Bsi bs en 60534 2 1 2011 (2015)

BS EN 60534-2-1:2011 Incorporating corrigendum April 2015 BS EN 60534-2-1:2011 BSI Standards Publication Industrial-process control valves Part 2-1: Flow capacity — Sizing equations for fluid flow under installed conditions BS EN 60534-2-1:2011 BRITISH STANDARD National foreword This British Standard is the UK implementation of EN 60534-2-1:2011 It is identical to IEC 60534-2-1:2011, incorporating corrigendum April 2015 It supersedes BS EN 60534-2-1:1999 which is withdrawn The start and finish of text introduced or altered by corrigendum is indicated in the text by tags Text altered by IEC corrigendum April 2015 is indicated in the text by  The UK participation in its preparation was entrusted by Technical Committee GEL/65, Measurement and control, to Subcommittee GEL/65/2, Elements of systems A list of organizations represented on this subcommittee can be obtained on request to its secretary This publication does not purport to include all the necessary provisions of a contract Users are responsible for its correct application © The British Standards Institution 2015 Published by BSI Standards Limited 2015 ISBN 978 580 90345 ICS 23.060.40; 25.040.40 Compliance with a British Standard cannot confer immunity from legal obligations This British Standard was published under the authority of the Standards Policy and Strategy Committee on 30 September 2011 Amendments/corrigenda issued since publication Date Text affected 30 June 2015 Implementation of IEC corrigendum April 2015 EN 60534-2-1 EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM May 2011 ICS 23.060.40; 25.040.40 Supersedes EN 60534-2-1:1998 English version Industrial-process control valves Part 2-1: Flow capacity Sizing equations for fluid flow under installed conditions (IEC 60534-2-1:2011) Vannes de régulation des processus industriels Partie 2-1: Capacité d'écoulement Equations de dimensionnement pour l'écoulement des fluides dans les conditions d'installation (CEI 60534-2-1:2011) Stellventile für die Prozessregelung Teil 2-1: Durchflusskapazität Bemessungsgleichungen für Fluide unter Betriebsbedingungen (IEC 60534-2-1:2011) This European Standard was approved by CENELEC on 2011-05-04 CENELEC members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the Central Secretariat or to any CENELEC member This European Standard exists in three official versions (English, French, German) A version in any other language made by translation under the responsibility of a CENELEC member into its own language and notified to the Central Secretariat has the same status as the official versions CENELEC members are the national electrotechnical committees of Austria, Belgium, Bulgaria, Croatia, Cyprus, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and the United Kingdom CENELEC European Committee for Electrotechnical Standardization Comité Européen de Normalisation Electrotechnique Europäisches Komitee für Elektrotechnische Normung Management Centre: Avenue Marnix 17, B - 1000 Brussels © 2011 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members Ref No EN 60534-2-1:2011 E BS EN 60534-2-1:2011 EN 60534-2-1:2011 BS EN 60534-2-1:2011 –2– EN 60534-2-1:2011 -2- Foreword The text of document 65B/783/FDIS, future edition of IEC 60534-2-1, prepared by SC 65B, Devices & process analysis, of IEC TC 65, Industrial-process measurement, control and automation, was submitted to the IEC-CENELEC parallel vote and was approved by CENELEC as EN 60534-2-1 on 2011-05-04 This European Standard supersedes EN 60534-2-1:1998 EN 60534-2-1:2011 includes EN 60534-2-1:1998: the following significant technical changes with respect to — the same fundamental flow model, but changes the equation framework to simplify the use of the standard by introducing the notion of ∆psizing; — changes to the non-turbulent flow corrections and means of computing results; — multi-stage sizing as an Annex Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights CEN and CENELEC shall not be held responsible for identifying any or all such patent rights The following dates were fixed: – latest date by which the EN has to be implemented at national level