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in order to promote transparency and accountability in the working of every public authority,
and whereas the attached publication of the Bureau of Indian Standards is of particular interest
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timely dissemination of this information in an accurate manner to the public.
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“Step Out From the Old to the New”
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Jawaharlal Nehru
IS 14641 (1999): Turbocompressor - Performance Test Code
[MED 22: Compressor, Blowers and Exhausters]
“!ान $ एक न' भारत का +नम-ण”
Satyanarayan Gangaram Pitroda
“Invent a New India Using Knowledge”
“!ान एक ऐसा खजाना > जो कभी च0राया नहB जा सकता ह”
है”
ह
Bhartṛhari—Nītiśatakam
“Knowledge is such a treasure which cannot be stolen”
..”..&_
,.
,<’.
IS 14641:1999
ISO 5389:1992
W?#v71m
dlmw
i
~
t.
‘,
‘r. -.,z
:,
‘“4
If
1: ‘
–m@wm%Kil
I
1:
Indian Standard
TURBOCOMPRESSOR
— PERFORMANCE
TEST CODE
ICS
23.140
,
.
0
BUREAU
MANAK
9 BAHADUR
NEW
Februaryl
999
BIS 1999
INDIAN
OF
BHAVAN,
DELHI
d
STANDARDS
SHAH
ZAFAR
MARG
110002
Price Rs. 400.QQ
I
1s14541 :1999
1s05389:1992
NATIONAL
0
FOREWORD
This Indian’Standard which is identical with ISO 5389:1992’Turbocompressom
— Performance test code’
issued by the international Organization for Standardization (ISO) was adopted by the Bureau of Indian
Standards on the recommendations
of the Compressor, Blowers and Exhausters Sectional Committee
(HMD 22) and approval of the Heavy Mechanical Engineering Divisiin Council.
J
~
““”--l“1
The text of ISO standard has been approved for pubiiition
as Indiin Standard without deviations.
Cettain terminology and conventions are, however, not identicat to those used in Indan Standards. Attention
“Eparticularly drawn to the following:
a)
Wherever
the words ‘International
Standard
appear
referring to this standard,
thev should
be read as ‘Indian Standard’.
b) Comma
practice
(,) has been used as a decimal marker while in Indian
is to use a point (.) as the decimal marker.
Standards,
the current
In this adopted standard,
reference appears to certain International
Standards
for which Indian
Standards also exist. The’corresponding
Indian Standards which are to be substituted in their place
are listed below along with their degree of equivalence
for the editions indicated:
CorrespondingIndian
Stan&rd
Degree of
Equivalence
ISO 31-0:1981
IS 1890(
Identical
iso
IS 1890 (Part
1 ) :1982
do
ISO 31-2:1978
lS1890(Part
2):1982
do
1S031-3
lS1890(Part
3):1982
do
/S0 31-4:1978
lS1890(Part
4):1982
do
1s0 31-5:1979
IS 1890 (Part
5)
do
ISO 31-6:1980
lS1890(Part
6):1983
do
ISO 31-7:1978
lS1890(Part
7):1983
do
ISO 31-8:1980
lS1890(Part
8):1983
do
ISO 31-9:1980
IS 1890 (Part
9)
:1983
C’k)
ISO 31-10:1980
iS1890(
Part 10):1983
do
ISO 31-11:1978
lS1890(
Part 11 ):1982
do
ISO 31-12:1981
IS 1890 (Part
12)
:1983
do
1S031-13
IS 1890 (Part
13):
1983
do
hternational Standard
31-1:
i978
:1978
:1981
iSO 1000:1992
The concerned
technical
committee
‘Measurement
of fiuid flow by means
Part O) :1983
IS 10005:1985
:1983
dc
has also reviewed
the provisions
of ISO 5167-1
of pressure differential devices — Part 1 : Orifice
: 1991
plates,
nozzies and Venturi tubes inserted in circular cross-section
conduits running fuii’ referred in this
adopted standard and has decided that it is acceptable for use in conjunction with this standard.
In reporting the resuits of a test or analysis made in accordance with this standard, if the final value,
observed or calculated,
is to be rounded off, it shall be done in accordance
with IS 2:1960 ‘Ruies for
rounding off numerical vaiues ( revised )’.
(i)
IS 14641:1999
ISO 5389:1992
r,
, ,. .-.
Introduction
The terms “guarantee” or “guaranteed” and “performance” used in this International
Standard are to be understood in the engineering rather than the contractual sense.
A guarantee relates to a specific aspect of the plant or its operation which ia defined in
the contract.
With the aid of the test described in this International Standard, the actual performance data cap be compared with the guaranteed values.
The contractual consequences of any deviations are not covered by this International
Standard. A setisfacto~ test result does not signify acceptance in the contractual
sense, as such acceptance may depend on other conditions stipulated in the contract.
This International Standard provides standard directions for conducting and,repotting
tests on compressors to establish their performance concerning one or m&e of the
following aspects under specified conditions and for comparing the results with the
guaranteed performance:
a)
the quantity of gas or vapour delivered;
b)
the pressure rise or pressure ratio produced;
c) the power required for compression or the efficiency of the compressor
Iaccording to specified definitions);
d)
the stable working range – surge and maximum flow limits.
To meet this purpose, this International Standard establishes rules concerning
a) the test procedure (including the rnaaeuremente to be taken, and the preparation and execution of the test);
b)
the instrumentation to be used to provide adequate accuracy;
c) the methods of converting the test results in order to provide values that may
be compared with the guaranteed figures;
d) the confidence limits of the converted test results according to the accuracy of
the particular measurements.
(ii)
.—
.
IS 14641:1999
ISO 5389:1992
Contents
Page
1 scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2
Normative references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
3
Definitions, formulae andreference processes . . . . . . . . . . . . . . . . . . . . . . . . . .
1
4
Symbols andsubscripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
5
Equipment, methods and accuracy of measurements . . . . . . . . . . . . . . . . . . . .
12
6
Preparation for the test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
7
Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
8
Calculation andadjustmentof testrasuks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
9 Comparison with guaranteed values and tolerances . . . . . . . . . . . . . . . . . . . . .
24
10 Test repon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
Annexes
Properties of gases and gas mixtures - Recommendations relating to the
compressibilityfactor and to derivative cornpreseibifityfactors . . . . . . . . . . . . .
31
B Viscosity ofgasesand gasmixturas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
c Conversionfactorefrom non-Siunits to Slunits. . . . . . . . . . . . . . . . . . . . . . . . .
48
D
~milariW of flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
E
Correction method for the influence of the Reynolds number on the
performance ofcentrifugal compraeeore. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
F
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
G
bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
171
A
(iii)
f,
d
IS 14641:1999
ISO 5389:1992
Indian Standard
TURBOCOMPRESSOR
— PERFORMANCE
TEST CODE
1
Scope
This International Standard covers blowers or compressors and
exhausters of the centrifugal, mixed flow, or axial flow types
(inclusively covered by the term turbocomprassors), with and
without intercooling, handling any vapour or gas the physical
properties of which are reliably known.
It maybe applied to any compression process, with or without
bleed-off or sidestreams, which takes place in one or more
casings.
This International Standard gives no rules for the measurement
of any other aspect of the compressor which may be the subject of a guarantee, such as
2
Normative
references
The following standards contain provisions which, through
reference in this text, constitute provisions of this International
Standard. At the time of publication, the editions indicated
were valid. All standards are subject to revision, and parties to
agreements based on this International Standard are enr.c:’-aqed
to investigate the possibilityof applying the moat recent editions
of the standards indicated below. Members of IEC and ISO main
tain registersof currently valid International Standards.
ISO 31 (parts O to 13)1), Quantities,
units and symbok.
ISO 1000: – 2), S1 units and recommendations
for the use of
their multiples end of certain other units.
a)
mechanical performance;
b)
vibrations;
c)
pulsations;
d)
noise level;
e)
sewice and reliabili~
f)
commercial questions.
The theory usad in this Internat”mnalStandard is baaad on the
laws of similarity of fluid flow (similar velocity triangles). The
observation of these laws determines s~cific requirements for
the execution of acceptance testa. In all cases, where a close
approximation to these requirements is not possible, this international Standard can only be applied by mutual agreement.
Compressors supplied to handle gases the physical properties
of which are not reliably known can only be tasted within
certain limits.
For identical compressors, produced in series, the testing of an
arbnrarily chosen sample may be agreed upon.
ISO 5167-1
: 1891,Measurement
of fluid flow
by means
of
pressure differential devices – Part 1: Orificeplates, nozzies
and Venturi tubes inserted in circular cross-section conduits
running full.
3
Definitions,
formulae
and
reference
processes
For the purposes of this International Standard, the following
definitions apply.
3.1
Definitions
performance
relating
to compressor
3.1.1 standard inlet point: The inlet point considered to be
representative of the compressor. It is generally at the compressor inlet flange.
1) Currentlyunderrevieion.
2) To be published.(Revisionof ISO 1000: 19S1.)
1
IS 14641:1999
ISO 5389:1992
3.3
3.1.2 standard discharga point: The discharge point considered to be representative of the compressor. It is generally at
the compressor discharge flange.
3.1.3
Quantity
process
The determination of the internal power (3.6.5) is based on the
assumption of a reversible reference process, hence the
necessity of a definition of the corresponding efficiency, taking
account of energy losses due to the irreversibility of the actual
compression process.
of gas or vapour delivared
3.1.3.1 usable mass rate of flow for a compressor: The
mess rate of flow delivered at the standard discharge point.
3.1.3.2 usabla mass rata of flow for an exhaustar:
Reference
The reference process is characterized by the law
p = f(v)
The
mese rate of flow aspirated at the standard inlet point.
which is used to determine the specific compression work:
3.1.3.3 actual inlet volume flow for a compressor: The
actual volwne rate of flow compressed and delivered at the
standard discharge point, referred to the conditions of
temperature, pressure and composition (for example humidity)
prevailing at the standard inlet point.
.
‘!
Wm =
~1
V dp
The total specific compression work is thus determined using
the equation
3.1.3.4 actual inlat volume flow for an axhauster: The
actual volume rate of flow aspirated at the standard inlet point.
C*2 – ~12
wm,t=wm+.
~
NOTES
1 Unless otherwisespecified, the actual inlet voluma flow will be
referredto total temperatureand total pressure.
2
By approximation with the low flow speeds (Ma < 0,2)
normally prevailing in the inlet and discharge nozzles, the total
pressuresand total temperatures can be used in the calculation
directly:
For gas-vapour mixtures, see A.4.2.7.
3.2
Basic formulae
for gases
2
Gas basic formulae are given in table 1.
Table 1 -
3.2.1
Equation of state
3.2.2 I Compressibility factor
(V dp)t
1
Gas basic formulaa
Formula
Term
No.
J
wm,t =
For e real gas
For a perfect gas
pV = ZRT
pV = RT
I
z
I
Z=l
3.2.3
Isothermal deviation
factor
‘=~(~)T=l-~(~)T
y=,
3.2.4
Isobaric deviation
factor
‘=
‘=0
3.2.5
Isentropic
axponent
H--)P-l=H--)P
ap
~=_~
Y
K=y=—
p-Ws=T
()
CP
Cv
NOTES
1 Tha data serving as a reference for the determination of gas properties shall be agreed between purchaser
and vendor.
2 Clause A. 1 deals with general recommendations relating to the thermodynamic data for gases and gas
mixtures.
3
Clause A.2 deals with specific recommendations for some of the more common gases.
, ~,,
-.-—-
Is 14641:1999
ISO 5389:1992
3.4
d
Reference
processes
near-perfect
gases
forusewith
perfecter
,.ti
3.4.1.2 The specific compression work based on static conditions is calculated using
>-----
n–1
The following methods of computation of specific compression
work are recommended to be applied
i
wrn,pol =
J:’vdp’pO’=(fi)
p’v’[6)y-1]
when agreed between purchaser and vendor, or
when the deviation of gas properties from perfect gas
laws at any state point of the compression process of an
uncooled compressor, or at any state point of a compression section included between two successive intercoolers of a cooled compressor, do not exceed the limits
given in table 2 for the appropriate pressure ratio.
Within the limits given, the errors in specific isentropic compression work and discharge specific volume will be leas than
1 % and 2 % respectively if calculations are made according to
perfect gas laws instead of real gas equations.
it is recommended that in most cases polytropic compression
be used as the reference process.
Polytropic compression should always be adopted for any case
in which the gas used for the acceptance test has a ratio of
specific heata which differs from that of the guarantee gas by
more than 1 %.
@
3.4.1 Polytropic compression
3.4.1.1
A polytropic compression process fallows the law
3.4.1.3
In its general form the polytropic compression offers,
owing to the free choice of the exponent n, great liberty in
adapting it to any change of state. With n = y the compression becomes isentropic. When n approaches unity, the
compression approaches an isothermal process. If, with
multistage compressors, a single-stage reference compression
does not represent the actual process with sufficient accuracy,
a multistage polytropic compression may be chosen. From the
above it follows that the polytropic compression is suited for
cooled and uncooled, and for single-stage and multistage,
compressors.
3.4.1.4 In the case of compressorswith interstage cooling the
polytropic compression approaches isothermal compression at
one extreme, and iaentropic compression at the other, depending on whether the process takes place at a constant
temperature or the aerodynamic flow losses only are removed
by the cooler. An approximation has to be made by suitable
choice of the exponent n and the number of stage groups according to tha arrangement and effectiveness of the cooling.
