IEC 60534-2-1:1998
(Main)Industrial-process control valves - Part 2-1: Flow capacity - Sizing equations for fluid flow under installed conditions
Industrial-process control valves - Part 2-1: Flow capacity - Sizing equations for fluid flow under installed conditions
Includes equations for predicting the fow of compressible and incompressible fluids through control valves. Not intended for use when non-Newtonian fluids, fluid mixtures, slurries, or liquid-solid conveyance systems are encoutnererd. Equations for compressible fluids are for use with gas or vapour and are not inteded for use with multiphase streams such as gas-liquid, vapour-liquid or gas-solid mixtures. Valid for valves with xT smaller or equal to 0,84. The contents of the corrigendum of February 2000 have been included in this copy.
Vannes de régulation des processus industriels - Partie 2-1: Capacité d'écoulement - Equations de dimensionnement des vannes de régulation pour l'écoulement des fluides dans les conditions d'installation
Le contenu du corrigendum de février 2000 a été pris en considération dans cet exemplaire.
General Information
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Standards Content (Sample)
INTERNATIONAL
IEC
STANDARD
60534-2-1
First edition
1998-09
Industrial-process control valves –
Part 2-1:
Flow capacity –
Sizing equations for fluid flow
under installed conditions
Vannes de régulation des processus industriels –
Partie 2-1:
Capacité d’écoulement –
Equations de dimensionnement des vannes
de régulation pour l’écoulement des fluides
dans les conditions d’installation
Reference number
Numbering
As from 1 January 1997 all IEC publications are issued with a designation in the
60000 series.
Consolidated publications
Consolidated versions of some IEC publications including amendments are
available. For example, edition numbers 1.0, 1.1 and 1.2 refer, respectively, to the
base publication, the base publication incorporating amendment 1 and the base
publication incorporating amendments 1 and 2.
Validity of this publication
The technical content of IEC publications is kept under constant review by the IEC,
thus ensuring that the content reflects current technology.
Information relating to the date of the reconfirmation of the publication is available
in the IEC catalogue.
Information on the subjects under consideration and work in progress undertaken by
the technical committee which has prepared this publication, as well as the list of
publications issued, is to be found at the following IEC sources:
• IEC web site*
• Catalogue of IEC publications
Published yearly with regular updates
(On-line catalogue)*
• IEC Bulletin
Available both at the IEC web site* and as a printed periodical
Terminology, graphical and letter symbols
For general terminology, readers are referred to IEC 60050: International Electro-
technical Vocabulary (IEV).
For graphical symbols, and letter symbols and signs approved by the IEC for
general use, readers are referred to publications IEC 60027: Letter symbols to be
used in electrical technology, IEC 60417: Graphical symbols for use on equipment.
Index, survey and compilation of the single sheets and IEC 60617: Graphical symbols
for diagrams.
* See web site address on title page.
INTERNATIONAL
IEC
STANDARD
60534-2-1
First edition
1998-09
Industrial-process control valves –
Part 2-1:
Flow capacity –
Sizing equations for fluid flow
under installed conditions
Vannes de régulation des processus industriels –
Partie 2-1:
Capacité d’écoulement –
Equations de dimensionnement des vannes
de régulation pour l’écoulement des fluides
dans les conditions d’installation
IEC 1998 Copyright - all rights reserved
No part of this publication may be reproduced or utilized in any form or by any means, electronic or
mechanical, including photocopying and microfilm, without permission in writing from the publisher.
International Electrotechnical Commission 3, rue de Varembé Geneva, Switzerland
Telefax: +41 22 919 0300 e-mail: inmail@iec.ch IEC web site http: //www.iec.ch
Commission Electrotechnique Internationale
PRICE CODE X
International Electrotechnical Commission
For price, see current catalogue
– 2 – 60534-2-1 © IEC:1998(E)
CONTENTS
Page
FOREWORD . 3
Clause
1 Scope . 4
2 Normative references . 4
3 Definitions. 5
4 Installation . 5
5 Symbols . 6
6 Sizing equations for incompressible fluids. 7
7 Sizing equations for compressible fluids . 9
8 Determination of correction factors . 11
Annex A – Derivation of valve style modifier F . 25
d
Annex B – Control valve sizing flow charts . 29
Annex C – Physical constants . 33
Annex D – Examples of sizing calculations. 34
Annex E – Bibliography. 45
60534-2-1 © IEC:1998(E) – 3 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
––––––––––––
INDUSTRIAL-PROCESS CONTROL VALVES –
Part 2-1: Flow capacity – Sizing equations for fluid flow
under installed conditions
FOREWORD
1) The IEC (International Electrotechnical Commission) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of the 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, the IEC publishes International Standards. 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 non-governmental organizations liaising
with the IEC also participate in this preparation. The 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 the 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 National Committees.
3) The documents produced have the form of recommendations for international use and are published in the form
of standards, technical reports or guides and they are accepted by the National Committees in that sense.
4) In order to promote international unification, IEC National Committees undertake to apply IEC International
Standards transparently to the maximum extent possible in their national and regional standards. Any
divergence between the IEC Standard and the corresponding national or regional standard shall be clearly
indicated in the latter.
5) The IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any
equipment declared to be in conformity with one of its standards.
6) Attention is drawn to the possibility that some of the elements of this International Standard may be the subject
of patent rights. The 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: Devices, of
IEC technical committee 65: Industrial-process measurement and control.
The text of this standard is based on the following documents:
FDIS Report on voting
65B/347/FDIS 65B/357/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.
The edition of IEC 60534-2-1 cancels and replaces the first edition of both IEC 60534-2
published in 1978, and IEC 60534-2-2 published in 1980, which cover incompressible and
compressible fluid flow, respectively.
IEC 60534-2-1 covers sizing equations for both incompressible and compressible fluid flow.
Annexes A, B, C, D and E are for information only.
A bilingual version of this standard may be issued at a later date.
– 4 – 60534-2-1 © IEC:1998(E)
INDUSTRIAL-PROCESS CONTROL VALVES –
Part 2-1: Flow capacity – Sizing equations for fluid flow
under installed conditions
1 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.
At very low ratios of pressure differential to absolute inlet pressure (Δp/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 Δp/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 gas or vapour and are not intended for use
with multiphase streams such as gas-liquid, vapour-liquid or gas-solid mixtures.
For compressible fluid applications, this part of IEC 60534 is valid for valves with x ≤ 0,84
T
(see table 2). For valves with x > 0,84 (e.g. some multistage valves), greater inaccuracy of
T
flow prediction can be expected.
Reasonable accuracy can only be maintained for control valves if K /d < 0,04 (C /d < 0,047).
v v
2 Normative references
The following normative documents contain provisions which, through reference in this text,
constitute provisions of this part of IEC 60534. At the time of publication, the editions indicated
were valid. All normative documents are subject to revision, and parties to agreements based
on this part of IEC 60534 are encouraged to investigate the possibility of applying the most
recent editions of the normative documents indicated below. Members of IEC and ISO maintain
registers of currently valid International Standards.
IEC 60534-1:1987, Industrial-process control valves – Part 1: Control valve terminology and
general considerations
IEC 60534-2-3:1997, Industrial-process control valves – Part 2: Flow capacity – Section 3: Test
procedures
60534-2-1 © IEC:1998(E) – 5 –
3 Definitions
For the purpose of this part of IEC 60534, definitions given in IEC 60534-1 apply with the
addition of the following:
3.1
valve style modifier F
d
The ratio of the hydraulic diameter of a single flow passage to the diameter of a circular
orifice, the area of which is equivalent to the sum of areas of all identical flow passages at a
given travel. It should be stated by the manufacturer as a function of travel. See annex A.