by publication of an identical national standard or by endorsement (dop) 2012-02-04 – latest date by which the national standards conflicting with the EN have to be withdrawn (dow) 2014-05-04 Annex ZA has been added by CENELEC Endorsement notice The text of the International Standard IEC 60534-2-1:2011 was approved by CENELEC as a European Standard without any modification –3– BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 EN 60534-2-1:2011 -3- EN 60534-2-1:2011 Annex ZA (normative) Normative references to international publications with their corresponding European publications The following referenced documents are indispensable for the application of this document For dated references, only the edition cited applies For undated references, the latest edition of the referenced document (including any amendments) applies NOTE When an international publication has been modified by common modifications, indicated by (mod), the relevant EN/HD applies Publication Year Title EN/HD IEC 60534-1 2005 Industrial-process control valves EN 60534-1 Part 1: Control valve terminology and general considerations 2005 IEC 60534-2-3 1997 Industrial-process control valves Part 2-3: Flow capacity - Test procedures 1998 EN 60534-2-3 Year BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 –4– –2– 60534-2-1  IEC:2011 CONTENTS FOREWORD Scope Normative references Terms and definitions Symbols 10 Installation 11 12 Sizing equations for incompressible fluids 10 6.1 6.2 12 Turbulent flow 10 13 Pressure differentials 11 13 Sizing pressure differential, ∆ p sizing 11 13 6.2.2 Choked pressure differential, ∆ p choked 11 13 6.2.3 Liquid critical pressure ratio factor, F F 11 13 6.3 Non-turbulent (laminar and transitional) flow 11 13 Sizing equations for compressible fluids 11 6.2.1 7.1 7.2 13 General 11 14 Pressure differentials 12 14 7.2.1 Sizing pressure drop ratio, x sizing 12 14 7.2.2 Choked pressure drop ratio, x choked 12 14 7.3 Specific heat ratio factor, F γ 12 15 7.4 Expansion factor, Y 13 15 7.5 Compressibility factor, Z 13 16 7.6 Non-turbulent (laminar and transitional) flow 14 16 Correction factors common to both incompressible and compressible flow 14 16 Piping geometry correction factors 14 16 Estimated piping geometry factor, F P 14 Estimated combined liquid pressure recovery factor and piping geometry factor with attached fittings, F LP 15 17 18 8.4 Estimated pressure differential ratio factor with attached fittings, x TP 16 18 Reynolds Number, Re V 16 20 Annex A (normative) Sizing equations for non-turbulent flow 18 8.1 8.2 8.3 23 Annex B (normative) Sizing equations for fluid flow through multistage control valves 21 31 Annex C (informative) Piping factor computational considerations 28 36 Annex D (informative) Engineering Data 34 43 Annex E (informative) Reference calculations 41 56 Bibliography 54 12 Figure – Reference pipe section for sizing 10 25 Figure B.1 – Multistage multipath trim 23 26 Figure B.2 – Multistage single path trim 24 Figure B.3 – Disk from a continuous resistance trim The complete trim consists of a number of these disks stacked together 25 27 Figure B.4 – Sectional view of continuous resistance trim with multiple flow passages 27 having vertical undulations 25 Figure C.1 – Determination of the upper limit of the flow coefficient by the iterative 34 method 32 –5– 60534-2-1  IEC:2011 BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 –3– 35 Figure C.2 – Determination of the final flow coefficient by the iterative method 33 39 Figure D.1 – Piping geometry factors 37 41 Figure D.2 – Pressure recovery factors 39 Figure D.3 – Liquid critical pressure ratio factor F F 40 42 19 Table – Numerical constants N 17 Table B.1 – Values of the stage interaction factors, k, and the reheat factors, r for 29 multistage single and multipath control valve trim 27 Table B.2 – Values of the stage interaction factors, k, and the reheat factors, r for 29 continuous resistance control valve trim 27 33 Table C.1 – Incompressible flow 31 33 Table C.2 – Compressible flow 31 Table D.1 – Typical values of valve style modifier F d , liquid pressure recovery factor F L 37 and pressure differential ratio factor