1、AN AMERICAN NATIONAL STANDARD Measurement of Gas Flow by Means of Critical Flow Venturi Nozzles ASMEIANSI MFC-7M- - 1987 - . REAFFIRMED 1992 FOR CURRENT COMMITTEE PERSONNEL PLEASE SEE ASME MANUAL AS-I 1 SPONSORED AND PUBLISHED BY THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS United Engineering Center
2、 345 East 47th Street New York, N. Y. 1001 7 Date of Issuance: May 31, 1987 This Standard will be revised when the Society approves the issuance of a new edition. There will be no addenda or written interpretations of the requirements of this Standard issued to this edition. This code or standard wa
3、s developed under procedures accredited as meeting the criteria for American National Standards. The Consensus Committee that approved the code or standard was balanced to assure that individuals from competent and concerned interests have had an opportunity to participate. The proposed code or stan
4、dard was made available for public review and comment which provides an opportunity for additional public input from industry, academia, regulatory agencies, and the public-at-large. ASME does not “approve,“ “rate,“ or “endorse“ any item, construction, proprietary device, or activity. ASME does not
5、take any position with respect to the validity of any patent rights asserted in connection with any items mentioned in this document, and does not undertake to insure anyone utilizing a standard against liability for infringement of any applicable Letters Patent, nor assume any such liability. Users
6、 of a code or standard are expressly advised that determination of the validity of any such patent rights, and the risk of infringement of such rights, is entirely their own responsibility. Participation by federal agency representative(s) or person(s) affiliated with industry is not to be interpret
7、ed as government or industry endorsement of this code or standard. ASME accepts responsibility for only those interpretations issued in accordance with governing ASME procedures and policies which preclude the issuance of interpretations by individual volunteers. No part of this document may be repr
8、oduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher. Copyright 0 1987 by THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS All Rights Reserved Printed in U.S.A. FOREWORD (This Foreword is not part of ASME/ANSI MFC-7M-1987.) This Standa
9、rd was prepared by Subcommittee 2, Working Group 5, of the American So- ciety of Mechanical Engineers Committee on Measurement of Fluid Flow in Closed Con- duits. The Committee is indebted to the many engineers who contributed to this work. This Standard is intended to assist the public with the use
10、 of critical flow nozzles. Critical flow nozzles are especially suited to flow calibration work and precise flow control applica- tions. They provide a stable flow of a compressible fluid through a closed conduit, the rate of which may be determined with a high degree of accuracy. The Committee has
11、attempted to blend the best available technical information with common practice to develop this Standard. It is as complete a specification as the Committee determined appropriate. Some latitude and variation on the application of the Standard to critical flow venturi nozzles is allowed. However, n
12、either these liberties nor this Standard is intended to replace proper judgment in the application of critical flow venturi nozzles. This Standard was approved by the American National Standards Institute (ANSI) on February 27, 1987. . 111 ASME STANDARDS COMMITTEE MFFCC Measurement of Fluid Flow in
13、Closed Conduits (The following is the roster of the Committee at the time of approval of this Standard.) OFFICERS R. W. Miller, Chairman W. F. 2. Lee, Vice Chairman C. J. Gomez, Secrerary COMMITTEE PERSONNEL R. B. Abernethy, Pratt or (b) it can be assumed that there is a large space up- stream of th
14、e venturi nozzle. The venturi nozzles specified in this Standard are called primary devices. Other instruments for the measurement are known as secondary devices. This Standard covers primary devices; secondary devices will be mentioned only occasionally. 2 SYMBOLS AND DEFINITIONS 2.1 Symbols The sy
15、mbols used in this Standard are listed in Table 1. 2.2 Definitions 2.2.1 Pressure Measurement wall pressure tap - hole drilled in the wall of a con- duit, the inside edge of which is flush with the inside surface of the conduit static pressure of a gas - the actual pressure of the flowing gas, which
16、 can be measured by connecting a pressure gauge to a wall pressure tap. Only the value of the absolute static pressure is used in this Standard. stagnation pressure of a gas - pressure that would exist in the gas if the flowing gas stream were brought to rest by an isentropic process. Only the value
17、 of the absolute stagnation pressure is used in this Standard. 2.2.2 Temperature Measurement static temperature of a gas - actual temperature of the flowing gas. Only the value of the absolute static temperature is used in this Standard. stagnation temperature of a gas - temperature that would exist
