Explicit Critical Pressure Ratio for Choked Two-Phase Homogeneous Nozzle Flow

2007 ◽  
Vol 30 (4) ◽  
pp. 530-533 ◽  
Author(s):  
D. Moncalvo ◽  
L. Friedel
Keyword(s):  
Critical Pressure ◽  
Pressure Ratio ◽  
Nozzle Flow ◽  
Two Phase

An investigation into oil—gas two-phase leakage flow through micro gaps in oil-injected compressors

2010 ◽  
Vol 224 (4) ◽  
pp. 925-933
Author(s):  
D Xin ◽  
J Feng ◽  
X Jia ◽  
X Peng
Keyword(s):  
High Speed ◽  
Critical Pressure ◽  
Pressure Ratio ◽  
Volume Ratio ◽  
Flow Patterns ◽  
Leakage Flow ◽  
Two Phase ◽  
Gas Leakage ◽  
Flow Through ◽  
Oil Gas

This article presents the investigation on the oil—gas two-phase leakage flow through the micro gaps in oil-injected compressors and provides a new way of investigating the internal leakage process in the compressors. The oil—gas leakage rates were measured through the micro gaps of various gap sizes, the volume ratios of oil to gas, and pressure differences/ratios; and the flow patterns reflecting the flow characteristics were observed by using a high-speed video. The experimental results showed that the leakage flowrate was significantly related to the flow patterns in the gap, which were similar to those found in the existing literature and agreed well with the predicted ones by the Weber number. The gas leakage flowrate through the gap increased rapidly with the increased pressure ratio until the pressure ratio reached the critical pressure ratio, which ranged from 1.8 to 2.7. At the critical pressure ratio, the flow pattern transition from churn flow to annular flow occurred, resulting in gas leakage driven by a different sealing mechanism. As the volume ratio of oil to gas increased by 0.5 per cent, the gas leakage flowrate decreased by 77 per cent.

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.

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.

Enhancement to the Traditional Ellipse Law for More Accurate Modeling of a Turbine With a Finite Number of Stages

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
W. F. Fuls
Keyword(s):  
Finite Number ◽  
Critical Pressure ◽  
Pressure Ratio ◽  
Axial Flow ◽  
Nozzle Flow ◽  
Flow Equations ◽  
Numerical Studies ◽  
Multistage Turbine ◽  
Definition Of ◽  
Stage Analysis

This paper studies the origin and applicability of the traditional Stodola ellipse law and demonstrates its deficiencies when applied in certain conditions. It extends the equation by Cooke and Traupel through the definition of a semi-ellipse law. This new law produces more accurate results as compared to the ellipse law (EL), especially for turbines with a low number of stages. It does, however, require knowledge of the choking behavior of the turbine, as well as an appropriate pressure ratio exponent. Through numerical studies and careful application of nozzle flow equations, correlations were developed to predict the critical pressure ratio of a multistage turbine, taking nozzle and blade efficiency into account. Correlations are also presented to obtain an appropriate pressure ratio exponent to use in the semi-ellipse law. A methodology is proposed through which the necessary semi-ellipse law terms can be calculated using only design base conditions and estimates of efficiencies. This was successfully validated on a steam turbine. The semi-ellipse law is believed to be the most accurate way of modeling an axial-flow multistage steam or gas turbine from design base conditions, without requiring a stage-by-stage analysis.

scholarly journals A new method for calculating the sonic conductance of airflow through a short-tube orifice

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401668726 ◽  
Author(s):  
Fan Yang ◽  
Gangyan Li ◽  
Dawei Hu ◽  
Toshiharu Kagawa
Keyword(s):  
Flow Rate ◽  
Critical Pressure ◽  
Pressure Ratio ◽  
Momentum Equation ◽  
Diameter Ratio ◽  
Test Method ◽  
Theoretical Formula ◽  
Engineering Applications ◽  
Short Tube ◽  
Length To Diameter Ratio

In this study, we proposed a method for calculating the sonic conductance of a short-tube orifice. First, we derived a formula for calculating the sonic conductance based on a continuity equation, a momentum equation and the definition of flow-rate characteristics. The flow-rate characteristics of different orifices were then measured using the upstream constant-pressure test method in ISO 6358. Based on these test data, the theoretical formula was simplified using the least squares fitting method, the accuracy of which was verified experimentally. Finally, the effects of the diameter ratio, the length-to-diameter ratio and the critical pressure ratio were analysed with reference to engineering applications, and a simplified formula was derived. We conclude that the influence of the diameter ratio is greater than that of the length-to-diameter ratio. When the length-to-diameter ratio is <5, its effect can be neglected. The critical pressure ratio has little effect on the sonic conductance of a short-tube orifice, and it can be set to 0.5 when calculating the sonic conductance in engineering applications. The formula proposed in this study is highly accurate with a mean error of <3%.