4 Installation
In many industrial applications, reducers or other fittings are attached to the control valves. The
effect of these types of fittings on the nominal flow coefficient of the control valve can be
significant. A correction factor is introduced to account for this effect. Additional factors are
introduced to take account of the fluid property characteristics that influence the flow capacity
of a control valve.
In sizing control valves, using the relationships presented herein, the flow coefficients calculated
are assumed to include all head losses between points A and B, as shown in figure 1.
Flow
l l
I1 I2
Pressure
1 2 Pressure
Pressure
Pressure
tap
tap
tap
tap
A B
Control valve with or without attached fittings
l = two nominal pipe diameters
l = six nominal pipe diameters
Figure 1 – Reference pipe section for sizing
– 6 – 60534-2-1 © IEC:1998(E)
5 Symbols
Symbol Description Unit
C Flow coefficient (K , C ) Various (see IEC 60534-1)
v v
(see note 4)
C Assumed flow coefficient for iterative purposes Various (see IEC 60534-1)
i
(see note 4)
d Nominal valve size mm
D Internal diameter of the piping mm
D Internal diameter of upstream piping mm
D Internal diameter of downstream piping mm
D Orifice diameter mm
o
F Valve style modifier (see annex A) 1 (see note 4)
d
F Liquid critical pressure ratio factor 1
F
F Liquid pressure recovery factor of a control valve without attached fittings 1 (see note 4)
L
F Combined liquid pressure recovery factor and piping geometry factor of a 1 (see note 4)
LP
control valve with attached fittings
F Piping geometry factor 1
P
F Reynolds number factor 1
R
F Specific heat ratio factor 1
γ
M Molecular mass of flowing fluid kg/kmol
N Numerical constants (see table 1) Various (see note 1)
p Inlet absolute static pressure measured at point A (see figure 1) kPa or bar (see note 2)
p Outlet absolute static pressure measured at point B (see figure 1) kPa or bar
p Absolute thermodynamic critical pressure kPa or bar
c
p Reduced pressure (p /p )
r 1 c
p Absolute vapour pressure of the liquid at inlet temperature kPa or bar
v
Differential pressure between upstream and downstream pressure taps kPa or bar
Δp
(p – p )
1 2
Q Volumetric flow rate (see note 5) m /h
Re Valve Reynolds number 1
v
T Inlet absolute temperature K
T Absolute thermodynamic critical temperature K
c
T Reduced temperature (T /T ) 1
r 1 c
t Absolute reference temperature for standard cubic metre K
s
W Mass flow rate kg/h
x 1
Ratio of pressure differential to inlet absolute pressure (Δp/p )
x Pressure differential ratio factor of a control valve without attached fittings 1 (see note 4)
T
at choked flow
x Pressure differential ratio factor of a control valve with attached fittings at 1 (see note 4)
TP
choked flow
Y Expansion factor 1
Compressibility factor 1
Z
ν Kinematic viscosity m /s (see note 3)
ρ Density of fluid at p and T kg/m
1 1 1
ρ /ρ Relative density (ρ /ρ = 1,0 for water at 15 °C) 1
1 o 1 o
Specific heat ratio 1
γ
60534-2-1 © IEC:1998(E) – 7 –
Velocity head loss coefficient of a reducer, expander or other fitting 1
ζ
attached to a control valve or valve trim
ζ Upstream velocity head loss coefficient of fitting 1
ζ Downstream velocity head loss coefficient of fitting 1
Inlet Bernoulli coefficient 1
ζ
B1
Outlet Bernoulli coefficient 1
ζ
B2
NOTE 1 – To determine the units for the numerical constants, dimensional analysis may be performed on the
appropriate equations using the units given in table 1.
2 5
NOTE 2 – 1 bar = 10 kPa = 10 Pa
–6 2
NOTE 3 – 1 centistoke = 10 m /s
NOTE 4 – These values are travel-related and should be stated by the manufacturer.
NOTE 5 – Volumetric flow rates in cubic metres per hour, identified by the symbol Q, refer to standard conditions.
The standard cubic metre is taken at 1013,25 mbar and either 273 K or 288 K (see table 1).
6 Sizing equations for incompressible fluids
The equations listed below identify the relationships between flow rates, flow coefficients,
related installation factors, and pertinent service conditions for control valves handling
incompressible fluids. Flow coefficients may be calculated using the appropriate equation
selected from the ones given below. A sizing flow chart for incompressible fluids is given in
annex B.
6.1 Turbulent flow
The equations for the flow rate of a Newtonian liquid through a control valve when operating
under non-choked flow conditions are derived from the basic formula as given in IEC 60534-1.
6.1.1 Non-choked turbulent flow
6.1.1.1 Non-choked turbulent flow without attached fittings
Applicable ifΔ
()
LF1 v
[]
The flow coefficient shall be determined by
ρρ/
Q
1o
C= (1)
NpΔ
NOTE 1 – The numerical constant N depends on the units used in the general sizing equation and the type of flow
coefficient: K or C .
v v
NOTE 2 – An example of sizing a valve with non-choked turbulent flow without attached fittings is given in annex D.
6.1.1.2 Non-choked turbulent flow with attached fittings
Applicable ifΔ
()
()
LP p 1 F v
The flow coefficient shall be determined as follows:
Q ρρ/
1 o
= (2)
C
NF Δp
1 p
NOTE – Refer to 8.1 for the piping geometry factor F .
P
– 8 – 60534-2-1 © IEC:1998(E)
6.1.2 Choked turbulent flow
The maximum rate at which flow will pass through a control valve at choked flow conditions
shall be calculated from the following equations:
6.1.2.1 Choked turbulent flow without attached fittings
Applicable ifΔ≥p F p −F × p
()
LF1 v
[]
The flow coefficient shall be determined as follows:
Q ρρ/
1 o
C= (3)
−×
NF p F p
1L 1 Fv
NOTE – An example of sizing a valve with choked flow without attached fittings is given in annex D.
6.1.2.2 Choked turbulent flow with attached fittings
Applicable ifΔ≥p F / F p −F × p
()
()
LP p 1 F v
The following equation shall be used to calculate the flow coefficient:
Q ρρ/
1 o
C= (4)
Np F −×Fp
1 LP 1 Fv
6.2 Non-turbulent (laminar and transitional) flow
The equations for the flow rate of a Newtonian liquid through a control valve when operating
under non-turbulent flow conditions are derived from the basic formula as given in IEC 60534-1.
This equation is applicable if Re < 10 000 (see equation (28)).
v
6.2.1 Non-turbulent flow without attached fittings
The flow coefficient shall be calculated as follows:
ρρ
Q /
1 o
C= (5)
NF Δp
1 R
6.2.2 Non-turbulent flow with attached fittings
For non-turbulent flow, the effect of close-coupled reducers or other flow disturbing fittings is
unknown. While there is no information on the laminar or transitional flow behaviour of control
valves installed between pipe reducers, the user of such valves is advised to utilize the
appropriate equations for line-sized valves in the calculation of the F factor. This should result
R
in conservative flow coefficients since additional turbulence created by reducers and expanders
will further delay the onset of laminar flow. Therefore, it will tend to increase the respective F
R
factor for a given valve Reynolds number.