x T at full rated travel a) 35 BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 –6– –4– 60534-2-1  IEC:2011 INTERNATIONAL ELECTROTECHNICAL COMMISSION INDUSTRIAL-PROCESS CONTROL VALVES – Part 2-1: Flow capacity – Sizing equations for fluid flow under installed conditions FOREWORD 1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising all national electrotechnical committees (IEC National Committees) The object of IEC is to promote international co-operation on all questions concerning standardization in the electrical and electronic fields To this end and in addition to other activities, IEC publishes International Standards, Technical Specifications, Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC Publication(s)”) Their preparation is entrusted to technical committees; any IEC National Committee interested in the subject dealt with may participate in this preparatory work International, governmental and nongovernmental organizations liaising with the IEC also participate in this preparation IEC collaborates closely with the International Organization for Standardization (ISO) in accordance with conditions determined by agreement between the two organizations 2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international consensus of opinion on the relevant subjects since each technical committee has representation from all interested IEC National Committees 3) IEC Publications have the form of recommendations for international use and are accepted by IEC National Committees in that sense While all reasonable efforts are made to ensure that the technical content of IEC Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any misinterpretation by any end user 4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications transparently to the maximum extent possible in their national and regional publications Any divergence between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in the latter 5) IEC itself does not provide any attestation of conformity Independent certification bodies provide conformity assessment services and, in some areas, access to IEC marks of conformity IEC is not responsible for any services carried out by independent certification bodies 6) All users should ensure that they have the latest edition of this publication 7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and members of its technical committees and IEC National Committees for any personal injury, property damage or other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC Publications 8) Attention is drawn to the Normative references cited in this publication Use of the referenced publications is indispensable for the correct application of this publication 9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of patent rights IEC shall not be held responsible for identifying any or all such patent rights International Standard IEC 60534-2-1 has been prepared by subcommittee 65B: Measurement and control devices, of IEC technical committee 65: Industrial-process measurement, control and automation This second edition cancels and replaces the first edition published in 1998 This edition constitutes a technical revision This edition includes the following significant technical changes with respect to the previous edition: • the same fundamental flow model, but changes the equation framework to simplify the use of the standard by introducing the notion of ∆ p sizing ; • changes to the non-turbulent flow corrections and means of computing results; • multi-stage sizing as an Annex The text of this standard is based on the following documents: BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 –7– 60534-2-1  IEC:2011 –5– FDIS Report on voting 65B/783/FDIS 65B/786/RVD Full information on the voting for the approval of this standard can be found in the report on voting indicated in the above table This publication has been drafted in accordance with the ISO/IEC Directives, Part A list of all the parts of the IEC 60534 series, under the general title Industrial-process control valves, can be found on the IEC website The committee has decided that the contents of this publication will remain unchanged