The pressure ratio of critical two-phase flows

1989 ◽  
Vol 12 (1) ◽  
pp. 89-96 ◽  
Author(s):  
Friedhelm Hardekopf ◽  
Dieter Mewes
Keyword(s):  
Pressure Ratio ◽  
Two Phase Flows ◽  
Two Phase

Effects of water ingestion on the tip clearance flow in compressor rotors

2018 ◽  
Vol 233 (11) ◽  
pp. 4235-4246 ◽  
Author(s):  
Lu Yang ◽  
Hai Zhang ◽  
Aqiang Lin
Keyword(s):  
Pressure Ratio ◽  
External Disturbance ◽  
Droplet Breakup ◽  
Tip Clearance ◽  
Suction Surface ◽  
Two Phase ◽  
Tip Clearance Flow ◽  
Water Ingestion ◽  
Clearance Flow ◽  
Compressor Performance

The tip region of compressor rotors may be filled with water when aircraft is flying in heavy rain environment. In order to explore the effects of water ingestion on the compressor performance and the characteristics of tip clearance flow, the Euler–Lagrange method has been utilized to simulate the two-phase flow inside a transonic rotor (NASA rotor 35). The typical trajectory of water droplet in compressor has been introduced firstly to simply understand the situation of water ingestion and to verify the reliability of some special droplet breakup models. The simulation results show that water droplets will change the distribution of airflow parameters along the span direction, which leads to the decrease of mass flow rate and the increase of attack angle at the tip region, as well as the separation of boundary layer on the suction surface. Furthermore, the momentum losses caused by droplet impingement and breakup directly causes a sharp increase in the static entropy at the blade tip region. On the other hand, the ingestion of droplet brings an external disturbance to airflow, and although it has some dissipated effects on the turbulence kinetic energy, it aggravates the unsteady characteristics of turbulent flow seriously at the tip region. Finally, by comparing the compressor performance under wet and dry states, it can be concluded that the pressure ratio and adiabatic efficiency of compressor decrease after water ingestion, and the compression efficiency drops by 1–2% on the whole while the operating point moves forward and the stable working boundary becomes narrow.

Effects of Wet Compression on the Flow Behavior of a Centrifugal Compressor: A CFD Analysis

2014 ◽  
Author(s):  
Anish Surendran ◽  
Heuy Dong Kim
Keyword(s):  
Flow Rate ◽  
Water Droplet ◽  
Evaporation Rate ◽  
Pressure Ratio ◽  
Phase Flow ◽  
Water Droplets ◽  
Compression Process ◽  
Two Phase ◽  
Wet Compression ◽  
Injection Ratio

Wet compression has been emerging as a prominent method for augmenting net power output from land based gas turbine engine. It is proven more effective than the conventional inlet cooling methods. In this method, fine water droplets are injected just upstream of the compressor impeller. These water droplets absorb the latent heat of evaporation during the compression process of gas-water droplet two-phase flow, consequently reducing the temperature rise. Many gas turbine engineers have performed the feasibility and usefulness studies on this wet compression, but physical understanding on the wet compression process is highly lacking, and related compression flow mechanism remains ambiguous. In the present study, a computational fluid dynamics method has been applied to investigate the wet compression effects on a low speed centrifugal compressor. A Langrangian particle tracking method was employed to simulate the air-water droplet two-phase flow. The power saving achieved with different injection ratio of water droplets has been calculated and it is found that significant saving can be obtained with a water droplet injection ratio of above 3%. The vapor mass fraction varies linearly along the streamwise direction, making the assumption for a constant evaporation rate is valid. With the increase in the injection ratio the polytropic index for compression is coming down. The diffuser pressure recovery has been improved significantly with the wet compression; while the total pressure ratio across the impeller does not improve much. Contrary to the expectation, the evaporation rate is found to be coming down with the increase in the compressor mass flow rate. It is observed that the operating point, at which the peak pressure ratio occurs, shift towards higher mass flow rate during wet compression due to the local recirculation region within the vaneless space between the impeller and diffuser.

Steady one-dimensional nozzle flow solutions of liquid–gas mixtures

2013 ◽  
Vol 737 ◽  
pp. 146-175 ◽  
Author(s):  
S. LeMartelot ◽  
R. Saurel ◽  
O. Le Métayer
Keyword(s):  
Two Phase Flow ◽  
Gas Mixtures ◽  
Ideal Gas ◽  
Nozzle Flow ◽  
Pure Liquid ◽  
Phase Flow ◽  
Two Phase ◽  
One Dimensional ◽  
Flow Models ◽  
Relaxation Effects

AbstractExact compressible one-dimensional nozzle flow solutions at steady state are determined in various limit situations of two-phase liquid–gas mixtures. First, the exact solution for a pure liquid nozzle flow is determined in the context of fluids governed by the compressible Euler equations and the ‘stiffened gas’ equation of state. It is an extension of the well-known ideal-gas steady nozzle flow solution. Various two-phase flow models are then addressed, all corresponding to limit situations of partial equilibrium among the phases. The first limit situation corresponds to the two-phase flow model of Kapila et al. (Phys. Fluids, vol. 13, 2001, pp. 3002–3024), where both phases evolve in mechanical equilibrium only. This model contains two entropies, two temperatures and non-conventional shock relations. The second one corresponds to a two-phase model where the phases evolve in both mechanical and thermal equilibrium. The last one corresponds to a model describing a liquid–vapour mixture in thermodynamic equilibrium. They all correspond to two-phase mixtures where the various relaxation effects are either stiff or absent. In all instances, the various flow regimes (subsonic, subsonic–supersonic, and supersonic with shock) are unambiguously determined, as well as various nozzle solution profiles.

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