60534-2-1 © IEC:1998(E) – 9 –
7 Sizing equations for compressible fluids
The equations listed below identify the relationships between flow rates, flow coefficients,
related installation factors, and pertinent service conditions for control valves handling
compressible fluids. Flow rates for compressible fluids may be encountered in either mass or
volume units and thus equations are necessary to handle both situations. Flow coefficients may
be calculated using the appropriate equations selected from the following. A sizing flow chart
for compressible fluids is given in annex B.
7.1 Turbulent flow
7.1.1 Non-choked turbulent flow
7.1.1.1 Non-choked turbulent flow without attached fittings
Applicable if x < F x
[]
γ T
The flow coefficient shall be calculated using one of the following equations:
W
C= (6)
NY xpρ
W TZ
C = (7)
NpY xM
Q MT Z
C = (8)
NpY x
NOTE 1 – Refer to 8.5 for details of the expansion factor Y.
NOTE 2 – See annex C for values of M.
7.1.1.2 Non-choked turbulent flow with attached fittings
Applicable if x < F x
[]γ TP
The flow coefficient shall be determined from one of the following equations:
W
C= (9)
NFY xpρ
61p 1
W TZ
= (10)
C
NF pY xM
81p
Q MT Z
C = (11)
NF pY x
91p
NOTE 1 – Refer to 8.1 for the piping geometry factor F .
P
NOTE 2 – An example of sizing a valve with non-choked turbulent flow with attached fittings is given in annex D.
7.1.2 Choked turbulent flow
The maximum rate at which flow will pass through a control valve at choked flow conditions
shall be calculated as follows:
– 10 – 60534-2-1 © IEC:1998(E)
7.1.2.1 Choked turbulent flow without attached fittings
Applicable if x ≥ F x
[]γ T
The flow coefficient shall be calculated from one of the following equations:
W
C= (12)
0,667NFx pρ
61γT1
TZ
W
C= (13)
0,667Np Fx M
81 γ T
MT Z
Q
C= (14)
0,667Np Fx
91 γ T
7.1.2.2 Choked turbulent flow with attached fittings
Applicable if x ≥ F x
[]
γ TP
The flow coefficient shall be determined using one of the following equations:
W
= (15)
C
NF F x p
0,667 ρ
61pTγ P1
W TZ
C= (16)
0,667NF p Fx M
81pTγP
Q MT Z
C= (17)
0,667NF p Fx
91pTγP
7.2 Non-turbulent (laminar and transitional) flow
The equations for the flow rate of a Newtonian fluid through a control valve when operating
under non-turbulent flow conditions are derived from the basic formula as given in IEC 60534-1.
These equations are applicable if Re < 10 000 (see equation (28)). In this subclause, density
v
correction of the gas is given by (p + p )/2 due to non-isentropic expansion.
1 2
7.2.1 Non-turbulent flow without attached fittings
The flow coefficient shall be calculated from one of the following equations:
W T
C= (18)
NF Δpp +p M
()
27R 12
Q MT
C= (19)
NF Δpp +p
()
22R 12
NOTE – An example of sizing a valve with small flow trim is given in annex D.
60534-2-1 © IEC:1998(E) – 11 –
7.2.2 Non-turbulent flow with attached fittings
For non-turbulent flow, the effect of close-coupled reducers or other flow-disturbing fittings is
unknown. While there is no information on the laminar or transitional flow behaviour of control
valves installed between pipe reducers, the user of such valves is advised to utilize the
appropriate equations for line-sized valves in the calculation of the F factor. This should result
R
in conservative flow coefficients since additional turbulence created by reducers and expanders
will further delay the onset of laminar flow. Therefore, it will tend to increase the respective F
R
factor for a given valve Reynolds number.
8 Determination of correction factors
8.1 Piping geometry factor F
P
The piping geometry factor F is necessary to account for fittings attached upstream and/or
P
downstream to a control valve body. The F factor is the ratio of the flow rate through a control
P
valve installed with attached fittings to the flow rate that would result if the control valve was
installed without attached fittings and tested under identical conditions which will not produce
choked flow in either installation (see figure 1). To meet the accuracy of the F factor of ±5 %,
P
the F factor shall be determined by test in accordance with IEC 60534-2-3.
P
When estimated values are permissible, the following equation shall be used:
F = (20)
p
C
Σζ
i
1+
N
2 d
In this equation, the factor Σζ is the algebraic sum of all of the effective velocity head loss
coefficients of all fittings attached to the control valve. The velocity head loss coefficient of the
control valve itself is not included.
Σζζ=+ζ +ζ −ζ
(21)
12 BB1 2
In cases where the piping diameters approaching and leaving the control valve are different,
the ζ coefficients are calculated as follows:
B
d
ζ =−1 (22)
B
D
If the inlet and outlet fittings are short-length, commercially available, concentric reducers, the
ζ and ζ coefficients may be approximated as follows:
1 2
d
Inlet reducer: ζ=−05, 1 (23)
D
d
Outlet reducer (expander): ζ=−10, 1 (24)
D
d
Inlet and outlet reducers of equal size: ζζ+=15, 1− (25)
D
– 12 – 60534-2-1 © IEC:1998(E)
The F values calculated with the above ζ factors generally lead to the selection of valve
P
capacities slightly larger than required. This calculation requires iteration. Proceed by
calculating the flow coefficient C for non-choked turbulent flow.
NOTE – Choked flow equations and equations involving F are not applicable.
P
Next, establish C as follows:
i
=
CC13, (26)
i
Using C from equation (26), determine F from equation (20). If both ends of the valve are the
i P
same size, F may instead be determined from figure 2. Then, determine if
P
C
≤C (27)
i
F
p
If the condition of equation (27) is satisfied, then use the C established from equation (26).
i
If the condition of equation (27) is not met, then repeat the above procedure by again
increasing C by 30 %. This may require several iterations until the condition required in
i
equation (27) is met. An iteration method more suitable for computers can be found in annex B.
For graphical approximations of F , refer to figures 2a and 2b.
P
8.2 Reynolds number factor F
R
The Reynolds number factor F is required when non-turbulent flow conditions are established
R
through a control valve because of a low pressure differential, a high viscosity, a very small
flow coefficient, or a combination thereof.
The F factor is determined by dividing the flow rate when non-turbulent flow conditions exist
R
by the flow rate measured in the same installation under turbulent conditions.
Tests show that F can be determined from the curves given in figure 3 using a valve Reynolds
R
number calculated from the following equation:
14/
NF Q FC
4 d Li
Re=+1 (28)
v
4
ν CF
ND
iL 2
This calculation will require iteration. Proceed by calculating the flow coefficient C for turbulent
flow. The valve style modifier F converts the geometry of the orifice(s) to an equivalent
d
circular single flow passage. See table 2 for typical values and annex A for details. To meet
a deviation of ± 5 % for F , the F factor shall be determined by test in accordance with
d d
IEC 60534-2-3.
NOTE – Equations involving F are not applicable.
P
Next, establish C as per equation (26).
i
Apply C as per equation (26) and determine F from equations (30) and (31) for full size trims
i R
or equations (32) and (33) for reduced trims. In either case, using the lower of the two F
R
values, determine if
C
≤C (29)
i
F
R
60534-2-1 © IEC:1998(E) – 13 –
If the condition of equation (29) is satisfied, then use the C established from equation (26). If
i
the condition of equation (29) is not met, then repeat the above procedure by again increasing
C by 30 %. This may require several iterations until the condition required in equation (29) is
i
met.