until the stability date indicated on the IEC web site under "http://webstore.iec.ch" in the data related to the specific publication At this date, the publication will be • • • • reconfirmed, withdrawn, replaced by a revised edition, or amended BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 –8– –6– 60534-2-1  IEC:2011 INDUSTRIAL-PROCESS CONTROL VALVES – Part 2-1: Flow capacity – Sizing equations for fluid flow under installed conditions Scope This part of IEC 60534 includes equations for predicting the flow of compressible and incompressible fluids through control valves The equations for incompressible flow are based on standard hydrodynamic equations for Newtonian incompressible fluids They are not intended for use when non-Newtonian fluids, fluid mixtures, slurries or liquid-solid conveyance systems are encountered The equations for incompressible flow may be used with caution for non-vaporizing multi-component liquid mixtures Refer to Clause for additional information At very low ratios of pressure differential to absolute inlet pressure (∆p/p ), compressible fluids behave similarly to incompressible fluids Under such conditions, the sizing equations for compressible flow can be traced to the standard hydrodynamic equations for Newtonian incompressible fluids However, increasing values of ∆p/p result in compressibility effects which require that the basic equations be modified by appropriate correction factors The equations for compressible fluids are for use with ideal gas or vapor and are not intended for use with multiphase streams such as gas-liquid, vapor-liquid or gas-solid mixtures Reasonable accuracy can only be maintained when the specific heat ratio, γ , is restricted to the range 1,08 < γ < 1,65 Refer to Clause 7.2 for more information For compressible fluid applications, this standard is valid for valves with x T ≤ 0,84 (see Table D.2) For valves with x T > 0,84 (e.g some multistage valves), greater inaccuracy of flow prediction can be expected Reasonable accuracy can only be maintained for control valves if: C < 0,047 N18 d Note that while the equation structure utilized in this document departs radically from previous versions of the standard, the basic technology is relatively unchanged The revised equation format was adopted to simplify presentation of the various equations and improve readability of the document Normative references The following referenced documents are indispensable for the application of this document For dated references, only the edition cited applies For undated references, the latest edition of the referenced document (including any amendments) applies IEC 60534-1:2005, Industrial-process control valves – Part 1: Control valve terminology and general considerations IEC 60534-2-3:1997, Industrial-process control valves – Part 2-3: Flow capacity – Test procedures BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 – 44 – – 42 – 60534-2-1  IEC:2011 The liquid critical pressure ratio factor, F F , should be determined using Equation (4): = FF 0,96 − 0,28 pv = 0,944 pc Since the valve is line-sized, F P =1 and F LP =F L The choked pressure differential, ∆ p choked , should be determined using Equation (3):  FLP    ( p1 − FF pv ) = ∆pchoked = 497 kPa  FP  Next, the sizing pressure differential, ∆ p sizing , should be determined using Equation (2): ∆p = p1 − p2 = 460 kPa ∆p  ∆psizing =  ∆p  choked if ∆p < ∆pchoked if ∆p ≥ ∆pchoked ∆psizing = 460 kPa It should be solved for K v after rearranging Equation (1): ρ1 ρo Q C= Kv = N1 FP ∆p sizing where ρ o is the density of water at 15 °C K v = 165 m h Next, it should be verified that the flow is turbulent by calculating the Reynolds number, Re v , using Equation (23): 1/  N F Q  F 2C Rev = d  L += 1 2,97×10 ν C FL  N d  Since Rev ≥ 10 000 the flow is turbulent It should be verified that the result is within the applicable scope of the standard: C = 0,0085 < 0,047 N18 d BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 – 45 – 60534-2-1  IEC:2011 – 43 – Example 2: Incompressible flow – choked flow without attached fittings, solve for Kv Process data: Fluid: water Inlet temperature: T = 363 K Density: ρ1 = 965,4 kg/m Vapour pressure: p v = 70,1 kPa Thermodynamic critical pressure: p c = 22 120 kPa Kinematic viscosity: ν = 3,26 × 10 –7 m /s Inlet absolute pressure: p = 680 kPa Outlet absolute pressure: p = 220 kPa Flow rate: Q = 360 m /h Pipe size: D = D = 100 mm Valve data: Valve style: ball valve Trim: segmented ball Flow direction: flow-to-open Valve size: d = 100 mm Liquid pressure recovery factor: F L = 0,60 (from Table D.2) Valve style modifier: F d = 0,98 (from Table D.2) Calculations: The applicable flow model for incompressible fluids in the turbulent flow regime is given in Equation (1): Q = CN1 FP ∆p sizing ρ1 ρo From Table 1, the numerical constants to use with the given dataset are: N = 1×10 –1 N = 1,60×10 –3 N = 7,07×10 –2 N 18 = 8,65×10 –1 The liquid critical pressure ratio factor, F F , should be determined using Equation (4): = FF 0,96 − 0,28 pv = 0,944 pc Since the valve is line-sized, F P =1 and F LP =F L The choked pressure differential, ∆ p choked , should be determined using Equation (3): BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 – 46 – – 44 – 60534-2-1  IEC:2011  FLP    ( p1 − FF pv ) = ∆pchoked = 221 kPa  FP  Next, the sizing pressure differential, ∆ p sizing , should be determined using Equation (2): ∆p = p1 − p2 = 460 kPa ∆psizing ∆p  =  ∆p  choked if ∆p < ∆pchoked if ∆p ≥ ∆pchoked ∆psizing = 221 kPa It should be solved for K v after rearranging Equation (1): ρ1 ρo Q C= Kv = N1 FP ∆p sizing where ρ o is the density of water at 15 °C K v = 238 m h Next, it should be verified that the flow is turbulent by calculating the Reynolds number, Re v , using Equation (23): 1/ Rev = N Fd Q  FL C  += 1 6,60×10  ν C FL  N d  Since Re v ≥ 10 000 the flow is turbulent It should be verified that the result is within the scope of the standard: C = 0,028 < 0,047 N18 d Example 3: Compressible flow – non-choked flow, solve for K v Process data: Fluid: carbon dioxide gas Inlet temperature: T = 433 K Inlet absolute pressure: p = 680 kPa Outlet absolute pressure: p = 450 kPa Kinematic viscosity: ν = 2,526×10 –6 m /s at 680 kPa and 433 K Flow rate: Q s = 800 standard m /h at 101,325 kPa and 273 K Density: ρ = 8,389 kg/m at 680 kPa and 433 K Compressibility: Z = 0,991 at 680 kPa and 433 K Standard compressibility: Zs = 0,994 at 101,325 kPa and 273 K Molecular mass: M = 44,01 Specific heat ratio: γ = 1,30 Pipe size: D = D = 100 mm BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 – 47 – 60534-2-1  IEC:2011 – 45 – Valve data: Valve style: rotary Trim: eccentric spherical plug Flow direction: flow-to-open Valve size: d = 100 mm Pressure differential ratio factor: x T = 0,60 (from Table D.2) Liquid pressure recovery factor: F L = 0,85 (from Table D.2) Valve style modifier: F d = 0,42 (from Table D.2) Calculations: The applicable flow model for compressible fluids in the turbulent flow regime with the dataset given is found in Equation (7): Qs = CN FP p1Y xsizing MT1Z1 From Table 1, the numerical constants to use with the given dataset are: N = 1,60×10 –3 N = 7,07×10 –2 N = 2,46×10 N 18 = 8,65×10 –1 Since the valve is line-sized, F P = and x TP = x T The specific heat ratio factor, F γ , should be calculated using Equation (11): γ = 0,929 Fγ = 1,40 The choked pressure drop ratio, x choked , should be determined using Equation (10): 0,557 xchoked = Fγ xTP = Next, the sizing pressure drop ratio, x sizing , should be determined using Equations (8) and (9): x= xsizing p1 − p2 = 0,338 p1 x  = x  choked if x < xchoked if x ≥ xchoked xsizing = 0,338 The expansion factor, Y, should be calculated using Equation (12): xsizing Y= = 0,798 1− xchoked BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 In Example 3, under Calculations, replace Dans l'Exemple 3, sous Calculs, r the existing equation calculating actual l'équation permettant d'obtenir volumetric flow rate volumétrique réel p1 Z sTs – 48 – p Z Ts C O R R I GQE= N Q = Qs = 16 100 m3 h = 16 100 m3 h QsD U1 M s Z1T1 ps Z1T1 ps – 46 – 60534-2-1  IEC:2011 by the following new equation: par la nouvelle équation suivante: IEC 60534-2-1:2011-03/COR1:2015-04(en-fr) IEC 60534-2-1:2011-03/COR1:2015-04(en-fr) It should be solved for K v after