3.4.1.5
For compressors without cooling (adiabatic compression) the isentropic process is often used as a reference,
but here too the polytropic process offers a better basis on
which to assess the aerodynamic losses of a compressor.
It takes into account the increased compression work caused
by the reheat losses. This increase is particularly noticeable at
either high pressure ratios or low efficiencies.
pv” = pl VI n = constant
where for perfect gases
3.4.2
()
()
Isentropic compression
Ig :
~=
Ig
3.4.2.1 In this reference process, compression takes place
over the whole part of the pressure range (depen-ding on
whether it is a single-stage or multistage machine) at constant
entropy, i.e. n = K.
p2 T,
—“—
pl
T2
Table 21) – Limits for the pressure ratio
Pressure
ratio z)
P2
Maximum ratio
between maximum
x rnax
Xrnin
Y rnax
Y~in
P1
and minimum values
Of K(= y)
1,4
1,12
0,279
-0,344
1,071
0,925
2
1,10
0,167
-0,175
1,034
0,964
4
1,09
0,071
-0,073
1,017
0,962
a
1,03
0,050
-0,041
1,011
0,966
16
1,07
0,033
– 0,031
1,006
0,991
32
1,06
0,026
-0,025
1,006
0,!393
1)
Table taken from [1].
2)
For pressure ratios between those shown, the limiting values shall be obtained by interpolation.
3
IS 14641:1999
ISO 5389:1992
.4
3.4.2.2
3.5.3
Isentropic compression follows the law
Methods of polytropic analysis (Schultz method)
k.,;,_,.-$,
PVK = p, VIK = constant
3.5.3.1 The formulae of the following method are derived
from the method developed by Schultz (see [21).
3.4.2.3 The sDecific comwession work based on static conditions is expressed by the equation
K-1
2
w m,s =
!
pl v,
(V dp)s = ;:
1
P2
—
PI
()–1
K
_,
3.5.3.2 The determination of exponent n for the general case
of real gases is carried out assuming that the efficiency remains
constant throughout the process:
..2
dp
~pol=v~=
3.4.3
Isothermal
11 (v dp)wl
h2 – hl
compression
In this reference orocess. commission takes Dart over the
whole (single stage) or part (multistage) of the pressure range
at a constant temperature. As a rule the inlet temperature T1 of
the compressor or stage group under consideration is used.
The exponent n = 1,and the specific compression work based
on static conditions is defined by the equation
3.5.3.3 This makes it possible to detarmine an average
polytropic exponent with sufficient exactitude:
1
‘=–k’~-)?dl+~M)
where
3.5
Reference
3.5.1
General
proceaaes
for use with
real gases
I
R ZM
When tables, equations of state or charts giving the appropriate thermodynamic data are available, it is recommended
that they be used to determine the specific compression work
(see 3.5.2).
~pol =
mcP~ – R ZM XM
with average values for the gas stream:
When such tables, equations of state or charts are not available
and the limits of table 2 are exceeded, it is recommended that
polytropic compression be adopted as the referance process
and the specific compression work should be computed by the
Schultz method of polytropic analysis (see 3.5.3 and [21).
x~=
3.5.2
CPM=
Method
using tables or charts
If possible, the gas properties, especially for gas mixtures, are
best determined from tables and equations of state since the
diagrams are in general less accurate (see clauses A. 1 to A.3).
The properties represented in diagrams and tables are today
frequently compiled in the form of computer programs which
can readily be included as subprograms in the calculation
programs for the design of the compressor and test evaluation.
Specific information about the determination of these gas
properties and changes of state cannot be listed here owing to
the multiplicity of the processes and values used. The user
of this International Standard is referred to the relevant
literature.
4
z~=
z, + Z2
z
x,
+ X2,
z
Cpl + CP2
2
The above averages are a simplification valid for pressure ratios
~<4.
P1
For higher pressure ratios, it is recommended that Schultz’s
method be followad, i.e. averages are formed with double
weight given to the mid-point. The mid-point can be chosen at
the square root of the pressure ratio and half the temperature
rise.
For pressure ratios Up to 4, the difference between the results
of both methods is less than 0,2 % for specific polytropic compression work and 0,5 ‘C for discharge temperature.
IS 14641:1999
ISO 5389:1992
3.5.3.4 Theoretically, the exact assessment of the specific
polytropic compression work assumes the previous computation of factor g by use of the formula
~
(C22– C12)
Wm+
~
~t=—
— ——
h’z – h,
<=
+
ht,2 – ht,l
R (Z2T2 – ZIT1)
Where there is deliberate cooling within the machine (or section of the machine) under consideration, this formula becomes
where
b
,!, ~
,}
h,
Unless otherwise agreed, the reference efficiency is baaed on
total conditions and the formula becomes
is the enthalpy at the inlet;
(C22– C,4
Wm +
h’2
is the resulting enthalpy at the outlet if the process
had bean isentropic.
NOTE – Where specific values of the factors X, Y and Z are not
available values may be obtained from the genaralizad curves gimm in
annex D.
3.5.3.5 The specific compression work based on static conditions may thus be determined:
2
wrrl,pol =
>- )
J
ZMRT1 ~.
(V dp)pol = ~
1
?t=h
2
t,z – ht,l – Q1 -2
where Q1 _ z is the heat removed by the cooling within the
machine (or section of the machine).
The above definition is complete only when the type of the
reference process adopted is indicated by the corresponding
subscript. Consequently reference efficiencies are given by the
following formulae.
p2 m
[() E
–1
3.6.1.1
]
NOTE – Thm equation is not strictly correct [sss [2]) and should only
be used in cases where the compressibility factor Z is substantially
constant throughout the compression process.
The polytropic efficiency
‘m,pol
~PfJ =
~2
_
~,
-Q1-2
The equation for Wm,Pd given in figure D.9 can also be used.
t
3.5.3.6
For compression ratios ~
<4
the correction factor ~
may be considered as equal to 1 and can therefore be neglected
in the computation.
3.5.3.7 For similarity testing of compressors without
intermediate cooling, a single-stage process should be
adopted, determining an avaraga polytropic exponent such as
defined above.
3.5.3.6 For tests of compressors with intermediate cooling a
multistage referance process should be adopted with polytropic
exponents suitad to each section included between two successive intercoolers.
3.5.3.9 Similarity calculations according to Schultz’s method
are shown schematically in figure D.7.
3.6
Definition
losses
of reference
efficiency,
power
end
3.6.1 reference efficiency, VW,, V. or qT: Ratio of the
specific compression work to the total enthalpy rise in the
machine (or section of the machine) within which there is no
deliberate cooling and when baaed on static conditions as
defined by the formula:
2
~1
V dp
‘=hz–hl=hz–hl
Wm
(C22– C12)
‘m,pol +
~pd,t = ~t z
2
-ht,l–
Q1_2
See also 3.5.3.3.
.
3.6.1.2
The iaentropic efficiency
w .,s
‘s=h2–~1
-Q1-2
(C22– C12)
Wm,s +
2
rls,t = hL2 – ht,l – QI -2
3.6.1.3
The isothermal efficiency
wm,J
?T = h2
-hl–
Wm,T +
Q1_2
(C22- C12)
*
qT,t=ht2-htl-Ql-2
3.6.2 reference power Pfl, Ps or PT: Power absorbed by
the gas during the reversible reference process excluding any
losses. The reference power shall be defined with the subscript
corresponding to the adoptad reference process.
5
IS 14641:1999
ISO 5389:1992
The formulae for the reference power are also different
depending on the calculation system of the specific compression work.
rnternel power, Pin: ‘Power effectively absorbed by
gas during the actual compression process. It is given by the
formula
3.6.5
Unless otherwise agreed the reference power is baaed on total
conditions and is given by the following formulae.
3.6.2.1 The polytropic reference power
‘pol, t = ~m
3.6.2.2
(
*
~22 _ ~12
~
)
The isothermal reference power
(
Qa+PL
P~ ~
Pin = A+
~T.t
Q=+PL
or
The isentropic reference power
PT, t = (?m wm,T +
P
Pin = *+
l’s,t
.)
P s,t = f?m ‘m, s +
3.6.2.3
Qa+PL
or
C22 _ ~12
‘m, pol +
(
Ppolt
Pin = _+
L’pol,t
C22 – C12
*
)
Where the local Mach number at tha standard inlet and
discharge points is lees than 0,2 it is sufficiently accurate to
calculate the reference power directly from total conditions
using the following approximate formulae:
2
Ppo,,~ = qm Wm,pol,t = qm
P s,t = qm Wm, s,t = qm
pT,t = qm ‘m,T,t = qm
~
I
!
, (V d~)t, POI
2
, (v dp)t,s
For compressors with intermediate cooling the sum of internal
powers in each section between two successive intercoolers
should be computed:
Pin = Pinl + Pinll + ... + Pin
1
mechenice} power losses, Pf: Losses due to friction
in the bearings and sealing rings and in any transmission gear
contractually included within the compressor.
3.6.6
3.6.7 effective compressor power, p~: power input $Jtthe
coupling of the compressor or at the coupling of the transmission gear depending on the contract agreement. It is given
by the formula
.
P* = Pin + Pf
2
(V d@t,T
1
beet transmission losses, Q.: Loeeee due to heat
transmission from the area A CSof the compressor casing to the
ambient atmosphere, expressed by the formula
3.6.8
power lose in driving machine, Ppr: Power loss in
the turbine or in any other driver of the compressor and the
intermediate driving system.
3.6.3
3.6.9
total power of the unit, Pun: Power given by the for-
mula
P un = Pe + Ppr
For values of Qa leas than 0,02 Per an approximate value can be
adopted for a, i.e.
a = 14 W/(rrr2. K)
3.6.10 internal efficiency, ~in: Ratio of the reference power
defined in 3.6.2 to the internal power.
3.6.4
power loss due to leakage, PL: LOSSSS
due to leakage
through external labyrinths; these can generally be calculated
using the formula
Its value depends on the type of adopted reference process.
Internal efficiency is given by the formulae
Pp~,t
~in,pol = ~
6
in
“
, ,’!
IS 14641:1999
ISO 5389:1992
d
3.6.14 overall efficiency of the unit, qun: Efficiency of the
unit which takea account of all energy losses of the unit,
including compressor, transmission gear and driver. It is given
by the formula
3.7
3.6.11 mechanical
efficiency, qf: Ratio of the internal
power to the effective power at the coupling of the %ompreaaor, or at the coupling of the transmission gear, depending
on the contract agreement. It is given by the formula
Pin
Pin
~f=~=pin+pf
3.6.12 affective efficiency,
qe: Ratio of the reference
power defined in 3.6.2 to the effective power at the coupling of
the compressor, or at the coupling of the transmission gear,
dapending on the contract agreement. It is given by the formula
Definition
uncertainty
of tolerance,
inaccuracy
and
As used in “thisInternational Standard, the terms “tolerance”,
“irraccuracy” and- “uncertainty” have specific and clearly
different meanings.
3.7.1 tolerance: Amount by ~ich
the value of a particular
parameter or a quantity is permitted to deviate from a eat value
by the terms of the contractor other agreement.
3.7.2 inaccuracy: Extent by which the measured or computed value of a ~Wrameter or quantity deviates from the true
value, resulting from the inevitable errors in measurement and
computation.
3.7.3 uncertainty: MaAmum likely magnitude of the inaccuracy of a particular parameter or quantity such that it can be
said with at least 95 % confidence that the measured or computed value does not deviate from the true value by an amount
greater than the statd uncertainty.
Its value depends on the type of adopted reference process.
4
3.6.13 primary afficiancy, VP,: Ratio of the effective power
of the compressor to the power or energy input to the driver. It
is given by the formula
Symbols ad
subscripts
The symbols, subscripts and definitions used in this international Standard are iri accordance with ISO 31 and ISO 1000,
and are given in teblea 3 and 4.
Equations used are dimensionally homogeneous.
Pe
~pr ===
un
P,
Pe + Ppr
To simplify use of this International Standard, conversion
factors are given in annex C.
7
.
‘.-.-k
IS 14641:1999
ISO
d
5389:1992
Table 3 – Symbols
Symbols
Quantities
A
Area
a
Sonic velocity
b
Definitions
and Observations
Dimansionsl)
L2
a = J=”
LT-1
Outlet tip width
L
Cp
Molar specific heat at constant
pressure
Cp = A4cp
ML27--2@-l
nlol-1
c“
Molar specific heat at constant
volume
Cv = Mev
ML2T-2@-l
~o[-l
c
Absolute velocity
CP
Spacific heat at constant pressure
L21--2@-l
Cv
Specific heat at constant volume
L2T-2@-l
D
Reference diameter of the rotor
L
F
Torque
ML2 T-2
G
Precision class
h
Specific enthalpy
dimensionless
L2 T-2
ht
Total specific enthalpy
L.
I
.. ...’