For full size trim where C/d ≥ 0,016 N and Re ≥ 10, calculate F from the following
i 18 v R
equations:
12/
03, 3F Re
Lv
F =+1 log (30)
R 10
14/
10000
n
for the transitional flow regime,
where
N
n = (30a)
C
i
d
or
0,026
=
F n Re (not to exceed F = 1) (31)
R 1 v R
F
L
for the laminar flow regime.
NOTE 1 – Use the lower value of F from equations (30) and (31). If Re < 10, use only equation (31).
R v
NOTE 2 – Equation (31) is applicable to fully developed laminar flow (straight lines in figure 3). The relationships
expressed in equations (30) and (31) are based on test data with valves at rated travel and may not be fully
accurate at lower valve travels.
NOTE 3 – In equations (30a) and (31), C /d must not exceed 0,04 when K is used or 0,047 when C is used.
i v v
For reduced trim valves where C/d at rated travel is less than 0,016 N and Re ≥ 10,
i 18 v
calculate F from the following equations:
R
12/
03, 3F Re
Lv
F =+1 log (32)
R 10
14/
10 000
n
for the transitional flow regime,
where
12/
C
i
nN=+1 (32a)
d
or
0,026
F = n Re (not to exceed F = 1) (33)
R
R 2 v
F
L
for the laminar flow regime.
NOTE 1 – Select the lowest value from equations (32) and (33). If Re < 10, use only equation (33).
v
NOTE 2 – Equation (33) is applicable to fully developed laminar flow (straight lines in figure 3).
– 14 – 60534-2-1 © IEC:1998(E)
8.3 Liquid pressure recovery factors F or F
L LP
8.3.1 Liquid pressure recovery factor without attached fittings F
L
F is the liquid pressure recovery factor of the valve without attached fittings. This factor
L
accounts for the influence of the valve internal geometry on the valve capacity at choked flow.
It is defined as the ratio of the actual maximum flow rate under choked flow conditions to a
theoretical, non-choked flow rate which would be calculated if the pressure differential
used was the difference between the valve inlet pressure and the apparent vena contracta
pressure at choked flow conditions. The factor F may be determined from tests in accordance
L
with IEC 60534-2-3. Typical values of F versus percent of rated flow coefficient are shown in
L
figure 4.
8.3.2 Combined liquid pressure recovery factor and piping geometry factor
with attached fittings F
LP
F is the combined liquid pressure recovery factor and piping geometry factor for a control
LP
valve with attached fittings. It is obtained in the same manner as F .
L
To meet a deviation of ±5 % for F , F shall be determined by testing. When estimated
LP LP
values are permissible, the following equation shall be used:
F
L
F = (34)
LP
F C
L
1+ Σζ
()
N
d
Here Σζ is the velocity head loss coefficient, ζ + ζ , of the fitting attached upstream of the
1 1 B1
valve as measured between the upstream pressure tap and the control valve body inlet.
8.4 Liquid critical pressure ratio factor F
F
F is the liquid critical pressure ratio factor. This factor is the ratio of the apparent vena
F
contracta pressure at choked flow conditions to the vapour pressure of the liquid at inlet
temperature. At vapour pressures near zero, this factor is 0,96.
Values of F may be determined from the curve in figure 5 or approximated from the following
F
equation:
p
v
F=−09, 6 0,28 (35)
F
p
c
8.5 Expansion factor
Y
The expansion factor Y accounts for the change in density as the fluid passes from the valve
inlet to the vena contracta (the location just downstream of the orifice where the jet stream
area is a minimum). It also accounts for the change in the vena contracta area as the pressure
differential is varied.
Theoretically, Y is affected by all of the following:
a) ratio of port area to body inlet area;
b) shape of the flow path;
c) pressure differential ratio x;
d) Reynolds number;
e) specific heat ratio γ.
60534-2-1 © IEC:1998(E) – 15 –
The influence of items a), b), c), and e) is accounted for by the pressure differential ratio factor
x , which may be established by air test and which is discussed in 8.6.1.
T
The Reynolds number is the ratio of inertial to viscous forces at the control valve orifice. In the
case of compressible flow, its value is beyond the range of influence since turbulent flow
almost always exists.
The pressure differential ratio x is influenced by the specific heat ratio of the fluid.
T
Y may be calculated using equation (36).
x
Y=−1 (36)
3Fx
γ T
The value of x for calculation purposes shall not exceed F x . If x > F x , then the flow
γ T γ T
becomes choked and Y = 0,667. See 8.6 and 8.7 for information on x, x and F
T γ.
8.6 Pressure differential ratio factor x or x
T TP
8.6.1 Pressure differential ratio factor without fittings x
T
x is the pressure differential ratio factor of a control valve installed without reducers or other
T
fittings. If the inlet pressure p is held constant and the outlet pressure p is progressively
1 2
lowered, the mass flow rate through a valve will increase to a maximum limit, a condition
referred to as choked flow. Further reductions in p will produce no further increase in flow
rate.
This limit is reached when the pressure differential x reaches a value of F x . The limiting
γ T
value of x is defined as the critical differential pressure ratio. The value of x used in any of the
sizing equations and in the relationship for Y (equation (36) shall be held to this limit even
though the actual pressure differential ratio is greater. Thus, the numerical value of Y may
range from 0,667, when x = F x , to 1,0 for very low differential pressures.
T
γ
The values of x may be established by air test. The test procedure for this determination is
T
covered in IEC 60534-2-3.
NOTE – Representative values of x for several types of control valves with full size trim and at full rated openings
T
are given in table 2. Caution should be exercised in the use of this information. When precise values are required,
they should be obtained by test.
8.6.2 Pressure differential ratio factor with attached fittings x
TP
If a control valve is installed with attached fittings, the value of x will be affected.
T
To meet a deviation of ±5 % for x , the valve and attached fittings shall be tested as a unit.
TP
When estimated values are permissible, the following equation shall be used:
x
T
F
p
x = (37)
TP
x ζ C
Ti i
1+
N
5 d
NOTE – Values for N are given in table 1.
In the above relationship, x is the pressure differential ratio factor for a control valve installed
T
without reducers or other fittings. ζ is the
...
IEC 60534-2-1
Edition 1.0 1998-09
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Industrial-process control valves –
Part 2-1: Flow-capacity – Sizing equations for fluid flow under installed
conditions
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
Copyright © 1998 IEC, Geneva, Switzerland
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IEC 60534-2-1
Edition 1.0 1998-09
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Industrial-process control valves –
Part 2-1: Flow-capacity – Sizing equations for fluid flow under installed
conditions
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
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
PRICE CODE
INTERNATIONALE
X
CODE PRIX
ICS 23.060.40; 25.040.40 ISBN 2-8318-4751-6
– 2 – 60534-2-1 © CEI:1998
SOMMAIRE
Pages
AVANT-PROPOS . 4
Articles
1 Domaine d'application . 6
2 Références normatives. 6
3 Définitions. 8
4 Installation . 8
5 Symboles .10
6 Equations de dimensionnement pour fluides incompressibles . 12
7 Equations de dimensionnement pour fluides compressibles . 16
8 Détermination des facteurs de correction. 20
Annexe A (informative) Calcul du coefficient de correction générique de vanne F . 48
d
Annexe B (informative) Organigramme de dimensionnement des vannes de régulation . 58
Annexe C (informative) Constantes physiques . 66
Annexe D (informative) Exemples de calculs de dimensionnement . 68
Annexe E (informative) Bibliographie . 90
60534-2-1 © IEC:1998 – 3 –
CONTENTS
Page
FOREWORD . 5
Clause
1 Scope . 7
2 Normative references . 7
3 Definitions. 9
4 Installation . 9
5 Symbols . 11
6 Sizing equations for incompressible fluids. 13
7 Sizing equations for compressible fluids . 17
8 Determination of correction factors . 21
Annex A (informative) Derivation of valve style modifier F . 49
d
Annex B (informative) Control valve sizing flow charts. 59
Annex C (informative) Physical constants . 67
Annex D (informative) Examples of sizing calculations . 69
Annex E (informative) Bibliography . 91
– 4 – 60534-2-1 © CEI:1998
COMMISSION ÉLECTROTECHNIQUE INTERNATIONALE
____________
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
AVANT-PROPOS
1) La Commission Electrotechnique Internationale (CEI) est une organisation mondiale de normalisation composée
de l'ensemble des comités électrotechniques nationaux (Comités nationaux de la CEI). La CEI a pour objet de
favoriser la coopération internationale pour toutes les questions de normalisation dans les domaines de
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des Spécifications techniques, des Rapports techniques, des Spécifications accessibles au public (PAS) et des
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conditions fixées par accord entre les deux organisations.