rearranging p s Z1T1Equation (7): p s Z 1T1 = 895,4 m h Q = Qs Q = Qs = 895,4 m h Z s Ts p1 Z s Ts Ep1Calculs de référe Annex E Reference calculations Annexe Q MT1Z1 C= K v =s In Example under replace Dans l'Exemple 3, sous Calc N3, F p Y xCalculations, P sizing the existing equation calculating actual l'équation permettant d'ob flow volumétrique Également dansréell'Exemple Also volumetric in Example 3, rate under Calculations, Calculs, changer change the K =Z67 p1v corresponding T,s2 m h p1 Z sTl'équation Reynolds s s = 16 100 mp Q = Rev, Qs calculation = 16using 100 mtheh correct Q = Qle s d'obtenir de Reyn Number, Z1T1 ps Z1Tnombre p s utilisant la valeur correcte de Q value for Q The actual volumetric flow rate should be found: by the following new equation: de par la nouvelle équation suiv from pps ZZsTTs 33 p Z T 100  QQ==QQs s 1 ==16895 1/ 4,4mm h h / ,4 m Q = Q s  s 12 =1895   N Fd Z QZs1TT1sFL ppCs1 N F Q F Cp1 Z T d L s s += Rev = += 1 2,52 ×10 Rev = 1 2,5   ν C FL  N d ν C FL  N d   Next, it should be verified that the flow is turbulent by calculating the Reynolds number, Re v , using Equation (23): to en Également dans l'Exem Also in Example 3, under Calculations, Calculs, changer l'équatio change the corresponding Reynolds 1/ /14/ 22  F  de  d'obtenir Number, calculation using 7the NN FF QQRev, C N Fd Q leFL 2nombre C2 FLL C correct d d ReRe ,40 = ×10  +11  2,1 52 = += ×10 += Re v =utilisant la valeur correcte 1  v = vvalue de ν ν CCfor FLFLQ N d   ν C FL  N d de from Since Rev ≥ 10 000 the flow is turbulent 1/ 1/   N Fd Q  FL C N Fd Q  FL C + 1 Rev = += 1 2,52 ×10 Rev =   It should be verified that the result is within the scope4 of the ν C FL  N d ν CF  standard:  L  N d C to = 0,0078 < 0,047 N18 d 1/  N Fd Q  FL C = 1,40 ×10 Re = +1   4solve for K v Example 4: Compressible flowv– choked flow, ν C FL  N d  Process data: Fluid: Inlet temperature: en Re v =  N Fd Q  FL C  + 1  ν C FL  N d carbon dioxide gas T = 433 K Inlet absolute pressure: p = 680 kPa Outlet absolute pressure: p = 250 kPa Kinematic viscosity: ν = 2,526×10 –6 m /s at 680 kPa and 433 K Flow rate: Q s = 800 standard m /h at 101,325 kPa and 273 K Density: ρ = 8,389 kg/m at 680 kPa and 433 K Density at standard conditions: ρ s = 1,978 kg/m at 101,325 kPa and 273 K Compressibility: Z = 0,991 at 680 kPa and 433 K Standard compressibility: Zs = 0,994 at 101,325 kPa and 273 K Molecular mass: M = 44,01 Specific heat ratio: γ = 1,30 Pipe size: D = D = 100 mm Valve data: Valve style: rotary Trim: eccentric spherical plug BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 – 49 – 60534-2-1  IEC:2011 – 47 – Flow direction: flow-to-open Valve size: d = 100mm Pressure differential ratio factor: x T = 0,60 (from Table D.2) Liquid pressure recovery factor: F L = 0,85 (from Table D.2) Valve style modifier: F d = 0,42 (from Table D.2) Calculations: The applicable flow model for compressible fluids in the turbulent flow regime with the dataset given is found in Equation (7): Qs = CN FP p1Y xsizing MT1Z1 From Table 1, the numerical constants to use with the given dataset are: N = 1,60×10 –3 N = 7,07×10 –2 N = 2,46×10 N 18 = 8,65×10 –1 Since the valve is line-sized, F P = and x TP = x T The specific heat ratio factor, F γ , should be calculated using Equation (11): γ Fγ = = 0,929 1,40 The choked pressure drop ratio, x choked , should be determined using Equation (10): 0,557 xchoked = Fγ xTP = Next, the sizing pressure drop ratio, x sizing , should be determined using Equations (8) and (9): x= xsizing p1 − p2 = 0,632 p1 x  = x  choked if x < xchoked if x ≥ xchoked xsizing = 0,557 The expansion factor, Y, should be calculated using Equation (12): xsizing Y= = 0,667 1− xchoked It should be solved for K v after rearranging Equation (7): BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 calculating actual volumetric flow rate p1 Z sTs Q = Qs = 16 100 m3 h Z1T1 ps – 50 – by the following new equation: le débit volumétrique réel p Z sTs = 16 100 m3 h Q = Qs Z1T1 ps par la nouvelle équation suivante: 60534-2-1  IEC:2011 p s Z1T1 – 48 – Q = Qs = 895,4 m h –Q2=–Q p s Z1T1 IEC 60534-2-1:20 Z s Ts p1 = 895 ,4 m h s Z T p s s Q MT1Z1 C= K v =s Similarly, 