LT-1
L2 T-2
ht=
h+;
()
M
Molar mass
Ma
Mach number of the flow
M
Maas which corresponds to one mole
Ma=~
dimensionless
a
Approximate Mach number of gas
flow through area A
Mat=G
Mau
Peripheral Mach number (arbitrary
definition)
Refers in this International Standard to inlet
conditions
dimensionless
m
Polytropic exponent in the P – T
diagram
Pm _ constant
T
dimensionless
Mat
9ttr
dimensionless
ZR Tt
r ~
See also 3.5.3.3
mi
Mace proportion of a gas
component
dimensionless
N
Speed of rotation
T-1
N,
Ratio of reduced speeds
dimensionless
‘r=(&l)JJ&)..
p Vn = constant
Polytropic exponent in the p – V
diagram
n
ML2 T-3
P
Power
P
Absolute static pressure
Pa
Atmospheric pressure
Pd
Dynamic pressure
See 8.1.3
Pe
Effective (or gauge) pressure
Pe=P–
Peat
Saturation pressure
Saturation pressure at temperature of the
vapour~gas mixture
Pt
Total pressure
Pt=P+Pcl
I
dimensionless
Sea also 3.4.1
ML-1 T-2
Force to be exerted on the unit area moving with
the gas
ML-1 T-2
I
ML-1 T-2
ML-1 T-2
Pa
ML-1 T-2
ML-1 T-2
I
.
,
IS 14641:1999
ISO 5389:1992
.-/
Table 3 – Symbols (continued)
Symbols
Quantities
Definitions
I
end observations
Partial vapour pressure
ML-1
Q
Heat flow
ML2 T-3
Q..
Corrected heat losses (equivalent)
ML2 T-3
Qin
Internal heat losses (equivalent)
ML2 T-3
Qnm
Mechanical heat losses (Souivaient)
Q.
Heat losses by thermal transmission
from the surface
9m
Mass rate of flow
I
MT-1
9V
Volume rate of flow
I
L3 T-1
R
Specific gas constant
Pv
Chantitv of heat supplied or delivered per unit time
I
T-2
ML2 T-3
ML2 T-3
+
R=—
Reu
. .
Dimensionslj
Peripheral Reynolds number
(arbitrary)
I
L2T-2@-l
Rmol
M
dimensionless’
Reu = *
Vt,
1
Refers in this International Standard to total inlet
conditions
Rmol
ri
Universal gas constant
I RmOl = 8314 J.kmol-l.
Volumetric proportion of a
component
i
K-’
--l
mol-l
dimensionless
s
Specific entropy
T
Absolute static temperature
Temperature on Kelvin scale
t
Usual static temperature
Temperature on Celsius scale
t~, Td
Dynamic temperature
Latv Tsat
Saturation temperature
tt, Tt
ML2T-2@-l
Stagnation temperature (total)
I
tt=t+t~
Tt=T+Td
See 8.1.4
u
v
Peripheral velocity
Volume
I
u = nDN
L3
I
Ratio of volume rate of flow ratios
(qv,t,z/qv,t,l)T~
v, =
v
Specific volume
LT-l
Peripheral velocity at reference diameter
dimensionless
(q~,~,z/qv,t,l)cjU
I Volume par unit mass
M-I
L3
Specific compression work
Wm=Jvdp
L2 T-2
x
Isobaric daviation factor
See 3.2.4
dimensionless
x
Variable
Y
Isothermal deviation factor
Y
Molar proportion
z
Compressibility factor
I Sea 3.2.2
dimensionless
z
Number of stagea considered
Indicates also number of stage groups separated by
intercoolera
dimensionless
a
Heat transfer coefficient
I
I
Rate of heat flow per unit area of surface per unit
temperature difference
MT-3 ~-l
Y
Ratio of specific heats
as used
See 3.2.3
dimensionless
dimensionless
dimensionless
Y=q
Cv
9
.,
1
IS 14641:1999
ISO 5389:1992
Table 3 – Symbols
Symbols
r
. ..—
Ax
——.
Ax
——.
Quantities
Work input coefficient
(concluded)
Definitions
r=—
end observations
Dimensionsl~
dimensionless
Aht
U2
Absolute difference or variation of x
same as for x
Relative difference or variation
dimensionless
x
——-—.
Blade position
a
. .—.-.—. —.
Cx
Absolute possible deviation of x
_ .-_.
Relative deviation
:x
Position of adjustable guide vanes or blades
same as for x
dimensionless
x
Coefficient
v
Efficiency
K
Isentropic exponent
~i~
Coefficient
P
Dynam”c viscosity
ML-1 T-1
Kinematic viscosity
L2T-1
v
i = 3, 4 orp (see clause 9)
dimensionless
(i
dimensionless
.
.
‘=-;(%)s
~
i = 1, 2, 3 . . . (see annex B)
k=l,2,3
...
v=— P
“mens’on’es
dimensionless
Q
t
Correction factor
See 3.5.3.4, 3.5.3.5 and 3.5.3.6
dimensionless
Q
Density
Mass per unit volume
ML-3
0
Standard deviation
See 5.9.4
same as for x
TX
Relative measuring uncertainty or
tolerance on x
See 3.7
dimensionless
@
Flow coefficient
dimensionleaa
@=-
D2 U
fP
Relative humidity
Sea A.4.2.1
dimensionless
x
Humidity content
See A.4.2.I
dimensionless
Y
Reference process work coefficient
Wm i
Pi = -
dimensionless
where i = pol, s or T
#z
.,I )
10
See A.3.I
Acentric factor
O.J
-..
..–a
.
..–.
.–.
–- mol
.- #–..
. . .
,L = ,.
.,
.
.
= amount 01 auosrance.
mngm; M = mass; I = ume; w = Iemperawre;
dimensionless
#,
——
- IS 14641:1999
ISO 5389:1992
.4
Table 4 – Subscripts
Subscripts
1, II ,...,
j
Observations
The Roman type figures relate to numbers of order of the compressor
sections
I
I
I
Cooled section
iic
I
Meaning
Section 1, Section ii, . . .. Section j
I
Inlet
1
I
Discharge
2
I
I
la
I Atmospheric
I
Cooied section when compressor is divided into uncooled section I and
cooied section ile
Relates to quantities measured at the standard iniet point. In combination
with other subscripts denotes “inlet”
Relates to quantities measured at the standard
nation with other subscripts denotes “outlet”
discharge
point.
I Characterizes atmos~heric measures and tem~eratures
adj
Additional
I
Cd
I Condensate
I
co
Converted
I
I
Additional uncertainty when
clause D.2)
inner toierance limit is exceeded
Cr
I Critical
I Characterizes criticai pressures and temperatures
I
Cs
I Casing
I Characterizes the quantities measured on the compressor casing
Combined
D
Id
(see
Relates to the quantities converted to specified conditions by similarity
computation
I
comb
In combi-
When ‘comb iS combined h suPerposition of resuits of *veral sta9es
Rotor
! Dvnamic
ICharacterizes dvnamic oressures and temr)eratures
1
En
I End
I
I
Ex
I Extreme
I
Characterizes the power input at the coupiing of the compressor
t-+--+=
--t----! Friction
If
I
1
Fluctuation
Additional uncertainty due to fluctuations of power input
G
Dry gas
Characterizes the quantities of dry gas
Gu
Guaranteed
Relates to the quantities specified in the contract
1---icl, Icll,
. . . . iCj
i
I
ICharacterizes the friction ioaaes (mechanical iosses)
1
fiuc
in
IL
intercooier 1, ii, . . .. j
Reiates to first, second, . . .. jth intercooler
Component
Relates to component i of a gas mixture
I Internai
I
I Leakage
I
M
Arithmetic mean
m
Mixture
mex
Maximum
I
rnfi
I “Minimum
I
moi
I Molar
Characterizes the arithmetical means of iniet and outlet quantities
I
I
I Characterizes lubricating (and sealing) oii (mechanical
I
losses)
I Primarv
I Characterizes the driver of the compressor
I Isobaric
! Characterizes an isobaric (constant pressure) process
DOI
I PolvtroDic
I Characterizes a poivtropic process
r
Reduced
Characterizes reduced pressures and temperatures
res
Resuiting
When x results from combination of several variables with individual errors
s
isentropic
Characterizes an isentropic process
Pr
ID
I
.
11
IS 14641:1999
ISO 5389:1992
Table 4 – Subscripts (coduded)
Subscripts
Obaenrations
Meaning
Sat
Saturation
T
isothermal
Characterizes an isothermal process
Te
Tested
Relates to the quantities measured during the test or fixad as test conditions
t
Stagnation (total)
tol
Tolerated
tot
Relative
included additional uncertainty Tadjand/Or TtluC
When TXCO~~
u
Peripheral
Relates to the reference rotor diameter
Unit
I
ut
I Usable
I
v
Vapour
v
Isochoric
Characterizes a constant volume process
w
Water
Characterizes cooling water
x
Variable
un
I
5
Equipment,
methods
and
accuracy
Characterizes thp unit comprising the compressor, the intermediate driving
I
system and the prime mover
I
of
measurements
5.1
General
5.1.1 This clause describes the instruments, equipment and
methods of measurement to be used in testing compressors in
accordance with this International Standard and describes the
measurement accuracy.
Where no specific requirements for a particular measurement
are included, the instruments and methods of measurement to
be used are subject to agreement.
5.1.2 Where an International Standard is available relating to
a particular measurement or type of instrument, any measurements used should be in accordance with such a standard.
5.1.3 Wherever possible, instruments with a defined and
guaranteed “quality grade” (accuracy class) should be used.
in this context an instrument can be said to be of quality
grade “G” when the maximum error at any level m the recommended range does not exceed + G % of the full-scale
reading.
5.1.4 Instruments shall only be used in that part of their range
recommended by the manufacturer or so defined in this international Standard.
5.1.5 While the instruments and measurement methods are
generally to be recommended for the purpose, it is not intended
to restrict the use of other equipment with the same or better
accuracy.
12
5.1.6 Measurement stations for the determination of the condition of flowing fluids shall wherever possible be located in
straight lengths of pipe where the flow is substantially uniform
and steady. For the main measuring stations at the inlets to and
discharges from the compressor, the arrangement shown in
figure 1 is recommended.
5.2
Apparatus
5.2.1 Instruments for determining the temperature of the
compressed fluid at the compressor inlets and discharges.
5.2.2 Manometers or pressure gauges for determining the
pressure of the compressed fluid at appropriate pointa on the
teat stand.
5.2.3
Baromater to measure the atmospheric pressure.
5.2.4 Flow measuring device to determine the flow through
the compressor.
5.2.5 Instruments to measure the power consumption of the
compressor.
5.2.6 Equipment for sampling the working gas and to determine its composition.
5.2.7
A device to measure the speed of rotation.
5.2.8 Arrangements to detect the occurrence of surge (when
applicable).
6.2.9 Devices for determining flow-rates and temperatures of
aacondav flows to enable energy balances to be established.
.,
.
f,
. .-—
IS 14641:1999
ISO 5389:1992
5.3
Measurement
of temperature
d
5.3.1 Each temperature measuring device shall be in accordance with the appropriate national standards and shall be
calibrated against an instrument certified by a recognized
authority. Recommended instruments for measuring temperature are
a)
5.3.7 With liquid-in-glass thermometers, when the measured
temperature differs from the ambient by more than 5 ‘C, an
emergent stem correction shall be made according to the formula
where
liquid-in-glass thermometers;
fTs is the true temperature of the gas stream;
b) thermocouples used with potentiometric-type instruments;
t
is the actual thermometer reading;
c)
tM
is the average temperature of the emergent fluid
column;
1
is the length of the emergent column expressed in
degreea on the thermometer scale;
B
is the apparent expansion coefficient of the thermometer fluid (for mercury-in-glass thermometers
/9 = l/6 X)O).
resistance thermometers.
5.3.2 The detecting element should be inserted directly into
the gas stream or, where this is not feasible, thermo-wells of
minimum thickness shall be used. Precautions shall be taken to
minimize measurement errors due to heat conduction in stems
or wells and radiation from or to parts at a temperature different
from that of the gas stream.
5.3.3 For machines assembled for test with an open inlet, the
inlet temperature shall be taken as the atmospheric temperature
measured in a region of substantially zero velocity in the vicinity
of the inlet flange.
5.3.4 The delivery temperature (or temperatures) and inlet
temperature (or temperatures), when a piped inlet is used on
test, shall be measured by several instruments inserted into the
pipe or duct symmetrically set in one plane. The number of
instruments and their precise location depends on the layout of
the piping and the precision required with due regard to heat
flow and radiation from the pipe surface. The fluid temperature
shall be the average of the single measured values corrected to
allow for the velocity recovery effect.
Except in the case of gases with a significant condensablephase
the use of shielded stagnation-type probee with a very high
recovery factor is recommended.
Where it can be shown that the velocity recovery effect is
insignificant, it may be neglected. In no case should it be
neglected if tha dynamic head exceeds 0,5 % of the specific
compression work. The velocity recove~ factor to be used
should be agreed on. In the absence of any more specific values
the following may be used:
a)
thermometers and thermocouples in wells :
0,65
b)
bare thermocouples
:
0,80
c)
bare thermocouples with insulation shields :
0,97
NOTE – For more precise information see [31and [4].
5.3.5 Each instrument should penetrate into the pipe or duct
for approximately one-third of the pipe diameter.
5.3,6 Thermocouples shall have a welded hot junction and
shall be calibrated together with their compensating leads over
the anticipated range.
5.3.8 When it is necessary to determine the heat extracted by
intercoolers, lubricant or sealant flows or leakage flows, the
accuracy of temperature and flow measurements shall permit
determination of the heat extraction with due regard to the effect of such heat flows on the overall accuracy of the test.
5.4
Measurement
of pressure
5.4.1 General
Each pressure measuring device shall comply with
appropriate national standards.
the
Each instrument shall be calibrated with the exception of vertical “U” tube manometers using a liquid of known density and
deed-weight gauges.
