jet pump with a mixing region of constant cross-sectional area. The analysis is capable of handling two-phase flows and the resulting flow phenomena such as condensation shocks and the Fabri limit on the secondary mass flowrate. This work presents a technique for quickly achieving first-approximation solutions for two-phase ejectors. The thermodynamic state of the working fluid, R-134a for this analysis, is determined at key locations within the ejector. From these results, performance parameters are calculated and presented for varying inlet conditions. The Fabri limit was found to limit the operational regime of the two-phase ejector because, in the two-phase region, the speed of sound may be orders of magnitude smaller than in a single-phase fluid.

scholarly journals Experimental Data of Supercritical Carbon Dioxide (sCO2) Compressor At Various Fluid States

2021 ◽  
Author(s):  
Alexander J. Hacks ◽  
Ihab Abd El Hussein ◽  
Haikun Ren ◽  
Sebastian Schuster ◽  
Dieter Brillert
Keyword(s):  
Experimental Data ◽  
Pressure Ratio ◽  
Phase Region ◽  
Experimental Results ◽  
Data Repository ◽  
Design Tools ◽  
Two Phase ◽  
Analysis And Design ◽  
Cad Models ◽  
Inlet Conditions

Abstract This paper presents experimental data on a centrifugal compressor operated with CO2. Temperature and pressure at the inlet of the compressor are varied to cover the supercritical region from the liquid-like to the gas-like region. In addition, inlet conditions in the two-phase region are also included. Thus, the experimental test campaign considers thermodynamic conditions relevant for the future energy conversion with sCO2-Joule cycles. Experimental results are presented as compressor pressure ratio vs inlet mass flow rate at different rotational speeds and throttle positions. Reliable conclusions can be drawn from the experimental results since the reproducibility of the measurements has been demonstrated by conducting experiments in two different test rigs, and measurement uncertainties are reported. The entire compressor geometry is disclosed in a data repository, including CAD models, and input files suitable for mean-line and grid generation programs. Thus, the experimental results are exploitable by the scientific community and pave the road for validated analysis and design tools in the context of the sCO2-Joule cycle. The presented results open the possibility to estimate uncertainties of analysis and design tools with little effort since geometry information can be quickly integrated. The experimental data is already used in this paper to obtain the accuracy of a CFD code and a mean-line program for sCO2. In addition to quantifying uncertainties, the results presented can be used to identify shortcomings of existing tools. This can be an essential step in the exploration of the sCO2-Joule cycle.

Effect of Non-Condensible Gas on the Subcooled Water Critical Flow in a Safety Valve

2002 ◽  
Author(s):  
Se Won Kim ◽  
Sang Kyoon Lee ◽  
Hee Cheon No
Keyword(s):  
Flow Rate ◽  
Critical Pressure ◽  
Safety Valve ◽  
Pressure Ratio ◽  
Water Flow Rate ◽  
Critical Flow ◽  
Inlet Temperature ◽  
Nitrogen Gas ◽  
Critical Flow Rate ◽  
Subcooled Water

The effect of non-condensable gas on the subcooled water critical flow in a safety valve is investigated experimentally at various subcoolings with 3 different disk lifts. To evaluate its effect on the critical pressure ratio and critical flow rate, three parameters are considered: the ratios of outlet pressure to inlet pressure, the subcooling to inlet temperature, and the gas volumetric flow to water volumetric flow are 0.15–0.23, 0.07–0.12, and 0–0.8, respectively. It turns out that the critical pressure ratio is mainly dependent on the subcooling, and its dependency on the gas fraction and the pressure drop is relatively small. When the ratio of nitrogen gas volumetric flow to water volumetric flow becomes lower than 20%, the subcooled water critical flow rate is decreased about 10% compare to the water flow rate of without non-condensable gas. However, it maintains a constant value after the ratio of gas volumetric flow to water volumetric flow becomes higher than 20%. The subcooled water critical flow correlation, which considers subcooling, disc lift, backpressure, and non-condensable gas, shows good agreement with the total present experimental data with the root mean square error 8.17%.