4, under N FinP p1Y Example xsizing De même, dans l'Exemple Calculations, replace the existing equation remplacerdans l'équation perme4 Également l'Exemple actual flow rate Also calculating in Example 4, under volumetric Calculations, le débit volumétrique réel Calculs, changer l'équation change thepK1v =Zexisting 62 m h corresponding sT,s6 = permettant pd'obtenir le nom Z sTs Q = Q 16 100 m3 h s Reynolds Number =utilisant 16 100 m3l Q = Qs(Re1 ) en Z1T1 ps(Re v ) calculation using Reynolds Z1Tv1 ps the correct value for Q The actual volumetric flow rate should be found: correcte de Q by the following new equation: par la nouvelle équation suiv from de pps1 ZZs1TTs1 895 ,4mm33hh  ==16 100  QQ= =QQ ss p s Z1T1 1/ ZZs1TTs1 p2ps1 1,/44 m Q = Qs = 895    F 2pC N Fd Q  FL C N F Q Z T 1 2,61×10 Re v = +=  1 2, Re v = d s s L + = ν C FL  N d  ν C FL Re   N, d Next, it should be verified that the flow is turbulent by calculating the Reynolds number, v using Equation (23): Également dans l'Exem to Also in Example 4, under Calculations, en Calculs, changer l'équat change the existing corresponding permettant d'obtenir le 11/ /4 22 22   1/ calculation using Reynolds Number (Re   NN F Q ) F C F Q FLL v )2 en utilisa d d Reynolds (Re ReRe 1 ,45×10 ×10   1= 21 ,61 = ++= N Fd Q  F Cv v = vthe L 1 1,4 Rev =correcte de +=  Q ν νcorrect CCFLFL  value NN22 d forQ ν C FL  N d  from de Since Re v ≥ 10 000 the flow is turbulent 1/  N Fd Q  FL C = 1 standard: 2,61×10 Reis v =within the scope4 of+the It should be verified that the result ν C FL  N d   N F Q  F 2C2 Re v = d  L + 1 ν C FL  N d  1/ C = 0,0073 < 0,047 en N18 d 1/  1/ N F Q  F 2C2  F 2C2  1 1,45 ×10 Rev = d  L += N F Q d L with attached fittings Re = + 1  Example 5: Incompressible fluid –ν choked C FL  Nflow v 2d  ν C FL  N d  Process data: to Fluid: unspecified Density: ρ1 = 780 kg/m Vapour pressure: p v = kPa Thermodynamic critical pressure: p c = 22 120 kPa Inlet absolute pressure: p =3 550 kPa Outlet absolute pressure: p = 240 kPa Flow rate: Q = 150 m /h Upstream Pipe size: D = 154,1 mm Downstream Pipe size: D = 202,7 mm Valve data: Valve style: Butterfly Valve size: d = 101,6 mm Flow Coefficient Data: BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 – 51 – 60534-2-1  IEC:2011 – 49 – Rotation 10 20 30 40 50 60 70 80 90 Cv 17,2 50,2 87,8 146 206 285 365 465 521 FL 0,85 0,85 0,84 0,79 0,75 0,71 0,63 0,58 0,56 0,54 The value of F L at shutoff was fixed at the value for 10 degrees to allow calculations within the to 10 degree interval Calculations: The following solution schema is based on the iterative method of Clause C.2 The governing equation is presented followed by the computed result based on the current values of all constitutive variables Constant Values: The following variables and terms are either constant or remain constant under the conditions supplied above N = 0,0865 N = 0,00214 N 18 = 1,00 Equation (4): pv = 0,956 pc = FF 0.96 − 0.28 Equation (18):   d 2  = ζ 0,51 −    = 0,160   D1     Equation (19):   d 2    = 0,561 = ζ 1 −    D2      d  Equation (17): ζ= B1 −   D  = 0,811  1 Equation (17): ζ= B2 −   D  = 0,937  2  d  Step 1: A flow function per Equation (C.2) should be defined: Equation (C.2): F (c) 750 − (c) N1FP = ∆psizing ρ1 ρo The root of this function corresponds to the solution for the supplied parameters Note that F P and ∆p sizing values will also change with each iteration BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 – 52 – – 50 – 60534-2-1  IEC:2011 Step 2: A lower flow interval limit per C.2.2 should be set: Set lower limit: CLower = From valve data: FL _ Lower = 0,85 Equation (15): FP_Lower = Equation (21): FLP_Lower = Σζ  C Lower  1+   N2  d  FL_Lower 1+ Equation (3): Equation (2): Function Value: = 1,0 ∆pchoked _ Lower ∆psizing _ Lower FL_Lower N2  (Σζ ) C Lower    d  FLP _ Lower =  FP _ Lower  = 0,85   ( p1 − FF pv ) = 418   ∆p  = ∆p  choked _ Lower FLower = Q − C Lower N1 FP _ Lower if ∆p < ∆pchoked _ Lower = 240 if ∆p ≥ ∆pchoked _ Lower ∆p sizing _ Lower ρ1 = 750 ρo Step 3: An upper flow interval limit per C.2.3 should be set: Set upper limit: CUpper = 0,075 d N18 = 774,192 From valve data: FL _ Upper = 0,54 