Connecting pipee shall be leak-free, as short as possible, and of
a sufficient diameter and so arranged as to avoid blockage by
dirt or condensed liquid.
If the saturation temperature of the fluid is higher than ambient
temperature, pressure instruments shall be situated below the
tapping points and connecting pipes shall be kept full of condensate. Condensing vessels shall be installed near the tapping
points to ensure constant level height.
Stations for the measurement of the pressure of flowing fluid
streams s@ll be located in a length of straight pipe or duct of
uniform cross-section in which the flow is essentially parallel to
the pipa wall.
Pressure instruments shall be mounted in a position substantially free from vibration.
The effective length of the scale of pressure measuring
instruments and the arrangement of the graduations shall
facilitate accurate readings within * 0,5 % of tha pressure
measurement.
.
*d
Is 14641:1999
ISO 5389:1992
5.4.2
Barometric
pressure
Barometric pressure shall be determined by any means with a
maximum error not exceeding 0,333 mbar l}. A barometer shall
be located in a stable place at the test site. Alternatively, the
barometric pressure may be obtained from a local meteorological station, with a correction for any dtierenca in altitude.
5.4.3
Static pressure
When the teat driver is a slip-ring type of induction motor, the
rotational speed may be obtained f rom accurate measurements
of both the supply frequency and the slip frequency.
In all other cases the rotational spaad shall be measured with a
mechanical or electrical tachometer permanently driven from
the shaft.
The preferred type is a digital puise counter based on a crystal
oscillator used in conjunction with a toothed wheel mounted on
the compressor shaft.
Static pressure shall be measured by a number of tappings
(normally four) spaced around the pipe at the rneesuremant
station in one plane normal to the direction of flow.
5,7
The tap-holes ahal! be normal to and flush with the pipe wall
and shall be free from burrs, countersinks or other irregularity
which could disturb the flow.
Where the performance is guaranteed in terms of the energy
input to the driver, this shall be measured in accordance with
the appropriate International Standards or national standards.
The diameter of the tap holes shall be as small as possible consistent with minimizing the risk of blockage.
Where it is the power input to the compressor which is
guaranteed, this shali be measured
It shall be established that the pressure measured at any one
tapping at the measurement station does not differ from the
mean of all pressure measurements by more than 1 % of the
absolute pressure.
–
by performing an energy’ balance on the driver in accordance with the appropriate test codes for the pwticular
type of machine,
Having established that this requirement is satisfied, all the
teppings at one station may be connected into a common collecting ring, provided that the effective cross-sectional area of
this collecting ring is not lees than four times the croasaectional area of any one tap-hole.
5.4.4
Measurementof flow
Fluid flow-rates
1s0 5187-1.
shall be measured in accordance with
When other methods of flow measurement are proposed it
shall be demonstrated that they are of equal or better accuracy.
Particular care is neceeaary when the compraeaad fluid contains
a condensibla fmction. With most types of flow-mater it is
essential that the fluid is homogeneous. In extreme cases it may
be neceaeew to install a suitable separating device, and to
maaaure separately the gasaous and liquid etreema leaving it.
5.6
MeasurementOf rotationalspeed
When the teat driier is a synchronous electric motor the rotational speed may be obtained from an accurate measurement
of the supply frequency.
1)
14
lber=l@Pa
Measurement
of power
–
by measuring the torque using a cradled Iswinging
field) type of motor or a precision torque-meter,
or, when these methods are not possible,
–
by establishing a total energy balance for tha compressor, by measuring all the Ioaeee and adding them to theenergy input to the compressed gas.
Total pressure
Total pressure shall normally be cetculated from the static
pressure and the calculated mean flow velocity heed (see
8.1 .3). Where the degree of non-uniformity of flow is eignificent, the chamctaristic parameters (a.g. total enthaipy) should
be obtaitwd from a mess-flow-weighted integration of the
results of probe traverses across the measuring plane.
5.5
I
Torquemetera shall not be used for measurement below onethird of their rated torque, They shall be calibrated with the
measuring element at the same temperature as used during the
test. The calibration shall be carried out twice, once with
continuously increasing load and once with continuously
decreasing load, and the mean of the two eats of readings shall
be used.
With both torque-meters and cradled electric motors it shall be
shown that the hysteresis affect, i.e. the difference between
the readings with increasing and decreasing load due to
mechanical friction etc., does not exceed 0,5 % of the
measured torque.
5.8,
Determination
of gas composition
The chemical composition of gas or gas-vapour mixtures shall
be determined at regular intervals by recognized methods of
analysis.
Patiicularly when the gas contains condensablefractions, care
shall be taken to ensure that the sample analyaed is truly
representative of the gas being compreeaed. In some cases this
may require that the condensable and non-condttr%ible fractions are sampled separately as they leave a suitable separating
device and that the rates of flow of the two frections are also
established separately.
d
f,
. .-.—
IS 14641:1999
ISO 5389:1992
If the working fluid on test is air, its humidity shall be determined from wet- and dry-bulb temperatures or by other
recognized methods such as dew-point, freezing or chemical
absorption techniques.
5.9
Accuracy
4
then the mean value x~ is given by
1“
—
xM.
n z
ixl
Xi
of measurement
and the standard deviation is given by
5.9.1 Owing to the very nature of physical measurements, it is
impossible to measure a physical quantity without error or, in
fact, to determine the true error of any one particular measurement.
However, if the conditions of the measurement are sufficiently
well known, it is possible to estimate or calculate a characteristic deviation of the measured value from the true value,
such that it can be asserted with a certain degree of confidence
that the true error is less than the said deviation.
The value of such a deviation (normally the 95 ‘k confidence
limits) constitutes a criterion of the accuracy of the particular
measurement, and in this International Standard is called the
uncertainty.
For a particular measurement the value of the uncertainty
(95 ‘%o confidence limits) can be determined in one of the
following ways.
/
‘=
“
(X-X.)2
]/*~
i=~
v
Hence the uncertainty can be taken as * 2 u.
5.9.5 In some cases the uncertainty (95 % confidence limits)
can be estimated by considering the fundamental principles of
the method of measurement.
For example, in the case of a simpie liquid-column manometer,
provided that the density of the liquid is known precisely, the
accuracy depends on how precisely the levels can be de
termined. Without special equipment an accuracy of i 1 mm
should be easily achievable with the necessary confidence.
Hence the uncertainty, rH, is given by
5.9.2 Where the measurement has been made in accordance
with an established International Standard or national standard
which defines the accuracy of such a measurement, then the
uncertainty confidence limits should be determined by
reference to that standard (e.g. for flow measurement refer to
ISO 5167-1).
~H=&L
H
where H is the reading in millimetres.
NOTE– Fordifferentialheedsinexcessof 1 massumeTH = + 0,1 %.
5.9.3 Where the quality grade of the instrument has been
defined and guaranteed by the manufacturer (see 5.1.3) the
uncertainty for a particular measurement can be determined by
reference to the quality grade. For example in the case of a
pressure gauge, the uncertainly, 7P, is given by
7P =kG—
A further example is an electronic digital tachometer in which a
precise crystal oscillator is used as the time base. In this case
the uncertainty, TN, can be taken as
TN=*7
PErl
s
PTe
where
where
G
is the quality grade;
S
is the digital measuring step;
&
is the full-scale reading of the gauge;
N
is the speed of rotation displayed.
PTe
is the actual test reading.
S and N shall be expressed in the same units.
NOTE– Where a pressuregaugehasa qualitygradeleesthan0,2 %,
usea valueof 0,2 to allowfor locationerrors.
5.9.4 If a sufficiently large number of readings of a particular
variable are available, then the standard deviation of these
readings can be calculated; it is accepted to assume that the
uncertainty is equal to twice the standard deviation.
For example, if the values of a set of readings of one variable
are
X1,X2,X3,
. . .. Xi. . . ..Xn
5.9.6 Where the value of a particular quantity is derived from
the measurement of two or more separate quantities, the accuracy of the result is dependent on the accuracy of the
separate measurements. For example, when the ahaft input
power to the compressor is determined by measuring the
electrical power input to the electric motor, having aeparatety
determined the motor efficiency, the uncertainty confidence
limits of the shaft input power are given by
rpe = * ~ rpJ
+ rnelz
*
15
IS 14641:1999
ISO 5389:1992
where
able it shall be agreed whir5h data shall be used and the
uncertainties which apply to such data.
Tpd
is the uncertainty
of the electrical power input;
7nel
is the uncertainty
of the motor efficiency.
In annexes A and B methods of calculating the physical properties of gas and gas-vapour mixtures are provided.
Tp& and Tqel shall both be expressed as a fraction of the
measured value.
5.9.7
In the absence of sufficient information to use any of
the above methods, table 5 provides a guide to the accuracy
that can be expected from good quality commercially available
instruments.
Table 5 – Guiding values for uncertainty
Pressure maaaured with
-
liquid column
* 0,5 %
dead-weight gauga
* 0,3 %
-
Bourdon tube gauge
*1,0%
suction temperature
* 0,5 Oc
– discharge temperature
— cooling water, oil, etc.
* 0,5 “c
* l,O”C
Flow measured with standard pressure
difference device (see ISO 5167-1)
*1,594
Speed measured with mechanical tachometer
*1,5%
*1,5%
*1,5%
Power determined from an energy balance for
the compressor
*l,5%to*4%
in-glaaa tharmometar is given in table 6.
Values in degrees Celsius
Maaauramant uncarteinty for the
following graduation intervals
0,1
0,2
0,5
1
0,6
0,3
0,5
—
—
—
—
0,8
0,4
0,6
1
—
—
—
1,7
1
1
2
3
—
—
2
1,4
2
3
4
5
6
TT
properties
If the specified conditions cannot be reproduced, either
because of the gas composition, or because the power
available is insufficient, the compressor should be run at such a
combination of speed and inlet conditions as to establish the
similarity conditions specified in 7.3.
Category 2 tests can themselves be subdivided into two types:
Catagov
2a}:
2
7
2
3
4
6
8
12
Open-loop air tests
In this case, the manufacturer shall state whether or not the
similarity conditions specified in 7.3 can be fulfilled.
In a case where the similarity conditions cannot be fulfilled,
the customer and the manufacturer should agree on the
tolerances to be applied to the test result.
Category 2b):
Closed-loop testa with air or another gas
of fluids
Physical properties and thermodynamic data and the appropriate confidence limits shall be obtained from established
International Standards. When such standards are not avail16
1
In this case, the driving unit and the lubricating and sealing
devices may also be different from those on the site.
Tabla 6 – Measuring uncertainty for calibrated
liquid-in-glass thermometers
5,10 Thermodynamic
required at the time of order
Category 2
●) A guide to the accuracy achievable with a good quality liquid-
fjo<e<llo
shall be reached
*1,5%
– d.c. motor of known efficiency
110<0<210
210<8<310
310< 0<410
410<0<625
Agreements
agreement
In this case, the test speed shall be as close as possible to the
specified speed of the compressor.
— a.c. motor of known efficiency
60
on which
The compressor may be tested under the conditions of the
guarantee, i.e. with the specified gas under the specified intake
conditions, with the guaranteed power input.
+2%
— mechanical torque-meter
— cradled motor
-w<e<-5
- 5<0<
6.1.1
Category
Power measured with
Tamparatura
range, O
Items
6.1.1.2 It shall be agreed which type of test is to be performed
in accordance with the following categories.
Temperature “t
-
6.1
Particularly in the case of a site test, agreement shall be
reached on the necessary safety requirements relating to the
test and it shall be agreed who shall have the responsibility of
ensuring compliance with these requirements.
Uncarteinty
–
Preparation for the test
6.1.1.1 Agreement shall be reached as to the location of the
test, i.e. at the manufacturer’s works, on site, or elsewhere.
of test
,J,vsae”,g,,,g,,w
Meaauramant
6
If the performance testing is carried out using a closed loop,
the manufacturer is free to choose any suitable test gas and
conditions, provided that the similarity requirements of this
International Standard are satisfied.
-
1*
IS 14641:1999
ISO 5389:1992
6.1.1.3 Whether ornotthe pressure ratio orpressure rise is
based on static or total conditions, the precise location at
which the guaranteed inlet and discharge pressures apply shall
be agreed. Unless there are good reasons otherwise, total conditions shall be assumed,
6.1.1.4 The basis for calculating the actual inlet volume flow
shall be agreed. Unless otherwise agreed, the inlet volume flow
shall be calculated from the measured usable mass flow and the
inlet density determined from the total temperature and total
pressure at the standard inlet point.
6.1.1.5 The gas composition, charts, reference tables or other
data relating to the guarantee conditions shall be agreed.
6.1.1.6 The criterion of acceptance of the test result, according to 9.3.2, shall be agreed.
6.1.1.7
In the case of a site test, a deadline for the test should
be agreed upon.
6.1.1.8 A schedule for agreements to be made on the matters
given in 6.1.2 should be established.
6.1.2
Agreements
required before the test
6.1.2.1 In the case of a factory test, the manufacturer should
supply the customer with
a) the indication of the gas if it is different from the gas
handled according to the contract agreement;
b) the calculations for the determination of the similarity
conditions;
c)
d
the way it has been specified in the guarantee. Where this is
not possible, however, due corrections shall be applied to compensate for gland leakage either into or out of the compressor,
condensate drained from intercoolers, bleed flows, etc. It is
often impossible to measure such quantities directly and in
these circumstances appropriate corrections shall be agreed
between the manufacturer and the purchaser. Particular care in
this matter is required when a compressor is being tested under
conditions far removed from those of the guarantee.