Low-Temperature Mechanical Alloying Of Cu-Fe and Cu-Ta Powders

1997 ◽  
Vol 481 ◽  
Author(s):  
J.-H. He ◽  
E. Ma
Keyword(s):  
Room Temperature ◽  
Single Phase ◽  
Composition Range ◽  
Dynamic Balance ◽  
Liquid Nitrogen Temperature ◽  
Phase Region ◽  
Two Phase ◽  
Forced Mixing ◽  
Single Phase Formation ◽  
Nonequilibrium Vacancies

ABSTRACTA model analysis is presented which explains ball-milling induced alloying in positive-heatof- mixing systems in terms of a dynamic balance between externally forced mixing and thermal phase decomposition mediated by deformation-enhanced population of defects. The possibility of eliminating the thermal decomposition to force single phase formation is examined by milling Cu- Fe and Cu-Ta powder mixtures at the liquid nitrogen temperature (LN2T). Over a range of compositions for Cu-Fe and almost the entire composition range for Cu-Ta, the two-phase region observed for room-temperature (RT) milling persisted after cryomilling. The moderate temperature dependence of milling-induced alloying is interpreted by analyzing the dynamics of the generation and annihilation of the nonequilibrium vacancies during deformation and impacts in a SPEX mill.

The f.c.c.+tetragonal two-phase region of the Cu–Ni–Zn system

1983 ◽  
Vol 16 (1) ◽  
pp. 99-102 ◽  
Author(s):  
O. S. Mayall
Keyword(s):  
Tetragonal Phase ◽  
Lattice Spacing ◽  
Single Phase ◽  
Phase Region ◽  
Unit Cell ◽  
Unit Cell Parameters ◽  
Two Phase ◽  
Cell Parameters ◽  
Tie Lines

The f.c.c. + tetragonal two-phase region of the Cu–Ni–Zn system has been delineated, and unit-cell parameters along the boundaries determined. Apparently anomalous parameter measurements prevented the determination of the tie lines. A pattern of diffraction broadening from the tetragonal phase common to both the two-phase and single-phase regions was related to the variation in lattice spacing of the tetragonal phase along the boundary. Reasons for this broadening are discussed.

Phase-Change Heat Transfer of Ethanol-Water Mixtures: Towards Development of a Distributed Hydrogen Generator

2013 ◽  
Author(s):  
Manoj Kumar Moharana ◽  
Rohan M. Nemade ◽  
Sameer Khandekar
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Phase Change ◽  
Transfer Coefficient ◽  
Single Phase ◽  
Flow Boiling ◽  
Phase Region ◽  
Design Flow ◽  
Two Phase ◽  
Vapor Region

Hydrogen fuel from renewable bio-ethanol is a potentially strong contender as an energy carrier. Its distributed production by steam reforming of ethanol on microscale platforms is an efficient upcoming method. Such systems require (a) a pre-heater for liquid to vapor conversion of ethanol water mixtures (b) a gas-phase catalytic reactor. We focus on the fundamental experimental heat transfer studies (pool and flow boiling of ethanol-water mixtures) required for the primary pre-heater boiler design. Flow boiling results (in a 256 μm square channel) clearly show the influence of mixture composition. Heat transfer coefficient remains almost constant in the single-phase region and rapidly increases as the two-phase region starts. On further increasing the wall superheat, heat transfer starts to decrease. At higher applied heat flux, the channel is subjected to axial back conduction from the single-phase vapor region to the two-phase liquid-vapor region, thus raising local wall temperatures. Simultaneously, to gain understanding of phase-change mechanisms in binary mixtures and to generate data for the modeling of flow boiling process, pool-boiling of ethanol-water mixtures has also been initiated. After benchmarking the setup against pure fluids, variation of heat transfer coefficient, bubble growth, contact angles, are compared at different operating conditions. Results show strong degradation in heat transfer in mixtures, which increases with operating temperature.

Tensile Property Improvements of Spinodal Cu-15Ni-8Sn by Two-Phase Heat Treatment

1982 ◽  
Vol 104 (3) ◽  
pp. 234-240 ◽  
Author(s):  
T. J. Louzon
Keyword(s):  
Heat Treatment ◽  
Single Phase ◽  
Phase Region ◽  
Two Phase ◽  
Heat Treated ◽  
Slow Kinetics ◽  
Increased Strength ◽  
Kinetics Of ◽  
Phase Solution ◽  
Strength And Ductility

A heat treatment has been developed which produces significant improvements in the tensile properties of Cu-15Ni-8Sn spinodal alloy. The treatment involves solution heat treatment in the two-phase region rather than the single-phase region normally used. After quenching and aging, increased strength and ductility of the alloy over single phase solution heat-treated and aged values were found. The mechanical properties obtained were superior to any previously observed for material of the compositions studied in the solution treated, quenched, and aged condition. Also, the alloys’ transformation kinetics were greatly slowed by the two phase heat-treatment. It is suggested that the increase in strength and slow kinetics of transformation observed are caused by grain size effects and by grain boundary modifications. Resistivity data and etching response corroborate these arguments.

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