Equation (15): Fp _ Upper = Equation (21): FLP_Upper = Σζ  CUpper  1+ N  d     = 0,625 FL_Upper 1+ FL_Upper N2 C (Σζ ) Upper  d     = 0,409 BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 – 53 – 60534-2-1  IEC:2011 Equation (3): Equation (2): Function Value: – 51 –  FLP _ Upper =  FP _ Upper  ∆pchoked _ Upper ∆psizing _ Upper   ( p1 − FF pv ) = 520   ∆p  = ∆p  choked _ Upper FUpper = Q − CUpper N1FP _ Upper if ∆p < ∆pchoked _ Upper = 1520 if ∆p ≥ ∆pchoked _ Upper ∆psizing _ Upper = −1,096 × 103 ρ1 ρo Step 4: It should be checked that interval bounds a solution per C.2.4: F Upper = -1,096 × 10 F Lower = 750 F Upper and F Lower are of opposite sign, therefore the selected interval bounds a solution to the problem Step 5: The interval mid-point and associated values should be computed: CUpper + C Lower Compute mid-point: C Mid = From valve data: FL _ Mid = 0,576 Equation (15): F p _ Mid = Equation (21): FLP_Mid = Σζ  C Mid  1+   N2  d  Equation (2): FL_Mid = 0,848 N2  (Σζ ) CMid   d   FLP _ Mid ∆pchoked _ Mid =   FP _ Mid  ∆p sizing _ Mid FL_Mid 1+ Equation (3): = 387,096 = 0,523   ( p1 − FF pv ) = 349   ∆p  = ∆p  choked _ Mid if ∆p < ∆pchoked _ Mid = 349 if ∆p ≥ ∆pchoked _ Mid BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 – 54 – – 52 – 60534-2-1  IEC:2011 F= Q − C Mid N1 FP _ Mid Mid Function Value: ∆p sizing _ Mid = −430,7 ρ1 ρo Step 6: The interval definition should be revised per C.2.5 It should be iterated until satisfactory convergence is achieved: F Upper = -1,096 × 10 F Mid = -430,7 F Lower = 750 Since the sign of the upper and midpoint function values are the same, the upper interval limit is set equal to the midpoint value and associated terms adjusted accordingly: C Upper = C Mid = 387,096 F L_Upper = F L_Mid = 0,576 F P_Upper = F P_Mid = 0,848 F LP_Upper = F LP_Mid = 0,523 ∆p choked_Upper = ∆p choked_Mid = 349 ∆p sizing_Upper = ∆p sizing_Mid = 349 F Upper = F Mid = -430,7 Repeat steps and until converged to solution Iteration summary: Iteration C Lower C Mid C Upper Mid-Point Values FL Fp F LP ∆p choked ∆p sizing F Mid 387 774 0,576 0,848 0,523 349 349 -431 194 387 0,718 0,954 0,690 856 856 -29,4 96,8 194 0,784 0,988 0,774 179 179 313 96,8 145 194 0,751 0,974 0,732 006 006 130 130 169 194 0,734 0,965 0,711 929 929 47,3 169 181 194 0,726 0,960 0,701 892 892 8,23 181 188 194 0,722 0,957 0,696 874 874 -10,8 181 184 188 0,724 0,958 0,698 883 883 -1,32 181 183 184 0,725 0,959 0,700 887 887 3,44 10 183 183,7 184 0,725 0,959 0,699 885 885 1,06 Final Value: C = 183,7 BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 – 55 – 60534-2-1  IEC:2011 – 53 – Step 7: The solution should be confirmed: Calculate the predicted flow rate using the computed value of the flow coefficient and compare to given value of flow rate: Q predicted = C N1 F ∆p sizing ρ1 = 749 ρo This compares favourably to the given value of 750 m /hr BS EN 60534-2-1:2011 BS EN 60534-2-1:2011 60534-2-1 © IEC:2011 – 56 – – 54 – 60534-2-1  IEC:2011 Bibliography BAUMANN, H.D., A Unifying Method for Sizing Throttling Valves Under Laminar or Transitional Flow Conditions, Journal of Fluids Engineering, Vol 115, No 1, March 1993, pp 166-168 BAUMANN, H.D Effect of Pipe Reducers on Control Valve Sizing, Instruments and Control Systems, December 1968, pp 99-102 STILES, G.F Liquid Viscosity Effects on Control Valve Sizing, Technical Manual TM 17A, October 1967, Fisher Governor Co., Marshalltown BAUMANN, H.D What’s New in Valve Sizing, Chemical Engineering, June 1996 BOGER, H.W Recent Trends in Sizing Control Valves, 1991, pp 117-121 Instruments and Control Systems, SINGLETON, E.W Adapting Single Stage Sizing Standards for Multistage Control Valves, Intech, August 1997 SINGLETON, E.W The Calculation of the Expansion Factor “Y” for Multistage Control Valves, Valve World, Vol 6, Issue 2, April 2001 BOGER, H.W The Control Valve Body – a Variable Flow Restrictor, ISA Preprint No 11, 11-266 BAUMANN, H.D The Introduction of a Critical Flow Factor for Valve Sizing, ISA Transactions, Vol 2, pp 107-111 _ This page deliberately left blank NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY 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