6.1.2.4 When a machine is to be tested under conditions
significantly different from the guarantee conditions, the
manufacturer shall propose for agreement how the mechanical
losses shall be converted from test to guarantee conditions.
6.1.2.5 Where any intermediate form of prover transmission,
such as a gearbox, is interposed between the driving unit and
the machine, the method by which ita power consumption shall
be taken into account shall be the subject of agreement.
When the power consumption is guaranteed in terms of the
power supply to the driving unit, any variations in its performance due to the difference between test and guarantee
conditions shall be allowed for, subject to agreement.
When the power consumption is guaranteed and the test has to
be carried out at reduced power, errors will be introduced into
the corrected power consumption because of those losses
which am not strictly proportional to the total power. An
agreed correction shall be made for these errors.
6.1.2.6 Where it is not feasible to test a machine under the
conditions laid down in 7.3, special conditions of test and
special corrections shall be agreed between purchaser and
manufacturer.
a sketch of the installation and instrumentation.
Before testing commences, the installation should be placed at
the customer’s disposal, in order that the customer may check
that it is in conformity with the requirements of this lntarnational Standard.
In the case of a site test, when the site layout plan is finished,
this is submitted by the customer to the manufacturer in order
that the latter may check that all provisions have been made to
carry out testing in conformity with the requirements of this
International Standard and may comment on these, if required.
Before testing commences, the installation should be placed at
the manufacturer’s disposal for examination of the teat equipment. The test programme should be agreed upon by the
customer and the manufacturer.
6.1.2.2 It shall be agreed that the calibrations of each instrument used in the test shall be according to the appropriate
national code.
6.1.2.3 Usually the flow will be measured on either the inlet to
or the delivery pipe from the compressor in accordance with
6.2
Preparation
of the machine
6.2.1 The compressor and associated equipment shall be in a
condition that is comparable to the condition when new with
respect to those aspects which can affect the performance.
6.2.2 If pipes or ducts are fitted for the purpose of by-passing
any component, or if bleed-off is used for any service, any
valves in such pipes or ducts shall be set so as to produce con
ditions specif~d in the guarantee.
6.2.3
All unused connections shall be blanked off.
6.2.4 Where Iubriiating oil, cooling water and seal-fluid consumption is signifwant, provision shall be made for measuring
these.
6.2.5 The recommended grade of oil shall be used; otherwise
corrections to the power and oil consumption shall be made.
17
‘,,
}...
.“.
:,
/
IS 14641:1999
ISO 5389:1992
6.3
Preparation
6.3.1
Diagrammatic
Initial calibration, where Doasible, of the instruments shall be
available prior to the test:
layout of test arrangement
Prior to the test a diagrammatic layout of the test arrangement
shall be established showing the agreed position of all measuring points and containing the reference numbers and letters
used in the test report.
6.3.2
Installation
Recalibration, where possible, after the test shall be made for
those instruments of primary importance which are liable to
variation in their calibration as a result of use during the test.
Any change in the instrument calibrations which will create a
variation exceeding that of the class of the instrument maybe a
cause for rejecting the part of the test which it invalidates.
of test equipment
See clause 5.
Tests
7
Inlet and discharge pressures shall be measured at agreed
points. A typical arrangement is shown in figure 1, taken
from [1].
7.1
—Inlet temperature
--4 measuring stations,
spaced 90°
Inlet velocitv rxessure \
– 2 taps, spaced 90°
(used only when
velocity pressure is
greater than 5 “A of
total pressure)
‘+
Preliminary
tests
Preliminary tests may be run for the purpose of
a) determining whether the compressor and associated
system is in a suitable condition to conduct an acceptance
test;
Where necessary, provision shall be made for determining the
humidity, chemical composition, density or viscosity of the gas
at the appropriate and agreed times during the test.
r
Calibration of instruments
6.3,3
of test equipment
n-ml-
L
I
II
I
I
f
/
spaced90°
-
4
1
Discharge static pressure
– 4 taps, spaced 90°
..
--
i
0,
m
Inlet static pressure _
– 4 taps, spaced 90°
Discharge velocity pressure
– 2 taps, spaced 90°
~
I
Baffle (perforatedplate
flow equalizer)
I
I
I
K
4
t
Capacity by ISO 5167-1
T
Throttle valve~
Figure 1 – Test arrangement
18
.
IS 14641:1999
ISO 5389:1992
b)
checking of instruments;
c)
training of staff.
Should, however, the conditions be such that changes cannot
be avoided, a distinction may be made between systematic
changes (drift) and fluctuations of high frequency.
After a preliminary test has been made, this may, by agreament, be considered to be the acceptance test, provided that all
requirements for acceptance have been met.
7.2
General rules for satting
for the acceptance
test
up the compressor
In the case of a drift an adjustment to maintain the allowable
deviations shall be made only if the operational conditions
exceed the limits given in 7.3.
During the fluctuations, the number of readings shall be
increased, but the results may still be accepted provided that
the fluctuations are within the limits given in table 7.
7.2.1 During the test all measurements that have any bearing
on the performance shall be made, h the following, the determination of the capacity and the power consumption of the
compressor will be treated in detail.
7.2.2 The measurements shall be carried out by competent
persons with measuring equipment according to clause 5.
7.2.3 The test conditions shall be as close as is reasonably
possible to the guaranteed conditions: deviations from these
shall not exceed the limits specified in 7.3.
7.2.4 During the test, the lubricant, and the adjustment of
lubricating pumps, lubricators or other lubricating means shall
comply with the operating instructions.
7.2.5 During the test adjustments other than those required
to maintain the test conditions, and those required for normal
operation as given in the instruction manual, shall not be made.
7.2.6
Before readings begin, the compressor shall be run long
enough to ensure that steady state conditions are reached, so
that no systematic changes occur in the instrument readings
during the test.
——.
7.2.7 For each guaranteed point a number of test points shall
be obtained (not lees than two) embracing the specified
point. The range covered by these test points shall be not less
than the range defined in figure 2, i.e. from the condition in
which the reference process work coefficient on test is equal to
that for the guaranteed point to the condition in which the
flow coti]cient on test is equal to that for the guaranteed
point.
The reference process selected for this purpose depends on the
type of compressor. Generally, for uncooled machines an isentropic or polytropic process shoul&Be sef&cted and for cooled
machines an isothermal process.
7.2.8 For each teat point the compressor shall be run for a
sufficient time and a sufficient number of sets of readings shall
be taken to indicate that steady conditions have bean reached,
to enable meaningful averages to be taken and to ensure that
the requirements of 7.4.1 have been met. Not leas than three
seta of readings shall be taken. If a computerized data acquisition system & used then one representative printout of the
test results should be taken. As far as possible all readings in
one sat shall be taken simultaneously at a given signal.
.——
I
Specifiedpoint
I
L
—
—
—
—
—
—
,
1
*
Flow coeffkient
Figure 2 – Minimun’i range to be covered by the test
19
IS 14641:1999
ISO 5389:1992
7.2.9 Where theusable stable range of thecompreasor is to
be proved, the capacity at which surge occurs is determined by
slowly raising the pressure ratio at constant speed until
unstable or pulsating flow appears. A test point shall be set as
close to the surge as possible. The precision of the determination shall be demonstrated by repeating the setting.
For variable speed and/or variable geometric compressors,
surg? points may be determined at different speeds or settings
to co Ier the anticipated range of operation.
It shali be understood that the surge point determined in a shop
test may not accurately represent the surge condition with
other pipe cofifigurations and other gas densities.
deviation on the performance of turbocompreasors is taken into
account by appropriate correction methods which should be
used only in a certain range of application.
The range of application of the correction formula and the
selection of a suitable test Reynolds number are influenced by
two factors, i.e.
— the accuracy of the correction formula at different
Reynolds numbers, and
— the reliability of tests carried out at reduced suction
pressures or low driving power.
For centrifugal
7,2.10 After the test the compressor plant and the measuring
equipment shall be inspected. Should any faults be found that
may affect the test results then a further test shall be run after
these faults have been corrected.
7.3
Particular
rules for setting
for the acceptance
test
7.3.1
up the compressor
Guiding principle
Before the beginning of a test run, the settings of the compressorshall be fixed so as to achieve the best possibleapproxk
mation to similarity of flow for test and specified conditions.
The conditions to be fulfilled in order to achieve similarity of
flow are dealt with in clause D. 1.
In practice it is often impossible to fulfiH all the above conditions. Admissible limits for the deviation from similarity are
considered in the following subclauses.
7.3.2
Allowed deviation from specified rate of flow
The magnitude of the permissible deviation of V, from 1 and the
additional uncertainty depend upon the characteristic curve
being flat or steep.
A characteristic curve is steep if, at the point being considered,
()
~
9v,t,l
dqv,t,l
(ICAAMC)
for correcting
the well-oroven
method
Air and Allied Machine~
the performance
of the
Committee
for variations
in
Reynolds number shall be used (see annex E).
The limit of application of the ICAAMC formula is given in
annex D, figure D.5, and annex E.
For axial compressors, the appropriate method of Reynolds
number corrections depends on the blade characteristics used
by the manufacturer. Therefore the method should be agreed
by the manufacturer and the customer, as well as the range of
its application.
7.3.4
Determination
of the settings
The formulae required for the determination of the settings are
evident from the flow charts given in clause D.5.
These charts, one for perfect and near-perfect gases (see
figure D.6), the other for real gases (see figure D.7), will be
followed according to the conditions prevailing. Each of them
includes the following cases:
a)
uncooled compressors;
b)
compressors with intercooling.
>1
P2
P1 t
(-)
If a flat characteristic curve is assumed according to a
calculated performance diagram supplied by the manufacturer,
this assumption shall be confirmed by the test result. Otherwise, the settings shall be corrected to satisfy the requirements
of this International Standard for a steep characteristic curve.
The range of values of the reduced speeds corresponding to
the permissible deviation of V, and any additional resulting
uncertainty can be determined in accordance with annex D.
7.3.3
Permissible variation from specified Raynolds
number
It is necessary to check the deviation of the test Reynolds
number from the specified conditions. The influence of this
20
Compressed
Both have two possibilitiesfor the isentropic exponent KTe for
the test conditions, i.e.
dP2_
PI t
compressors,
International
a)
same as for specified conditions, or
b)
different.
Furthermore, three alternatives are considered for the determination of the isentropic eXPOnent KTe:
a)
constant (perfect and near-perfect gases only);
b) known from characteristic equations as a function of
pressure and temperature;
c) calculated from conditions of state referred to the
critical pressure and temperature of the test gas, following
Schultz.
The input values for the above flow charts are to be found
in D.5.1.
.
d
f,
IS 14641:1999
ISO 5389:1992
The relationships shown in the flow charts for determining the
limits of the permissible setting up conditions for the compreesor on testare shown in figure D.3 for KTe = KGU,and in
figure D.4 for KTe * KGU.
These are referred to in clause 8.
The charts giving the generalized compressibility factors
necessary to calculate Z, X and Y as a function of reduced
pressure and temperature are to be found in clause A.3.
7.4
Evaluation
8
Calculation and adjustment of test results
8.1
Computationof results
8.1.1
Purpose of evaluation
For the acceptance test only those values which are essential
for the verification of the specified data are calculated and
compiled.
From the average values of the readings, determined according
to clauses 5 to 7, the results maybe computed according to the
following subclauses.
of the readings
8.1.2
7.4.1 Before final calculations are undertaken, the recorded
date shall be scrutinized for consistency of the operating conditions. The fluctuation of readings during one test shall not
exceed the limits given in table 7.
Table 7 – Maximum allowable fluctuation of readings
from average during one test run
Variable
Absolute inlet pressure
Maximum allowabla
fluctuation of readinga
from averaga during
one test run
+ly~
Absolute inlet temperature
(of eachsectionin the caseof a
cooledcompressor)
*1%
Speed
* r),5 %
Ratio
()
P2 – PI
PI
-4
Mass rate of flow and inlet volumetric
flow
The actual inlet capacity is obtained by converting the gas flow
measured by the measuring device from the condition there to
the total condition at the standard inlet point, due consideration being paid to any leakage flow and condensate flow, i.e.
.—
–
qv,t,l
qm, ut
~t,l
.
qm,utZ@Tt,~
Pt, 1
where
usable mass rate of flow;
qm,ut
is the measured
et, 1
is the density based on total conditions;
R
is the gas constant (see annex A);
Pt, 1
is the total pressure;
Tt,,
is the total temperature;
z,
is the compressibility factor.
* 2,0 %
t
* 2,0 %
8.1.3
●) Whare Ap is the pressure drop across a flow measuring
device, p is the absolute pressure at this inatrurnant.
NOTE – Durirm the test tha erascom~oaition should not vary by an
amount greater-than that equ~alent to a variation in either R or K of
*l%.
If these limits are exceeded, the testis invalid except by special agraement, in which case such an agreement is to include consideration of
the appropriate tolerance.
Dynamic pressure (velocity pressure)
In most cases the static pressure p can be directly measured at
the standard inlet and discharge points.
If the velocity distribution across the area A is uniform, the
dynamic pressure, p~, can be derived from the continuity
equation and the measured mass rate of fiow:
Pt_l+Pd_l
_
P
P
{
1
[
(K–l)&fU:
(K–l)Ma~
–
K
7.4.2 All accepted sets of readings from any test run shall be
consecutive.