2) Les décisions ou accords officiels de la CEI concernant les questions techniques représentent, dans la mesure
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l’objet de droits de propriété intellectuelle ou de droits analogues. La CEI ne saurait être tenue pour
responsable de ne pas avoir identifié de tels droits de propriété et de ne pas avoir signalé leur existence.
La Norme internationale CEI 60534-2-1 a été établie par le sous-comité 65B: Dispositifs, du
comité d'études 65 de la CEI: Mesure et commande dans les processus industriels.
La CEI 60534-2-1 annule et remplace la première édition de la CEI 60534-2, publiée en 1978,
et de la CEI 60534-2-2, publiée en 1980, qui couvraient respectivement les fluides
incompressibles et compressibles.
La CEI 60534-2-1 couvre les équations de dimensionnement à la fois des fluides
compressibles et incompressibles.
La présente version bilingue, publiée en 1999-03, correspond à la version anglaise.
Le texte anglais de cette norme est basé sur les documents 65B/347/FDIS et 65B/357/RVD. Le
rapport de vote 65B/357/RVD donne toute information sur le vote ayant abouti à l'approbation
de cette norme.
La version française de cette norme n'a pas été soumise au vote.
Les annexes A, B, C, D et E sont données uniquement à titre d'information.
Le contenu du corrigendum de février 2000 a été pris en considération dans cet exemplaire.
60534-2-1 © IEC:1998 – 5 –
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 non-
governmental 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 provides no marking procedure to indicate its approval and cannot be rendered responsible for any
equipment declared to be in conformity with an IEC Publication.
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: Devices, of
IEC technical committee 65: Industrial-process measurement and control.
IEC 60534-2-1 cancels and replaces the first edition of both IEC 60534-2, published in 1978,
and IEC 60534-2-2, published in 1980, which covered incompressible and compressible fluid
flow, respectively.
IEC 60534-2-1 covers sizing equations for both incompressible and compressible fluid flow.
This bilingual version, published in 1999-03, corresponds to the English version.
The text of this standard is based on the following documents:
FDIS Report on voting
65B/347/FDIS 65B/357/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.
Annexes A, B, C, D and E are for information only.
The contents of the corrigendum of February 2000 have been included in this copy.
– 6 – 60534-2-1 © CEI:1998
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
1 Domaine d'application
La présente partie de la CEI 60534 comprend des équations permettant de prédire le débit de
fluides compressibles et incompressibles dans les vannes de régulation.
Les équations relatives aux fluides incompressibles sont fondées sur l'équation de Bernoulli
pour les fluides newtoniens incompressibles. Elles ne sont pas destinées à être utilisées pour
des fluides non newtoniens, des mélanges de fluides, des boues ou des systèmes de transport
de particules solides en suspension dans un liquide.
Aux très basses valeurs du rapport de la pression différentielle à la pression absolue d'entrée
(Δp/p ), les fluides compressibles se comportent de manière analogue aux fluides
incompressibles. Dans de telles conditions, les équations de dimensionnement pour les fluides
compressibles peuvent être déduites de celles de l'équation de base de Bernoulli pour les
fluides newtoniens incompressibles. Cependant, des valeurs croissantes de Δp/p provoquent
des effets de compressibilité qui nécessitent de modifier l'équation de base en y introduisant
des facteurs de correction appropriés. Les équations présentées s'appliquent aux gaz ou aux
vapeurs, mais ne conviennent pas pour les fluides multiphasiques tels que les mélanges gaz-
liquide, vapeur-liquide ou gaz-solide.
Pour les fluides compressibles, la présente partie de la CEI 60534 est valable pour les vannes
telles que x ≤ 0,84 (voir tableau 2). Pour les vannes avec x > 0,84 (par exemple certaines
T T
vannes multi-étagées), on peut s’attendre à une plus grande imprécision sur la prédiction du
débit.
Une précision raisonnable ne peut être assurée que pour les vannes de régulation telles que
2 2
K /d < 0,04 (C /d < 0,047).
v v
2 Références normatives
Les documents normatifs suivants contiennent des dispositions qui, par suite de la référence
qui y est faite, constituent des dispositions valables pour la présente partie de la CEI 60534.
Pour les références datées, les amendements ultérieurs ou les révisions de ces publications ne
s’appliquent pas. Toutefois, les parties prenantes aux accords fondés sur la présente partie de
la CEI 60534 sont invitées à rechercher la possibilité d'appliquer les éditions les plus récentes
des documents normatifs indiqués ci-après. Pour les références non datées, la dernière édition
du document normatif en référence s’applique. Les membres de la CEI et de l'ISO possèdent
le registre des Normes internationales en vigueur.
CEI 60534-1:1987, Vannes de régulation des processus industriels – Première partie:
Terminologie des vannes de régulation et considérations générales
IEC 60534-2-3:1997, Vannes de régulation des processus industriels – Partie 2: Capacité
d'écoulement – Section 3: Procédures d'essai
60534-2-1 © IEC:1998 – 7 –
INDUSTRIAL-PROCESS CONTROL VALVES –
Part 2-1: Flow capacity – Sizing equations for fluid flow
under installed conditions
1 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.
At very low ratios of pressure differential to absolute inlet pressure (Δp/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 Δp/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 gas or vapour and are not intended for use
with multiphase streams such as gas-liquid, vapour-liquid or gas-solid mixtures.
For compressible fluid applications, this part of IEC 60534 is valid for valves with x ≤ 0,84
T
(see table 2). For valves with x > 0,84 (e.g. some multistage valves), greater inaccuracy of
T
flow prediction can be expected.
2 2
Reasonable accuracy can only be maintained for control valves if K /d < 0,04 (C /d < 0,047).
v v
2 Normative references
The following normative documents contain provisions which, through reference in this text,
constitute provisions of this part of IEC 60534. For dated references, subsequent amendments
to, or revisions of, any of these publications do not apply. However, parties to agreements
based on this part of IEC 60534 are encouraged to investigate the possibility of applying the
most recent editions of the normative documents indicated below. For undated references, the
latest edition of the normative document referred to applies. Members of IEC and ISO maintain
registers of currently valid International Standards.
