Computation of the Critical Flow Function, Pressure Ratio, and Temperature Ratio for Real Air

1964 ◽  
Vol 86 (2) ◽  
pp. 169-173 ◽  
Author(s):  
Robert M. Reimer
Keyword(s):  
Critical Temperature ◽  
Speed Of Sound ◽  
Critical Pressure ◽  
Pressure Ratio ◽  
Elevated Pressure ◽  
Stagnation Pressure ◽  
Critical Flow ◽  
Stagnation Temperature ◽  
Flow Function ◽  
Temperature Ratio

A method of computing the critical flow function, critical pressure ratio, and critical temperature ratio is presented. Use is made of the NBS Circular 564 tabulated data of the speed of sound, enthalpy, and compressibility. Computations are made for dry real air at stagnation temperature from 60 to 100 F and stagnation pressure from zero to 300 psia. The change in the flow function and ratios is 0.9, 0.5, and 0.4 percent, respectively, over this range. Calculations are also performed at elevated pressure and temperature.

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.

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%.

The Critical Flow Function for Superheated Steam

1964 ◽  
Vol 86 (3) ◽  
pp. 507-516 ◽  
Author(s):  
J. W. Murdock ◽  
J. M. Bauman
Keyword(s):  
Superheated Steam ◽  
Compressibility Factor ◽  
Practical Method ◽  
Ideal Gas ◽  
Critical Flow ◽  
Stagnation Temperature ◽  
Flow Function ◽  
Critical Function ◽  
Inlet Conditions ◽  
Reduced Coordinates

Computations are made of the theoretical critical flow rate of superheated steam through nozzles or other passages. Flow maximization was used in determining the critical function φ=GT11/2/p1. Tabulations of the critical flow function are given for the “superheated vapor” region defined by Keenan and Keyes “Steam Tables” with a pressure limitation of 5000 psia. Two approaches are presented to relate the critical flow function to an ideal state. In the first approach the temperature of the throttled vapor, from inlet conditions, to a very low pressure (p = 0.08854 psia) was used. The second approach utilized the equivalent ideal-gas stagnation temperature that steam would have if its compressibility factor was unity. A dimensionless correlation on reduced coordinates is presented for the second approach, which permits the correlation of steam data to hydrocarbons or other nonideal gases the compressibility factors of which are available as functions of reduced coordinates. A practical method for calculating theoretical critical flow is presented utilizing the properties of steam as taken directly from the Keenan and Keyes “Steam Tables.”

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.

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%.

Super-Fine Structure in the Critical Flow-Rate of Critical Flow Venturi Nozzles

2002 ◽  
Author(s):  
Masahiro Ishibashi
Keyword(s):  
Fine Structure ◽  
Steady State ◽  
Discharge Coefficient ◽  
Constant Pressure ◽  
Pressure Ratio ◽  
Critical Flow ◽  
Time Intervals ◽  
Critical Flow Rate ◽  
A Value ◽  
Long Time

It is shown that critical flow Venturi nozzles need time intervals, i.e., more than five hours, to achieve steady state conditions. During these intervals, the discharge coefficient varies gradually to reach a value inherent to the pressure ratio applied. When a nozzle is suddenly put in the critical condition, its discharge coefficient is trapped at a certain value then afterwards approaches gradually to the inherent value. Primary calibrations are considered to have measured the trapped discharge coefficient, whereas nozzles in applications, where a constant pressure ratio is applied for a long time, have a discharge coefficient inherent to the pressure ratio; inherent and trapped coefficients can differ by 0.03–0.04%.

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