1–K
-Jl+2(K-l)Ma:
+1
1}
where
7.4.3 Seta of readings showing excessive fluctuation may be
discarded but only at the beginning or the end of a test run. All
readings in any set should be taken as nearly as possible
simultaneously.
Mat=:=—
ZR Tt
—
qm
Ap
/
K
For low gas velocities an approximate simplified formula is
7.4.4 Test results shall be calculated from the arithmetic
average values of the accepted readings.
Pt
—~
P
1 + f Maf
21
f,
-——
IS 14641:1999
ISo 5389:1992
a
This approximation may be used provided that the value of
~ so calculated does not exceed 1,05.
If the velocity distribution across the area A ia significantly nonuniform, the dynamic pressure shall be found from a messflow-weighted integration over the area (sea 5.4.4).
measurements of the performance of the compressor are taken
under precisely the specified conditions. if the operating conditions prevailing during the tests differ from those on which
the guarantee is based, the test resultashall be converted to the
conditions specified for the guarantee. These converted results
may then be compared with the specified figures.
b-k. .- .-J
,/
8.1,4
8.2.1.2
Total temperature
Normally the pressure ratio and temperature ratio are based on
total conditions (see 6.1.1 .3).
In most cases the total temperature maybe rnbasuredat normal
aspiration and exhalation points.
If static conditions are specified in a particular case, the static
temperature shall be obtained from the following relation:
—=
Tt
1
T,
_— (K-1) ~a*
t
2
Individual results to be converted
The particular results with which the conversion is concerned
are
a)
the actual inlet VOIUme flow q ~,t, 1,
b)
the pressure ratio (p2/pl)t,
c)
the power consumption at the coupling Pe.
and
The power consumption at the coupling is made up of the internal compression power Pin and the mechanical power lossPf
which will be converted separately.
where
8.2.1.3
Theoretical basis of conversion
The principle of the theory of similarity of flow upon which the
following conversion rules are based, together with the permissible approximations to this theory are covered in annex D.
8.1.5
Reference
power for compression
The reference power consumption shall be computed according to 3.6.2 after the appropriate choice of the reference process has bean decided upon.
8.1.6
Actual power consumption
The actual power consumption can be computed in three
ways:
a) from direct measurement of the input torque using a
torque-meter or a dynamometer;
b) from an energy balance for the prime mover using the
formula
Pin = P“n – P~f – Pf
c) from an energy balance for the compressor itself using
the formulae given in 3.6.5.
Methods b) and c) should not be used unless the energy
balance can be established with sufficient accuracy.
8.2
Conversion
conditions
8.2.1
8.21.1
of test results
Conversion of mechanical
losses
The sum of all mechanical losses may vary considerably with
the particular test and specified conditions especially with
regard to speed, power input, thrust and viscosity of the lubricant.
Mechanical losses occur mainly in the bearings, lubricant
pumps, gearing belonging to the compressor, liquid seals,
sliding-ring seals, and so on.
These losses are normally determined by measuring the rise in
temperature of the oil, etc., or from the physical dimensions
and teat results, using recognized formulae. The various
individual losses have to be converted aeparetely, their sum
giving the desired figure of mechanical lossesPf with the aid of
which Pe can be calculated, as follows:
P. = Pin + Pf
Tha formula for the conversion of the mechanical losses shall
be agreed upon before the test (see 6.1 .2.4).
to specified
8.2.3 Conversion of test reaulta for uncooled
compmeaors
General
Purpose of conversion
The teat results can only be compared directly with the
guaranteed values when, during the acceptance tests, the
22
8.2.2
8.2.3.1 In the case of all uncmled compressors, whethar the
iaentropic exponents are equal or not and whether the apeed or
inlet temperature is adjustable or not, the test results can be
converted to the Specifti conditions using the formulae given
in figure D.8.
4
f,
. ——
,
‘
~
IS 14641:1999’
ISO 5389:1992
i
8.2.3.2
Where~Te = KGu, theconver$ion iSesfollowe.
The same can be applied for KTe * KGUprovided that the ratio
a
If the speed or intake temperature is adjustable, the requirement
(N/~~l)Te
/ (Nld~)Gu
of equal peripheral Mach numbers or that (JV/~-)Te
should be equal to (N/<~)GU
can easily be complied
with within the inner tolerance Iim’it[sea figure D.3a)l and converaion may be carried out in accordance with the formulae
given in figure D.8.
In this case no additional uncertainty is introduced.
If tha speed or intake temperature cannot be adjusted with sufficient accuracy, or not at all, deviation of the ratio
up to the outer tolerance limit is permissible.
In this case an additional uncertainty is introduced (according
to instructions given in clause D.2).
Outside the outer tolerance limit there is no point in converting,
unless special agreements have been reached.
8.2.3.3
Where KTe * KG., the conversion is as follows.
Regardless of whether the speed or intake temperature is
adjustable or not, check with the aid of graphs (see figure D.41,
whether the ratio
(NIJ~;)Te
/ (N/xf_l)Gu
is within the inner or outer tolerance limit. In the letter case en
additional uncertainty will be introduced according to instructions given in clause D.2.
If this ratio falls outside the outer tolerance limit, th~ test shall
be invalid except by special agreement. The conversion
formulaa are given in figure D.8.
8.2.3.4 If the test results are to be computed according to
Schultz’s method of polytropic analysis, the conversion
formulae given in figure D.9 shall be used, after checking
whether the test is valid (as outlined in 8.2.3.3).
8.2.4
Conversion of test results for cooled compressors_
8.2.4.1 In the case of cooled compressors in which the ratios
of the absolute temperatures after the intercoolers to the compressor inlet temperature are the same under test and specified
Corrdhions, KTe = KGU, the conversion may be as foiiows.
If the speed and the temperature at the inlet to individual stages
are adjustable by varying the ratio of flow of cooling water
through the intercoolersr the condition of equal Mach
numb~rs, or (N/J~)T=
= (N/~~)Gu
Should
aaaily be met at each stage; to within the inner tolerance limit
[see figure D.3a)l, so that the conversion to specified conditions can be carried out using the formulaa in fiiure D.1O. No
additional uncertainty is incurred.
for any stage between two intercooler.sdoes not exceed the
Iimite (sea figu”reD.4). If these ratios are within the outer but
outside the inner tolerance limit, an additional uncertainty as
given in clause D.2 is introduced. Outside the outer tolerance
limit, the test is invalid except by special agreement.
If the speed is not adjustable, but the temperetura at the inlet to
@dividualstages can be varied by regulating the flow of cooling
watar to the intercoolers, such that the ratio of these absolute
inlet temparaturksto one another and to the temperature at the
compressor inlet on “tast.are the same as laid down in the
specified conditions, the formulae in figure D.1O may also be
used for conversion, provided that the ratio
is within the outer tolerances [see figures D.3a) and ‘D.3b)l. In
ths case an additional uncertainty as given by clause D.2 is
introduced. Outaide the outer tolerance limit, there is no poinl
in converting.
8.2.4.2 In the case of cooled compressors in which the ratios
of the absolute temperature after the intercoolers to one
another are the same under test and specified conditions but
the ratios of these temperatures to the compressor inlet
temperature are not the same, and when KT= = KGU,the conversion may be carried out as follows.
Whether the speed is adjustable or not, and if the ratio of the
absolute temperatures after intercoolera during the test is the
same as in the guarantee, but the ratio of these temperatures to
the temperature at the compressor inlet is not, the results
obtained for tha uncoolad part I and the cooled part II of the
compressor may be converted separately to specified conditions according to the formulae given in figure D.3 provided
that the ratios
are within the outer tolerance limit given in figure D.8 for part I
and for any stage of part II between intercoolere.
If KTe # KGU the above ratios shall lie within the respective
tolerance limits given in figure D.4.
When the compressor is considered in two separate parts in
this way, the discharge conditions for the uncooled part (part 1)
should be taken as the temperature and pressure before the
first intercooler. The inlet conditions for the cooled part (part 11)
should be taken as the pressure before the first intercooler (i.e.
the discharge pressure of part I) together with the temperature
after the first intercooler.
Where it is not possible to obtain a representative measurement
of the temperature after the first intercooler, this temperature
may be estimated from the cooling water temperature and the
design terminal temperature ditYerence in the intercooler
making due allowance for any difference in heat transfer in the
intercooler between test and apecif’ied conditions.
23
IS 14641:1999
ISO 5389:1992
The absolute temperatures after the intercoolers may be
assumed to be in the same ratio to one another under test and
specified conditions if the cooling water temperatures are in the
same ratio and provided that the mass flow of gas through the
intercoolers under test and specified conditions is the same
within 5 %.
The measured power consumption of the compressor shall be
separated into part I for the uncooled section and part II for the
cooled section. In general, this separation will be possible by
providing the proper measuring devices. If this is impossible,
the division may be in relation to the stage heads according to
the design data.
8.2.4.3
In the case of cooled compressors in which neither
the ratios of the absolute temperatures after the intercoolers to
one another nor the ratios of these temperatures to the compressor inlet temperature are the same under test and specified
conditions, the conversion may be made as follows.
If the conditions of constant relationship between the gas
temperatures after the intercoolers are not fulfilled, the values
shall be converted separately for all cooled stages and the
results combined.
If the test results are computed according to Schultz’s method
of polytropic analysis, the conversion formulae for a stage
between intercoolers are given in figure D.9.
Where, in accordance with the above rules the compressor is
considered in two or more parts, the converted results shall
then be put together in order to compare them with the
specified values. An additional uncertainty as described in 9.2.9
may be introduced.
8.2.5
Speciel note
if in the intercoolers of the compressor, some of the working
fluid is lost due to condensation, either on test or under
specified conditions, this loss shall be taken into account in
working out the power consumption and the discharge flow. It
must be borne in mind that the quantity actually lost in such an
intercooler is generally smaller than the figure calculated
thermodynamically (efficiency of separation less than 1). See
A.4.2.8.
Moreover, during the process of compression it is possible for
chemical combination to take place, which will change the gas
parameters, especially density and temperature.
If a compressor has intermediate inputs andlor extractions, the
corresponding incoming or outgoing volume flow and the
temperatures of any incoming streams shall have the same relationships to the main flow and temperatures under test as
under specified conditions. Otherwise each section of the compressor between intermediate inputs or extractions shall be
considered separately.
If the compressor is run at different pressureson test and under
specified, conditions, the change in external leakage, if any,
shall be allowed for in the effective volume flow and power
consumption.
In the case of multiple or series-connected compressors it may
be advantageous to consider each casing separately.
24
9 Comparison with guaranteed values and
tolerances
9.1
General
9.1.1 The test results, converted to the specified operating
conditions in accordance with clause 8, shall be compared with
the guaranteed or specified performance.
9.1.2
The comparison shall include
a) comparison of the converted power consumption
(specific power consumption, fuel consumption or efficiency depending on the terms of the guarantee) with the
guaranteed power consumption (specific power consumption, fuel consumption or efficiency);
b) comparison of the converted capacity with the
guaranteed capacity. This may be defined as either the
pressure rise (or pressure ratio, or specific compression
work) at the specified flow-rate or the flow-rate at the
specified pressure rise (or pressure ratio, or specific compression work);
c) comparison of the acceptable operating range with the
guaranteed range where this has been stated.
9.1.3 It is recommended that in most cases the comparison
should be presented graphically (see 9.3).
9.1.4 Unless otherwise agreed, the comparison of the
measured and corrected performance with the guaranteed performance shall be made
a) in the case of a compressor with a steep characteristic,
by comparison at the guaranteed pressure rise (or pressure
ratio or specific%ompression work);
b) in the case of a compressor with a flat characteristic, by
comparison at the guaranteed actual inlet volume flow-rate.
NOTE – For the definition of the flat or steep characteristic see 7.3.2.
9,1.5 In making the comparison the following shall be taken
into account:
a)
measuring uncertainties (see cbuse 5);
b) errors due to the inaccuracy or uncertainty in the
thermodynamic properties of the gases used;
c) errore due to the”inaccuracy of the methods used to
convert the test results to the guaranteed operating conditions;
d)
errors due to non-steady conditions during the test;
e) any tolerance in the performance of the compressor
permitted by the terms of the guarantee. (See 5.9.)
IS 14641:1999
ISO 5389~199z
The errors listed above [91.5a) to d)] should be combined
together todeterminethet
teitest uncertainty (limits oft.onfi4
dence). This end the manufacturing tolerance [9.1 .5e)l should
be clearly and separately stated or illustrated in the presentation
of the comparison.
These additional uncertainties should be added in accordance
with 9.2.9 to the value obtained from combining the measuring
error, thermodynamic date error and conversion errors.
9.2.5
9.1.6 In the presantetion of the comparison, a conclusion
should be included skting whether the results of the test
indicate that the compressor does or does not meet the terms
of the guarantee.
9.2
Total
test uncertainty
9.2.1
Meesunng
(95 % confidence
limit)
Total uncarteinty
in flow-rate
The total uncertainty in the volumetric flow-rate is obtained
from
~ree,qv = * @j~
+ 7~,Te + ‘~1 ,Te + ‘;’l,Te + ‘~1 ,Te
where rqm,Te is the uncertainty in the mesa flow-rate according
uncertainties
to ISO 5167-1.
The confidence limits a%cwiated with the various measurements are determined using one of the methods described
in 5.9.