IEC 60534-1:1987, Industrial-process control valves – Part 1: Control valve terminology and
general considerations
IEC 60534-2-3:1997, Industrial-process control valves – Part 2: Flow capacity – Section 3: Test
procedures
– 8 – 60534-2-1 © CEI:1998
3 Définitions
Pour les besoins de la présente partie de la CEI 60534, les définitions données dans la
CEI 60534-1 sont applicables ainsi que la définition suivante:
3.1
coefficient de correction générique de vanne F
d
rapport entre le diamètre hydraulique d'un chemin d'écoulement unique et le diamètre d'un
orifice circulaire de section équivalente à la somme des sections de tous les chemins
d'écoulement identiques, à une course donnée. Il convient que ce coefficient soit indiqué par le
fabricant en fonction de la course. Voir l'annexe A
4 Installation
Dans beaucoup d'applications industrielles, des réducteurs ou autres raccords sont fixés aux
vannes de régulation. L'effet de ces types de raccords sur le coefficient de débit nominal de la
vanne peut être notable. Un facteur correctif est introduit pour tenir compte de cet effet. Des
facteurs supplémentaires sont introduits pour tenir compte des caractéristiques du fluide qui
influencent la capacité d'écoulement d'une vanne de régulation.
Dans le dimensionnement des vannes de régulation, en utilisant les relations présentées ci-
après, les coefficients de débits calculés sont supposés inclure toutes les pertes de charge
entre les points A et B disposés comme le montre la figure 1.
Ecoulement
l lI
I
11 2 Prise de
Prise de
pression
pression
A B
Vanne de régulation avec ou sans raccords
IEC 588/99
l = 2 × diamètre nominal de la tuyauterie
l = 6 × diamètre nominal de la tuyauterie
Figure 1 – Section de tuyauterie de référence pour dimensionnement
60534-2-1 © IEC:1998 – 9 –
3 Definitions
For the purpose of this part of IEC 60534, definitions given in IEC 60534-1 apply with the
addition of the following:
3.1
valve style modifier F
d
the ratio of the hydraulic diameter of a single flow passage to the diameter of a circular orifice,
the area of which is equivalent to the sum of areas of all identical flow passages at a given
travel. It should be stated by the manufacturer as a function of travel. See annex A
4 Installation
In many industrial applications, reducers or other fittings are attached to the control valves. The
effect of these types of fittings on the nominal flow coefficient of the control valve can be
significant. A correction factor is introduced to account for this effect. Additional factors are
introduced to take account of the fluid property characteristics that influence the flow capacity
of a control valve.
In sizing control valves, using the relationships presented herein, the flow coefficients calculated
are assumed to include all head losses between points A and B, as shown in figure 1.
Flow
l l
I
I1 2 Pressure
2 Pressur
Pressur
Pressure
tap
tap
tap
tap
A B
Control valve with or without attached fittings
IEC 588/99
l = two nominal pipe diameters
l = six nominal pipe diameters
Figure 1 – Reference pipe section for sizing
– 10 – 60534-2-1 © CEI:1998
5 Symboles
Symboles Description Unités
C Coefficient de débit (K , C ) Diverses (voir CEI 60534-1)
v v
(voir note 4)
C Coefficient de débit supposé, pour calcul itératif Diverses (voir CEI 60534-1)
i
(voir note 4)
d Dimension nominale de la vanne mm
D Diamètre intérieur de la tuyauterie mm
D Diamètre intérieur de la tuyauterie amont mm
D Diamètre intérieur de la tuyauterie aval mm
D Diamètre de l'orifice mm
o
F Coefficient de correction générique de vanne (voir annexe A) 1 (voir note 4)
d
F Facteur de rapport de pression critique du liquide 1
F
F Facteur de récupération de pression du liquide dans une 1 (voir note 4)
L
vanne de régulation sans raccords adjacents
F Facteur combiné de récupération de pression du liquide et de 1 (voir note 4)
LP
géométrie de la tuyauterie d'une vanne de régulation avec
raccords adjacents
F Facteur de géométrie de la tuyauterie 1
P
F Facteur du nombre de Reynolds 1
R
F Facteur de correction correspondant au rapport des chaleurs 1
γ
massiques
M Masse moléculaire du fluide en mouvement kg/kmol
Constantes numériques (voir tableau 1) Diverses (voir note 1)
N
p Pression statique absolue d'entrée mesurée au point A (voir kPa ou bar (voir note 2)
figure 1)
p Pression statique absolue de sortie mesurée au point B (voir kPa ou bar
figure 1)
p Pression thermodynamique critique absolue kPa ou bar
c
p Pression réduite (p /p ) 1
r 1 c
Pression de vapeur absolue du liquide à la température kPa ou bar
p
v
d'entrée
Pression différentielle entre les prises de pression amont et kPa ou bar
Δp
aval (p – p )
1 2
Q Débit volumétrique (voir note 5) m /h
Re Nombre de Reynolds de la vanne 1
v
T Température absolue d'entrée K
T Température absolue critique, ou sens thermodynamique K
c
T Température réduite (T /T ) 1
r 1 c
t Température absolue de référence pour mètre cube standard K
s
W Débit massique kg/h
x Rapport de la pression différentielle à la pression absolue 1
d'entrée (Δp/p )
x Facteur de rapport de pression différentielle d'une vanne de 1 (voir note 4)
T
régulation sans raccords adjacents, à débit engorgé
x Facteur de rapport de pression différentielle d'une vanne de 1 (voir note 4)
TP
régulation avec raccords adjacents, à débit engorgé
60534-2-1 © IEC:1998 – 11 –
5 Symbols
Symbol Description Unit
C Flow coefficient (K , C ) Various (see IEC 60534-1)
v v
(see note 4)
C Assumed flow coefficient for iterative purposes Various (see IEC 60534-1)
i
(see note 4)
d Nominal valve size mm
D Internal diameter of the piping mm
D Internal diameter of upstream piping mm
D Internal diameter of downstream piping mm
D Orifice diameter mm
o
Valve style modifier (see annex A) 1 (see note 4)
F
d
F Liquid critical pressure ratio factor 1
F
F Liquid pressure recovery factor of a control valve without attached fittings 1 (see note 4)
L
F Combined liquid pressure recovery factor and piping geometry factor of a 1 (see note 4)
LP
control valve with attached fittings
F Piping geometry factor 1
P
F Reynolds number factor 1
R
F Specific heat ratio factor 1
γ
M Molecular mass of flowing fluid kg/kmol
N Numerical constants (see table 1) Various (see note 1)
p Inlet absolute static pressure measured at point A (see figure 1) kPa or bar (see note 2)
p Outlet absolute static pressure measured at point B (see figure 1) kPa or bar
p Absolute thermodynamic critical pressure kPa or bar
c
p Reduced pressure (p /p ) 1
r 1 c
p Absolute vapour pressure of the liquid at inlet temperature kPa or bar
v
Differential pressure between upstream and downstream pressure taps kPa or bar
Δp
(p – p )
1 2
Q Volumetric flow rate (see note 5) m /h
Re Valve Reynolds number 1
v
T Inlet absolute temperature K
T Absolute thermodynamic critical temperature K
c
T Reduced temperature (T /T ) 1
r 1 c
t Absolute reference temperature for standard cubic metre K
s
W Mass flow rate kg/h
x 1
Ratio of pressure differential to inlet absolute pressure (Δp/p )
x Pressure differential ratio factor of a control valve without attached fittings 1 (see note 4)
T
at choked flow
x Pressure differential ratio factor of a control valve with attached fittings at 1 (see note 4)
TP
choked flow
– 12 – 60534-2-1 © CEI:1998
Symboles Description Unités
Facteur de détente 1
Y
Z Facteur de compressibilité 1
Viscosité cinématique m /s (voir note 3)
ν
Masse volumique du fluide à p et T kg/m
ρ
1 1
ρ ρ ρ ρ 1
/ Densité relative ( / = 1,0 pour l'eau à 15 °C)
1 o 1 o
γ Rapport des chaleurs massiques 1
ζ Coefficient de perte de charge d'un réducteur, d'un divergent 1
ou d'un autre raccord adjacent à une vanne de régulation ou
organe de détente
Coefficient de perte de charge dynamique du raccord amont 1
ζ
Coefficient de perte de charge dynamique du raccord aval 1
ζ
Coefficient de Bernoulli à l'entrée 1
ζ
B1
ζ Coefficient de Bernoulli à la sortie 1
B2
NOTE 1 – Pour déterminer les unités des constantes numériques, on peut effectuer l'analyse dimensionnelle
des équations appropriées en se servant des unités données au tableau 1.