18、 in the gas if the flowing gas stream were brought to rest by an adiabatic process. Only the value of the absolute stagnation temperature is used in this Standard. 2.2.3 Critical Flow Nozzles venturi nozzle - a convergent divergent restriction in- serted in a system intended for the measurement of f
19、low rate throat - the minimum diameter section of the venturi nozzle critical venturi nozzle - a venturi nozzle for which the nozzle geometrical configuration and conditions of use are such that the flow rate is critical 2.2.4 Flow mass flow rate - the mass of gas per unit time passing through the v
20、enturi nozzle. In this Standard, flow rate is always the steady-state or equilibrium mass flow rate. throat Reynolds number - In this Standard the noz- zle throat Reynolds number is calculated from the gas velocity, density at the nozzle throat, and gas viscosity 1 ASME/ANSI MFC-7M-1987 TABLE 1 SYMB
21、OLS MEASUREMENT OF GAS FLOW BY MEANS OF CRITICAL FLOW VENTURI NOZZLES Dimensions SI (Metric) US (Customary) Symbol Description Note (111 Unit Unit A* A2 B c CRi C *; D d e h M Ma Pl p2 PO P* P*; Qm 9m; Area of venturi nozzle throat Area of venturi nozzle exit Bias Coefficient of discharge Critical f
22、low function for one- dimensional isentropic flow of a real gas (Critical flow function for one- dimensional isentropic flow of a perfect gas Real gas critical flow coefficient for one-dimensional real gas flow Diameter of upstream conduit Diameter of venturi nozzle throat Relative uncertainty Speci
23、fic enthalpy of the gas Molecular mass Mach number Absolute static pressure of the gas at the nozzle inlet Absolute static pressure of the gas at nozzle exit Absolute stagnation pressure of the gas at nozzle inlet Absolute static pressure of the gas at nozzle throat Absolute static pressure of the g
24、as at nozzle throat for one- dimensional isentropic flow of a perfect gas Ratio of nozzle exit static pressure to stagnation pressure for one- dimensional isentropic flow of a perfect gas Mass flow rate Mass flow rate for one-dimensional isentropic flow L2 L2 Dimensionless Dimensionless Dimensionles
25、s Dimensionless L L Dimensionless L2 T- M Dimensionless ML-T- ML-T- ML- T- ML- T- ML-T-= Dimensionless MT- MT- m2 m2 . m m J/kg kg/kgmole Pa Pa Pa Pa Pa in. in. . in. in. BTU/lbm Ibm/lbm-mole Ibf/in.* Ibf/in. Ibf/in. Ibf/in. Ibf/in.* Ibm/sec Ibm/sec 2 MEASUREMENT OF GAS FLOW BY MEANS OF CRITICAL FLO
26、W VENTURI NOZZLES ASMElANSl MFC-7M-1987 TABLE 1 SYMBOLS (CONTD) Dimensions SI (Metric) US (Customary) Symbol Description Note (1 11 Unit Unit L2T-2e- J BTU R Universal gas constant kg-mole-K Ibm-mole-OR Red Nozzle throat Reynolds number Dimensionless C Radius of curvature of nozzle inlet L r* Critic
27、al pressure ratio P*/Po S Specific entropy of the gas Dimensionless L2T-2e- T* Absolute static temperature at e nozzle throat ts 5 Two-tailed Students t uRSS, . u95 Uncertainty at the 95% confidence level UADD. . u99 Uncertainty at the 99Y0 confidence level TO Absolute stagnation temperature of e V*
28、 Throat sonic flow velocity LT - V Average fluid velocity LT - the gas Z Compressibility factor Dimensionless ZO Compressibility factor at To and Po Dimensionless CY Temperature probe constant Dimensionless P The ratio of d/D Dimensionless Y Ratio of specific heats Dimensionless m . . K x Isentropic
29、 exponent Dimensionless P* Dynamic viscosity of the gas at ML- T- Pass nozzle throat PO Dynamic viscosity of the gas at ML- 7- stagnation conditions eo Gas density at stagnation condi- ML- tions at nozzle inlet e* Gas density at nozzle throat ML- 0 Standard deviation . Pa-s kgm- kg.m-3 . in. BTUllbm
30、-OR OR . . . OR ft/sec ft/sec Ibm/ft-sec Ibm/ft-sec Ibm/ft3 Ibm/ft3 . 3 ASME/ANSI MFC-7M-1987 MEASUREMENT OF GAS FLOW BY MEANS OF CRITICAL FLOW VENTURI NOZZLES TABLE 1 SYMBOLS (CONTD) Symbol Description Dimensions SI (Metric) US (Customary) Note (111 Unit Unit Superscript * Value at the nozzle throa
31、t at critical flow Subscripts 0 1 2 a d I i m Stagnation property Nozzle inlet Nozzle exit Upstream static condition Nozzle throat Isentropic Any location Mass Critical flow NOTE: (1 1 Fundamental dimensions: M = mass; L = length; T = time; 0 = temperature. at nozzle inlet stagnation condition. The
32、characteristic dimension is taken as the throat diameter at working conditions. Nozzle throat Reynolds number can be de- termined from: isentropic exponent X - the thermodynamic state property defined by wherep and e are the absolute static pressure and den- sity, respectively; v is the local speed
33、of sound; and s refers to constant entropy. For a perfect gas (see Note),this exponent X is the same as the ratio of specific heats y and is equal to Y3 for monatomic gases, 75 for diatomic gases and Y7 for triatomic gases, etc. NOTE: In real gases, the forces exerted between molecules, as well as t