9.2.2
Thermodynamic
date uncetiainties
Totsi uncertainty
8.2.6
The total uncertainty in the pressure ratio is
The confidence limits associated with the thermodynamic
properties of the gases used should be obtained from the same
source as the values used, or otherwise agreed Xparately.
r reS#P21Pl=*
‘{N,2
+ ?:,Te +
9.2.3
in pressura ratio
Conversion uncertainties
[In(pzlpl)l+e
(4T:,T,+ ‘$l,Te +
‘~t,Tel
+ ‘~l,Te + ‘&Te
} “7
where
Where the pattern of flow on test cannot be made the same as
the pattern of flow under the guaranteed conditions at all
p61nts throughout the compressor, then the methods of converting the test results defined in clause 8 are only approximate. If the deviations from true similarity of flow are significant, then additional errors are introduced by the conversion.
The magnitude of any such additional errors can be determined
from the charts given in annex D.
9.2.4
Errore due to non-steady test conditions
If the operating conditions during a test run are not steady,
then additional errors may occur. The maximum fluctuations in
test conditions which are normally allowable are specified
in 7.4.1.
In some cases, however, if the testis conducted on site it may
not be possible to maintain steady conditions within these
limits. In such cases, by mutual agreement the test may be
considered valid but an additional error is introduced, the likely
maximum value of which (confidence limit) can ba obtained
fro”rntable 8.
Table 8 – Uncertainties dua to the instability
of test conditions
Valuesin per cent
Fiuctustion in powef input
ebout the meen velue
Uncertainty
(confidence limit)
2
3
4
‘5
0
0,5
1,0
1,5
N2
N,2 =
() RZ1 Tt,1 T~
N2
RZ1 Tt,1 @
()
9.2.7 Totel uncertainty in power consumption,
power consumption, specific fual consumption
efficiency
specifk
or
The total uncertainty in power consumption (or fuel consumption) is obtained by calculating the square root of the sum
of the squares of the appropriate individual uncertainties each
multiplied by an appropriate factor.
The relevant individual uncertainties and the appropriate
factors by which each should be multiplied for each type of
compressor and each type of test are given in table 9.
Similarly the individual uncertainties and their. a~wropriate
multiplying factors to determine the total uncertainty mspecific
power consumption, specific fuel consumption or @ficiency
are given in table 10.
EXAMPLE
In the case of a cooled compressor in accordance with,.8.2.4.2
in,which tha power consumption was obtained by maasuring
25
.
“
,5
“’ :
!
::.:4
-—#,
d
IS 14641:1999
ISO 5389:1992
,the shaft torque and spaad, the totai uncertainty in power
consumption is given by
‘r=’e=’{(+rpf’er+(
l+~~fi’er+
9.2.9
([
1–
1
In (~2/~l)t
Additional
uncertainties
,*... .,
{
Where additional uncertainties due to the conversion from the
test conditions to the guaranteed conditions (sss 9.2.3) or to
non-steady test conditions (sss 9.2.4) are appropriate, theaa
should be addad to the total uncertainty statistically:
+ [2 (p In (P2/Pl)t,l, co ‘N,Te ]2 +
+
The factor (1 + 0,2 &Z – 1) is included in each of the above
formulae to allow for the unavoidable inaccuracies involved in
measuring each stage or stage group aeparatety and combining
the results.
2
7PI Te +
1)
Ttot =
i
+ ?:di+ ?;uc
~Trw2
+ [4PInbdm)t,l,co
TTl,Te]2 +
+ [Cp
In @2/PIA,l,cO?Zl,Te ]’+
9.3
Graphical
comparison
9.3.1
Normal case
Normally (sss 7.2.7) at Iaaat two test points will be obtained
close to and bridging the guarantee point or each of several
guarantee pointa. The comparison is made as follows.
‘[,n(p:,pl)tTpt21:e+
((p7T1’’cEe+
+((przl,,,c)~e+
(~TTt,l,j)~~’2
where
z
is the number of stage groups separated by intercoolers;
j
is the number of the stage group.
9.2.8 Total uncertainties in the performance of a
multistage compressor obtained by combining the
results of separate tests on the individual stages or stege
groups
A chart is constructed in which the parameter to b compared
(specifii compression work, pressure ratio, pressure rise,
power consumption, specific power consumption, efficiency,
etc. ) is plotted as the ordinate against flow-rate as the abscissa
(see figure 3). Each test point is plottad on this chart and
around each point is constructed an ellipse, the axea of which
indicate the magnitude of the uncertainties in the relevant
parameters. Upper and lower curves are drawn tangential to
theaa ellipses. It can be statad, with at least 95 % confidence,
that the true performance of the compressor lies within this test
band.
The comparison is made by plotting the guaranteed operating
point or points on the graph.
9.3.2
In this caaa the overall uncertainties can be computed as
follows.
9.2.8.1
Volumetric flow
‘comb, qv = +(1
+ o,2@)
~
rq,j
The guarantee shall be deemed to have been aati~ied if the
guarantee point lies within the test band or if the extent by
which it lies outaide the test band (measured either horizontally
or vertically depending on how the guarantee was stated) does
not exceed the agreed manufacturing tolerance.
Pressure ratio
z
7comb,p’lpl = (1 + 0,2 ~)
~
j=l
9.2.8.3
26
Power consumption
The criterion of acceptance of the test result shall be subject to
specific agreement between manufacturer and customer taking
account of the teat uncertainty and the agreed manufacturing
tolerance.
Where no such agreement has been reached the following
criterion shall apply.
j=l
9.2.8.2
Cnlerion of acceptance
rpJpl,j *
w
9.3.3
Special cases
Where it is not possible to satisfy the requirement of 7.2.7, a
single teat point may be compared with a guaranteed performance curve (sea figure 4). In this case, the guaranteed
curve is drawn on the chart together with the agreed manufacturing tolerance giving a guaranteed band. The single test
result is plotted together with the ellipse indicating the
magnitude of the teat uncertainty.
.
.
--”Q-
IS 14641:1999
ISO 5389:1992
Inthiscaae, unleae otherwise agreed, theguarantee shall be
considered to have been met provided that some part of the
test ellipse touches or cuts the guaranteed band.
Non-graphical
comparison
9.4
In the exceptional case that only one test point is possible and
this has to be compared with one guaranteed point, the
measured power requirement which has been converted to
guarantee conditions Pe,co is further reduced to guarantee
values using the formula
6’V,t,l,Gu” ‘m, Gu .P
Pe, CO,GU =
9v,t,l, c0” Wm, co
co
e,
assuming a constant efficiency, and is compared with the
guaranteed power requirement P., @ The applicability of this
method is limited by the admissibility of the constant efficiency
assumption.
Test report
10
After completion of the acceptance test, a test report shall be
drawn up recording ail the necesaew information as to the procedure and results of the test. It shall contain the following
items:
a) date and place of the test and the names of the supervisor and other participants;
b)
technical data as follows
compressor: owner, site end purpose of installation,
manufacturer, type and serial number, year of manufacture, a short technical description giving operational
date, auxiliaries and their drive, and any other special
features (intercooling and lubricating system, utc. ),
— driving unit: generally the same items as for the compressor, but in particular those which are essential for
establishing the specfled petiormance;
c) conditions and scope of the guarantees according to
the contract;
d) programme of the procedure and diagram of the test
arrangement indicating location of measuring poinfe, type
of instruments used and their calibration records;
e) a record of the test run together with a table of the
average values of the important readings and the time they
were taken; if possible, a record of the maximum and
minimum readings; copies of the log sheets and of any
readouts from an automatic recorder, as well as duplicates
of the gas analysis, etc.;
f) an indication of any unscheduled occurrences which
were noted during the test;
g) the formulae used for the calculation of the results,
with due regard to the propagation of the mean uncertainties as they influence the final results;
h) a statement of the method used for converting the :wt
results to specified conditions with reference to the tables
and charts used (8.2); a clear definition of the reference process chosen;
i) a comparison of the actual performance with the
guaranteed values or date; a statement of whether the contract values have been met or not.
The test report shall be signed by represant6fives of the
manufacturer and customer. The original log sheate shall
remain in the custody of the engineer in charge of the acceptance test.
27
IS 14641:1999
ISO 5389:1992
Tabla 9 – Individual uncertainties and appropriate multiplying factors 1)to ba used to calculata
tha total uncertainty in power or fuel consumption)
Method of power messursmsntsJ
2
1
1
Cooled compressor
(see8.2.4.2)
Coolsd compressor
(sea8.2.4.1)
Uncooled compressor
(see8.2.3)
Individual
uncartsinty
Method of power meaaurementsJ
3
1
o
0
2
1
Method of power measurements}
3
1
0
0
2
3
1
0
~P,, ‘re
0
~fin,TO
Pin co
Pe, co
1
1
1
1
‘h,Te
Pe, co
l+c~
l+lg~
Pe, co
l+cg
l+CQ
Ps, co
l+cg
l+CQ
Te
rqv,
o
0
0
0
0
0
0
0-
0
rF, Te
0
0
0
0
0
0
?N, T’~
1
1
1
1
1 + JI<4
1 + ~1[~
1 + ~1(~
—
Pf, co
0
—
Pin,c~
0
1
—
1
0
Pe, co
-
1
0
—
1–
‘pf, Te
0
0
-
Pf co
1
1 + ~ic~
0
.
“ 1 + 2~Pin(~
1
1 + JIIJ
P2
P2
)
,,cO
2Q”(;
) ,,CC
‘
In (P2/~I)Te
‘Tl, Te
o
0
0
0
0
0
~P’fl (:
) ,,co
‘ZI, Te
o
0
0
0
0
0
On
) ,,co
(:
1
‘P2, Te
TR,Te
h (Pz/Pl)Te
rK, Te
$4-3
[3
[3
o
0
0
0
0
0
7Tl,ll, Te
o
0
0
0
0
0
{p
(p
(p
7Zl,ll, Te
o
0
0
0
0
0
[p
Cp
(p
r T1,j, Te
o
0
o
z–1
—
z
z–1
z–1
—
—
z
1) Correction factors are given by the formulae
1
43 =
_—
(~-l)Te
In (P2/Pl)Te
1
KTe
[1 – KTe)/KTe
1 – (P2/Pl)Te
‘e,
(4=
Te
pin Te
Pf, co -Pin,co
[p=
Pf,T~
Pin II co
a
Pin, co
2) z = number of atage groupe separated by intermediate coolers.
3)
Pin,co
‘e, Co
Pf co
1 + ~1(~
0
Methods of power maaeurament:
Mathod 1: by measuring the intarnal power Pin and the mechanical losses Pf.
Method 2: by measurement at the drive unit.
Method 3: by measuring the torque F and the spaedN.
z
z–2
z–1
—
Z–2
z–2
—
—
z–1
z–l
~.,
IS 14641:1999
ISO 5389:1992
-
;
.
------
.. . .
.
.
rable m — individual uncertainties and appropriate multiplying factors l) to be used to calculata tha total uncarteinty
in spacific power consumption, specific fuel consumption or efficiency)
Individual
uncertainty
Uncooled compressor
Cooled compressor
(see 8.2.3)
(SW 8.2.4.1)
Method pf power meaeurementa)
1
1
0
7PwTe
12
1 + ~/(4
Pin co
‘fin,Te
o
Pe, co
- Pf co
‘Pr, Te
‘e, Co
‘qv, Te
1
0
0
0
Cooled compressor
(Sef38.2.4.2)
Method of power measurementa~
3
2
1
1 + ~/c4
Pi” co
o
1
o
0
1
1
0
0
1
.
1+(4
-
Pf co
—
Pe, co
1
1
—
l+lgj
Method of power measurement)
3
1
0
0
0
-Pin co
‘e, Co
‘e, Co
—
l+lg~
1
1+[4
-
Pf co
21
1
o
0
1
‘e, Co
0
0
1
1
1
1+(4
1
0
1
1
1
1
1
1
0
0
1
P2
2*~’n (; ) ,,CO
1 + JICJ
1
*{Pln
~
()P1 I,c(
1
l–
Tp,, Te
1 + ~1(4
o
1 + ~J~4
—
1+{4
1
3
0
1 + ~1(~
~.+
In(~2/pl)Te
—
7Tl, Te
rR, Te
1
‘ZI, Te
o
111
0
0
P2
(~ ) ,,co
1
1
1
‘ + @
0
0
0
1 + CPln Q
()P1 1,co
1
‘P2, Te
—
1)
.
[n (p2/pl)Te
TX,Te
<3
C3
(3
o
0
0
0
0
0
7Tl,ll, Te
o
0
0
0
0
0
Cp
Cp
[p
‘Zl,ll, Te
o
0
0
0
0
0
ip
(p
[p
‘Tl, j, Te
o
0
o
z–1
—
z
z–1
—
z
Correction factors are given by the formulae
h (@pI)Te
1
(3=
‘
‘—
k – 1)Te
‘Te
1 – (p2/j@Te
(1 - KTe)lKTe
Pe, Te
(4=
pin Te
– pf,Te
% co ‘in,Co
_ Pi”, Il,co
Cp
Pin,co
2)
z = number of stega groups separated by intermediate coolers.
3)
Methods of power measurement:
Method 1: by meaeuring the internal power Pin and the mechanical Ioeaea pf.
Method 2: by measurement at the drive unit.