2 5
NOTE 2 – 1 bar = 10 kPa = 10 Pa
–6 2
NOTE 3 – 1 centistoke = 10 m /s
NOTE 4 – Ces valeurs varient en fonction de la course. Elles seront indiquées par le fabriquant.
NOTE 5 – Les débits volumétriques en mètres cubes par heure, identifiés par le symbole Q, se réfèrent
aux conditions normalisées. Le mètre cube standard est pris à 1 013,25 mbar et à 273 K ou 288 K (voir
tableau 1).
6 Equations de dimensionnement pour fluides incompressibles
Les équations énumérées ci-dessous établissent les relations entre les débits, les coefficients
de débit, les facteurs de l'installation concernée et les conditions de service appropriées
applicables aux vannes de régulation véhiculant des fluides incompressibles. Les coefficients
de débit peuvent être calculés en utilisant l'équation appropriée parmi celles proposées. Un
organigramme de dimensionnement est donné à l'annexe B pour les fluides incompressibles.
6.1 Ecoulement turbulent
Les équations du débit d'un liquide newtonien à travers une vanne de régulation, lorsque cette
vanne fonctionne dans des conditions de non-engorgement, sont dérivées de la formule de
base donnée dans la CEI 60534-1.
6.1.1 Ecoulement turbulent non engorgé
6.1.1.1 Ecoulement turbulent non engorgé sans raccords adjacents
Applicable siΔ
()
[]LF1 v
Le coefficient de débit doit être déterminé comme suit:
Qρ/ρ
1o
C= (1)
NpΔ
NOTE 1 – La constante numérique N dépend des unités utilisées dans l'équation générale de dimensionnement et
du type de coefficient de débit: K ou C .
v v
NOTE 2 – Un exemple de dimensionnement d'une vanne sans raccords adjacents en régime turbulent non engorgé
est donné à l'annexe D.
60534-2-1 © IEC:1998 – 13 –
Symbol Description Unit
Expansion factor 1
Y
Z Compressibility factor 1
Kinematic viscosity m /s (see note 3)
ν
ρ Density of fluid at p and T kg/m
1 1 1
ρ /ρ Relative density (ρ /ρ = 1,0 for water at 15 °C) 1
1 o 1 o
Specific heat ratio 1
γ
Velocity head loss coefficient of a reducer, expander or other fitting 1
ζ
attached to a control valve or valve trim
Upstream velocity head loss coefficient of fitting 1
ζ
Downstream velocity head loss coefficient of fitting 1
ζ
Inlet Bernoulli coefficient 1
ζ
B1
ζ Outlet Bernoulli coefficient 1
B2
NOTE 1 – To determine the units for the numerical constants, dimensional analysis may be performed on the
appropriate equations using the units given in table 1.
2 5
NOTE 2 – 1 bar = 10 kPa = 10 Pa
–6 2
NOTE 3 – 1 centistoke = 10 m /s
NOTE 4 – These values are travel-related and should be stated by the manufacturer.
NOTE 5 – Volumetric flow rates in cubic metres per hour, identified by the symbol Q, refer to standard conditions.
The standard cubic metre is taken at 1 013,25 mbar and either 273 K or 288 K (see table 1).
6 Sizing equations for incompressible fluids
The equations listed below identify the relationships between flow rates, flow coefficients,
related installation factors, and pertinent service conditions for control valves handling
incompressible fluids. Flow coefficients may be calculated using the appropriate equation
selected from the ones given below. A sizing flow chart for incompressible fluids is given in
annex B.
6.1 Turbulent flow
The equations for the flow rate of a Newtonian liquid through a control valve when operating
under non-choked flow conditions are derived from the basic formula as given in IEC 60534-1.
6.1.1 Non-choked turbulent flow
6.1.1.1 Non-choked turbulent flow without attached fittings
Applicable ifΔ
()
[]LF1 v
The flow coefficient shall be determined by
Qρ/ρ
1o
C= (1)
NpΔ
NOTE 1 – The numerical constant N depends on the units used in the general sizing equation and the type of flow
coefficient: K or C .
v v
NOTE 2 – An example of sizing a valve with non-choked turbulent flow without attached fittings is given in annex D.
– 14 – 60534-2-1 © CEI:1998
6.1.1.2 Ecoulement turbulent non engorgé avec raccords adjacents
Applicable siΔ
LP P 1 F v
Le coefficient de débit doit être déterminé comme suit:
ρ /ρ
Q
1 o
C= (2)
NF Δp
1 P
F
NOTE – Voir 8.1 pour le facteur de géométrie de la tuyauterie .
P
6.1.2 Ecoulement turbulent engorgé
Le débit maximal qui passe dans une vanne de régulation dans des conditions d'écoulement
engorgé doit être calculé à partir des équations suivantes.
6.1.2.1 Ecoulement turbulent engorgé sans raccords adjacents
Applicable siΔ≥p F p −F × p
()
LF1 v
[]
Le coefficient de débit doit être déterminé comme suit:
Q ρ/ρ
1 o
C= (3)
NF p−×F p
1L 1 Fv
NOTE – Un exemple de dimensionnement d'une vanne en régime engorgé sans raccords adjacents est donné à
l'annexe D.
6.1.2.2 Ecoulement turbulent engorgé avec raccords adjacents
Applicable siΔ≥p F / F p −F × p
()( )
LP P 1 F v
L'équation suivante doit être utilisée pour le calcul du coefficient de débit:
Q ρ/ρ
1 o
C (4)
=
Np F −×Fp
1 LP 1 Fv
6.2 Ecoulement non turbulent (laminaire et intermédiaire)
Les équations du débit d'un liquide newtonien à travers une vanne de régulation fonctionnant
en régime non turbulent sont dérivées de la formule de base donnée dans la CEI 60534-1.
Cette équation est applicable si Re < 10 000 (voir équation (28)).
v
6.2.1 Ecoulement non turbulent sans raccords adjacents
Le coefficient de débit doit être calculé comme suit:
/
Q ρ ρ
1 o
C= (5)
NF Δp
1 R
60534-2-1 © IEC:1998 – 15 –
6.1.1.2 Non-choked turbulent flow with attached fittings
Applicable ifΔ
LP P 1 F v
The flow coefficient shall be determined as follows:
ρ /ρ
Q
1 o
C= (2)
NF Δp
1 P
NOTE – Refer to 8.1 for the piping geometry factor F .