34、he volume occupied by the molecules, have a significant effect on gas behavior. In a perfect gas, intermolecular forces and the vol- ume occupied by the molecules are neglected. discharge coefficient - the dimensionless ratio of the actual flow rate to the ideal flow rate that would be ob- tained wi
35、th one-dimensional isentropic flow for the same upstream stagnation conditions. This coefficient corrects for viscous and flow field curvature effects. For the nozzle design and installation conditions spec- ified in this Standard, it is a function of the throat Reynolds number only. critical flow -
36、 the maximum flow rate for a particular venturi nozzle that can exist for the given upstream conditions. When critical flow exists, the throat veloc- ity is equal to the local value of the speed of sound (acoustic velocity), the velocity at which small pres- sure disturbances propagate. isentropic p
37、erfect gas critical flow function - a di- mensionless function that characterizes the thermody- namic flow properties along an isentropic and 4 MEASUREMENT OF GAS FLOW BY MEANS OF CRITICAL FLOW VENTURI NOZZLES ASME/ANSI MFC-7M-1987 one-dimensional path between inlet and throat. It is a function of t
38、he nature of the gas and of stagnation conditions. (Y + 1)4Y - 1) . c,; = J Y(*) isentropic real gas critical flow function - a dimen- sionless function that characterizes the thermody- namic flow properties of a real gas along an isentropic one-dimensional path between the nozzle inlet and throat.
39、It is a function of the nature of the real gas and of the stagnation conditions. The function is the isen- tropic perfect gas critical flow function divided by the square root of the compressibility factor for the real gas. CRi = c*j/fi real gas critical flow coefficient - a flow coefficient defined
40、 by the equation shown below The real gas critical flow coefficient is often estimated by the isentropic real gas critical flow function. A method of computing CR is presented in Appendix E along with some references for a selection of fluids. Appendix D presents a discussion of the various criti- c
41、al flow functions and coefficients. criticalpressure ratio - the ratio of the absolute static pressure at the nozzle throat to the absolute stagnation pressure for which gas mass flow through the nozzle is a maximum chokingpressureratio - the ratio of the absolute noz- zle exit static pressure to th
42、e absolute nozzle upstream pressure at which the flow becomes critical Mach number - the ratio of the fluid velocity to the velocity of sound in the fluid at the same temperature and pressure 3 BASIC EQUATIONS 3.1 State Equation The behavior of a real gas can be described by: p/e = (R/M)TZ 3.2 Flow
43、Rate in Ideal Conditions Ideal critical flow rates require three main condi- (a) the flow is one-dimensional; (b) the flow is isentropic; and (e) the gas is perfect (Z = 1 and x = y). Under these conditions, the value of critical flow tions: rate is where 3.3 Flow Rate in Real Conditions For the cri
44、tical flow of real gases the foregoing for- mulae become A*CC,P, or In practice sometimes CR is estimated by CRi. How- ever, it should be noted that CRi and Gi are not equal to CR because the gas is not perfect and C is less than unity since the flow is not one-dimensional and a boundary layer exist
45、s due to viscous effects. 4 APPLICATIONS FOR WHICH THE METHOD IS SUITABLE Each application should be evaluated to determine whether a critical fl0.w venturi nozzle or some other device is more suitable. An important consideration is that the flow through the venturi nozzle is indepen- dent of the do
46、wnstream pressure within the pressure 5 ASME/ANSI MFC-7M-1987 range for which the venturi nozzle can be used for crit- ical flow measurement. The following are some other considerations. (a) For critical flow nozzles, the only measure- ments required are the pressure and temperature or density upstr
47、eam of the critical venturi nozzle, as the throat conditions can be calculated from thermody- namic considerations. Care must be taken when using an equation of state at or near the dew point of the gas. However, no evidence has been presented that would indicate that the correct operation of the cr
48、itical flow nozzle is affected. Furthermore, studies have shown that condensation rates in the.presence of favorable pressure gradients and rapidly falling temperatures are much slower than the transit time of the fluid from the nozzle entrance to the nozzle throat. Therefore, the critical flow nozz
49、le will operate correctly and yield the correct flow, provided that the calculation for the speed of sound and density at the throat is correct. (b) The velocity in the critical venturi nozzle throat is the maximum possible for the given upstream stag- nation conditions; therefore, the sensitivity to instal- lation effects is minimized, except for swirl, which must not exist in the inlet part of the venturi nozzle. (c) When comparing sonic venturi nozzles with subsonic pressure difference meters, it can be noted that in the case of the critical nozzle, th