P
6.1.2 Choked turbulent flow
The maximum rate at which flow will pass through a control valve at choked flow conditions
shall be calculated from the following equations.
6.1.2.1 Choked turbulent flow without attached fittings
Applicable ifΔ≥p F p −F × p
()
LF1 v
[]
The flow coefficient shall be determined as follows:
Q ρ/ρ
1 o
C= (3)
NF p−×F p
1L 1 Fv
NOTE – An example of sizing a valve with choked flow without attached fittings is given in annex D.
6.1.2.2 Choked turbulent flow with attached fittings
Applicable ifΔ≥p F / F p −F × p
()( )
LP P 1 F v
The following equation shall be used to calculate the flow coefficient:
Q ρ/ρ
1 o
C= (4)
Np F −×Fp
1 LP 1 Fv
6.2 Non-turbulent (laminar and transitional) flow
The equations for the flow rate of a Newtonian liquid through a control valve when operating
under non-turbulent flow conditions are derived from the basic formula as given in IEC 60534-1.
This equation is applicable if Re < 10 000 (see equation (28)).
v
6.2.1 Non-turbulent flow without attached fittings
The flow coefficient shall be calculated as follows:
Q ρ /ρ
1 o
C= (5)
NF Δp
1 R
– 16 – 60534-2-1 © CEI:1998
6.2.2 Ecoulement non turbulent avec raccords adjacents
En régime non turbulent, l'effet des raccords accolés ou d'autres éléments altérant
l'écoulement est inconnu. Bien qu’on ne dispose pas de renseignement sur le comportement
des vannes de régulation installées avec des raccords adjacents en régime laminaire et
intermédaire, il est conseillé d’utiliser dans ce cas les équations correspondant à des vannes
de même diamètre que la tuyauterie pour le calcul de facteur F . Il devrait en résulter des
R
valeurs du coefficient de débit conservatrices car la turbulence supplémentaire créée par les
raccords adjacents repousse plus loin l’émergence du régime laminaire. En conséquence,
cette approche tend à augmenter la valeur respective du facteur F pour un nombre de
R
Reynolds donné.
7 Equations de dimensionnement pour fluides compressibles
Les équations énumérées ci-dessous établissent les relations entre les débits, les coefficients
de débit, les facteurs de l'installation concernée et les conditions de service appropriées
applicables aux vannes de régulation véhiculant des fluides compressibles. Les débits des
fluides compressibles peuvent être exprimés soit en unités de masse, soit en unités de
volume; c'est pourquoi il est nécessaire de donner les équations pour les deux cas. Les
coefficients de débit peuvent être calculés en utilisant les équations appropriées choisies parmi
les équations suivantes. Un organigramme de dimensionnement pour fluides compressibles
est donné à l'annexe B.
7.1 Ecoulement turbulent
7.1.1 Ecoulement turbulent non engorgé
7.1.1.1 Ecoulement turbulent non engorgé sans raccords adjacents
Applicable si x < F x
[]γ T
Le coefficient de débit doit être calculé en utilisant l'une des équations suivantes:
W
C= (6)
NY xpρ
W TZ
C = (7)
NpY xM
Q MT Z
C = (8)
NpY x
NOTE 1 – Voir 8.5 pour les détails du facteur de détente Y.
NOTE 2 – Voir l'annexe C pour les valeurs de M.
7.1.1.2 Ecoulement turbulent non engorgé avec raccords adjacents
Applicable si x < F x
[]γ TP
Le coefficient de débit doit être calculé en utilisant l'une des équations suivantes:
W
C= (9)
NF Y xpρ
61P 1
60534-2-1 © IEC:1998 – 17 –
6.2.2 Non-turbulent flow with attached fittings
For non-turbulent flow, the effect of close-coupled reducers or other flow-disturbing fittings is
unknown. While there is no information on the laminar or transitional flow behaviour of control
valves installed between pipe reducers, the user of such valves is advised to utilize the
appropriate equations for line-sized valves in the calculation of the F factor. This should result
R
in conservative flow coefficients, since additional turbulence created by reducers and
expanders will further delay the onset of laminar flow. Therefore, it will tend to increase the
respective F factor for a given valve Reynolds number.
R
7 Sizing equations for compressible fluids
The equations listed below identify the relationships between flow rates, flow coefficients,
related installation factors and pertinent service conditions for control valves handling
compressible fluids. Flow rates for compressible fluids may be encountered in either mass or
volume units and thus equations are necessary to handle both situations. Flow coefficients may
be calculated using the appropriate equations selected from the following. A sizing flow chart
for compressible fluids is given in annex B.
7.1 Turbulent flow
7.1.1 Non-choked turbulent flow
7.1.1.1 Non-choked turbulent flow without attached fittings
Applicable if x < F x
[]
γ T
The flow coefficient shall be calculated using one of the following equations:
W
C= (6)
NY xpρ
W TZ
C = (7)
NpY xM
Q MT Z
C = (8)
NpY x
NOTE 1 – Refer to 8.5 for details of the expansion factor Y.
NOTE 2 – See annex C for values of M.
7.1.1.2 Non-choked turbulent flow with attached fittings
Applicable if x < F x
[]
γ TP
The flow coefficient shall be determined from one of the following equations:
W
C= (9)
NF Y xpρ
61P 1
– 18 – 60534-2-1 © CEI:1998
W TZ
C = (10)
NFpY xM
81P
Q MT Z
C = (11)
NFpY x
91P
NOTE 1 – Voir 8.1 pour le facteur de géométrie de la tuyauterie F .
P
NOTE 2 – Un exemple de dimensionnement d'une vanne en écoulement turbulent non engorgé avec raccords
adjacents est donné à l'annexe D.
7.1.2 Ecoulement turbulent engorgé
Le débit maximal qui passe dans une vanne de régulation en régime engorgé doit être calculé
comme suit.
7.1.2.1 Ecoulement turbulent engorgé sans raccords adjacents
Applicable si x ≥ F x
[]
γ T
Le coefficient de débit doit être calculé à partir d'une des équations suivantes:
W
C= (12)
0,667NFx pρ
61γT1
W TZ
C= (13)
0,667Np Fx M
81 γ T
Q MT Z
C= (14)
0,667Np Fx
91 γ T
7.1.2.2 Ecoulement turbulent engorgé avec raccords adjacents
Applicable si x ≥ F x
[]γ TP
Le coefficient de débit doit être calculé à partir d'une des équations suivantes:
W
C= (15)
0,667NF F x pρ
61PTγ P1
W TZ
C= (16)
0,667NF p Fx M
81PTγP
Q MT Z
C= (17)
0,667NF p Fx
91PTγP
60534-2-1 © IEC:1998 – 19 –
W TZ
C = (10)
NFpY xM
81P
Q MT Z
C = (11)
NFpY x
91P
NOTE 1 – Refer to 8.1 for the piping geometry factor F .
P
NOTE 2 – An example of sizing a valve with non-choked turbulent flow with attached fittings is given in annex D.
7.1.2 Choked turbulent flow
The maximum rate at which flow will pass through a control valve at choked flow conditions
shall be calculated as follows.
7.1.2.1 Choked turbulent flow without attached fittings
Applicable if x ≥ F x
[]γ T
The flow coefficient shall be calculated from one of the following equations:
W
C= (12)
0,667NFx pρ
61γT1
W TZ
C= (13)
0,667Np Fx M
81 γ T
...
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