Method 3: by rnaaeuring the torque F and the speed IV.
z-1
—
z
z–2
—
z–l
z–2
—
z–1
z–2
—
z–1
IS 14641:1999
ISO 5389:1992
r
Guaranteed point
Ellipses representing ~
the teat uncertainties
Flow-rate
Figure
3 – Comparison of a singla guarantaad
point with a test curve
.
r
Guaranteed curve
Agreed manufacturing
tolerance
Single test point J
UX
-
Test uncertainties /
Flow-rate
30
Figure 4 – Comparison of a single test point with a guaranteed
curva
IS 14641:1999
ISO 5389:1992
.
Annex A
(normative)
P
Properties
of gases
compressibility
A.1
and
gas
factor
mixtures
and
–
Recommendations
relating
to the
to derivative compressibility factors
General recommendations
which includes the acentric factor, as the simpler method
specified in [8] is subject to particular inaccuracy in this area.
A.1.1
The following generel recommendations relating to
thermodynamic data for gases and gas mixtures shall be used
in connection with this International Standard.
A.1.5
In the case of gas mixtures, except in the case of
mixtures containing polar gases and particularly
These recommendations should not be considered to be
exclusive, but to represent the most up-to-date information.
More data are becoming available continually and in any
specific case the user of this International Standard should
.
water vapourr
.
ammonia,
refer to the latest published information.
— hydrogen sulfide, and
A.1.2
— halogenated hydrocarbon refrigerant mixed with other
gases of a very different molecular structure,
Where suitable coefficients are available to be used in
conjunction
with an established
equation
of state (e.g.
B. W. R. S., see [51)for the particular gas or gas mixture in ques-
tion, then these shall be used.
simple linear mixing rules may be used to determine the
pseudo-critical conditions of the mixture, i.e.
A.1.3
In the case of gas mixtures where suitable coefficients
for use with an equation of state are available for the separate
components of the mixture but not for the actual mixture in
question, then the coefficients for the mixture can be obtained
from the coefficients for the components by using the mixing
rules appropriate to the equation of state being used. Suitable
mixing rules are presented in [61.
R,
= Zqpcr
and
~cr = ~ ri Tcr
A.1.4
When suitable coefficients are available neither for the
particular gas or gas mixture in question nor, in the case of a
mixture, for the component gases, then the gas properties may
be obtained by using generalized compressibility functions
based on the concept of reduced temperature and reduced
pressure.
It is recommended that the method employing the concept of
the acentric factor (see [7]) be used rather than the simpler
two-parameters charts given in [8].
CO = E/’j O.)i
provided that the following conditions are satisfied:
‘Cr mex < ~
‘Cr min
Tables and charts, from which the compressibility factors Z(o)
and Z ‘1) for use with the method can be obtained, are
presented in [911). The isothermal derivative factors Z}o) and
Z}l) and the isobaric derivative factors Z;) and Z:) can be obtained from the method given in [101, chapter 26.
and either
Where the conditions of the gas in question are close to the
critical conditions (i.e. within the shadad area shown in the
charts for Z(o) published in [9]), it is essential to use the method
is close to unW, where Tcr msx, Tcr rein,Pcr max,~Cr rein, vcr mex
ancf Vcr ~in are respectively the maximum. and minimum values
of the critical properties of the components of the mixtures.
Rr mex or (Vcrkf)mx
PCr min
(vl#)fin
1) Other tables based on the method of calculation of Lee and Kesler have bean published in [6]. The deviation-function table of Lee snd Kester
(see [61) dtiera somewhat from those of Pitzer (see [7]) and Curl (sss [61), but it seams according to R.C. Reid and T.K. Sherwood [61 that extensive
tasting indicates that this new table is the more accurate.
31
..-!
IS 14641:1999
ISO 5389:1992
A.2
Specific recommendations
sources
of thermodynamic
equations
of state and the coefficients
used therewith
common
for the
data and suitable
for some
to be
of the more
gases
Theaa recommendations should not be considered to be
exclusive nor necessarily to be the best data available. They are
mainly based on the results of a survey among compressor
manufacturers and usera.
More data are becoming available continually and the user of
this International Standard is recommended to refer to the
latest published literature.
A.2. I
Specifically for ethylene and propylene, more accurate data are
available in [51, [271 [281 and [291.
Where it is desired to use an equation of state, the equations
given by Benedict, Webb and Rubin [30] and by Redlich and
Kwong [31] or the slightly leas accurate but simpler Beattie –
Bridgeman [321 equation (sea [241 and [101) may be used provided that the compression process under consideration does
not extend into the mixed-phase region.
Where saturated or mixed-phase conditions are involved, the
use of one of the “extended B,W. R.S .“ equations is recommended (see [5]). However, a great many experiments are
rwuir~ to determine the values of the many constants used in .
theaa equations.
The values derived from the selected equation should be compared with the data recommended above over the field of
interest.
Air
The data currently in use are those given in [111 and [121.
A.2.5
These are believed to be adequate for most compressor purposes. However, later and probably more accurate data, particularly at extreme temperatures and pressures, are available
(see [131, [141 and [151).
See [331.
Carbon dioxide
A.2.6
Helium
see [341.
A.2.2
Refrigerants (halogenated
hydrocarbons)
Data are available in [161, [171 [181, [191, [201 and [211.
A.3 Compressibility factors of hydrocarbon
gases and isentropic coefficient
A.3.1
A.2.3
Ammonia
The data in use are those published in [161. However, these
data are based on experiments made 50 years ago and published then (see [22]); they are inaccurate at high pressures,
close to saturation conditions, and near the critical point.
More data are available in [121.
A new equation of state taking account of recent work,
particularly that by Frank and Baehr, has been developed by
L. Haar and is published in [231 to replace [221.
Compressibility
hydrocarbon gases
factor of pure
The following equation can be used to predict the cornpraseibilityfactor, Z, of pure hydrocarbon gases:
z(o) + ~ z(l)
z =
where
Z(o) is the compressibility factor for the simple fluid, which
is tabulated as a function of ~ and pr in table A. 1;
Z(l) is the correction term for molecular acentricity, which
is tabulated as a function of ~ and p, in table A.2;
(see also [61, tables 3.1 and 3.2)
A.2.4
Pure hydrocarbons
co is the acentric factor, which is defined as
The data in use are those published by Edmister [241 and
Starling [51.
For saturated hydrocarbons the Edmister data, or other data
baaed on [251, are considered to be satisfactory for moat compressor purposes. However, new data are currently being produced by the National Bureau of Standards (see [261).
cl.) =
–(log~,
T
–
=t +1)
at
Tti
—=
“at – Tcr
0,7
Ig
[1
or, more conveniently,
For unsaturated hydrocarbons the situation is more confused
and many data in common use are known to be inaccurate by
reference to more recent experiments.
32
3
u = ~
pcr
(Tcr/T=t)
-
1
-1
-
IS 14641:1999
ISO 5389:1992
... *
x
%, is the critical pressure in atmospheres (1 atm =
760 mmHg = 1,013 bar);
Tcr is the critical temperature, in kelvins;
where the values of Z?! Z?! Z!) and Z!) are given in figures
A.1 and A.2. (See also [101.)
The correlation between the Edmister derivative compressibility
factors and the Schultz coefficients X and Y is given by the
formulae
TWt is the boiling temperature, in kelvins;
.zT
X=
——k
A.3.2
Derivative compressibility
[seafigures A.1 and A.2)
y-1
Zp
Y=—
‘r’ ‘t – R,
z
factors
The derivative compressibility factors, ZT and ZP, are 9iven by
the equations
‘
1
EL,:
A.3.3
Isentropic exponent
The ieantropic exponent K of a real gas differs from the value
cP/cv which it assumes for an ideal gas. The calculation of
the specific haat capacity and of the isentropic exponent for a
real gas shall take into account the effect of pressure.
The definition of the iaantropic exponent for a reel gas is given
in tebie 3.
33
“J
:,
.
.9 A
IS 14641:1999
ISO 5389:1992
Table A.1 –Velues
ofcompressibility
factor ZIO)
—
z (o)
q
0,30
o,~~
0,44)
o,~~
0,50
0,55
0,63
0,65
0,70
0,75
0,60
0,85
0,90
0,83
0,85
pr = 0,050
p, = 0,100
p, = 0,200
pr = 0,400
p, = Oreoo
pr = O,w
0,0029
0,0Q26
0,0024
0,0145
0,0130
0,0280
0,0261
0,0579
0,1158
0,1737
0,2315
0,0119
0,0110
0,0103
0,0239
0,0522
0,0477
0,0442
0,0413
0,1043
0,0853
0,0662
0,2064
0,1804
0,0625
0,1564
0,1429
0,1322
0,1236
0,0022
0,0021
0,9604
0,9649
o,8&3 1
0,8804
0,9822
0,8835
0,9946
0,8854
0,8859
0,9861
0,0221
0,0207
0,0088
0,0093
0,8377
0,9504
0,8598
0,9669
0,0380
0,0371
0,0778
0,0741
0,1166
0,1109
0,0356
0,0344
0,0336
0,0710
0,0667
0,0670
0,1063
0,1027
0,1001
0,1366
0,1330
0,9319
0,8436
0,6539
0,6810
0,0661
O,(M6 1
0,0985
0,0963
0,1307
0,1301
0,9528
0,8573
0,8015
0,9115
0,9174
0,7800
0,8059
0,6206
0,1006
0,6835
0,1321
0,1359
0,6967
0,1410
0,8800
0,8615
0,8621
0,8825
0,9637
0,8863
1,01
0,8868
1,02
1,05
1,10
0,8869
0,9842
0,8871
0,8875
1,15
1,20
0,1553
0,1476
0,1415
0,92227
0,8338
0,9648
0,8659
0,8669
0,9253
0,9277
0,9300
0,6398
0,6455
0,6509
0,7240
0,7360
0,7471
0,7574
0,9322
0,6561
0,7671
0,%7 9
0,9707
0,9747
0,9343
0,6610
0,9655
0,8874
0,8401
0,8465
0,8743
0,8930
0,7761
0,8002
0,8878
0,9861
0,8681
0,8804
0,9780
0,8608
0,8654
0,8611
0,8061
0,9205
1,30
1,40
0,8865
0,8868
0,8826
0,8842
0,8852
0,8864
0,9702
0,9768
1,50
1,60
1,70
0,8991
0,8883
0,8854
0,8864
0,8809
0,8828
0,8818
0,W66
0,8636
0,9714
0,9575
0,8984
0,9871
0,8843
0,8866
0,9775
0,8667
0,8885
0,8886
0,8887
0,8888
0,8889
0,8877
0,8855
0,8810
0,8859
0,8864
0,8872
0,8863
0,8881
0,8829
0,9844
0,8867
0,8863
0,8623
0,8661
0,8682
0,8837
0,8969
0,9739
0,8862
0,8866
0,8882
0,8886
0,9796
0,8642
0,8810
0,8857
0,9735
0,9786
0,W66
0,8848
0,8888
0,8887
1,0000
1,0001
0,8880
1,0013
0,8880
1,CU121
1,0002
1,0004
1,0008
0,8884
1,0002
1,0008
1,0017
1,0030
1,0065
1,0043
1,0075
1,0010
1,0021
1,0066
1,0080
1,m
2,60
2,60
3,00
3,50
4,00
0,8865
0,8866
0,8967
1,0000
1,0000
I,oooo
1,0001
1,0001
0,9626
0,8632
0,8637
1,0004
1,0005
:
,
0,8323
0,6578
0,5560
0,5667
0,6138
0,6353
0,6542
0,6710
0,7130
0,7649
0,6032
0,8779
0,8330
0,8386
0,9063
0,9534
0,9288
0,8458
0,6764
0,8062
0,8881
1,0007
1,0018
1,0035
1,0043
...
‘i
—
0,1762
0,1647
0,0195
0,0186
0,0178
0,6858
0,9165
0,9725
0,9768
0,9790
0,8603
0,97
0,96
0,98
1,00
1,90
2,00
2,20
2,40
34
p, = 0,010
0,9278
0,8439
0,8563
—
IS 14641:1999
ISO 5389:1992
Table A.1 – Values of compressibility
factor Z(Oj(conc/uded)
~ (o)
q
p, =
1,000
J+
=
1,200
/Jr =
l,WO
pr = 2,000
p, = 3,000
p, = 5,000
p, = 7,000
p, = 10,OW
0,5775
0,5195
0,4744
0,6648
0,7775
0,7085
1,4366
1,2802
1,1758
2,0048
1,7887
1,6373
2,8507
2,5539
2,3211
0,4384
0,4092
0,6551
0,6110
1,0641
1,0084
1,5077
1,4017
2,1338
1,9801
0,30
0,35
0,2882
0,2604
0,40
0,2379
0,3470
0,3123
0,2853
0,45
0,50
0,2200
0,2056
0,2638
0,2465
0,3563
0,3284
0,3077
0,55
0,1939
0,2323
0,2689
0,3653
0,5747
0,%75
I
1,3137
0,60
0,1642
0,2207
0,2753
‘
1,2398
0,1765
0,1703
0,1656
0,2113
0,2038
0,1981
0,2634
0,2538
0,2464
0,5446
0,5197
0,4991
0,4823
0,6859
0,65
0,70
0,75
0,3657
0,3495
0,3364
0,3260
~
1,1773
1,1241
1,0787
0,80
0,65
0,80
0,83
0,85
0,1626
0,1614
0,1630
0,1664
0,1842
0,1924
0,1935
0,1863
0,1888
0,2411
0,3182
0,3132
0,3114
0,3122
0,4690
0,4581
0,7588
0,7368
0,7220
“1,4456
I
1,0400
1,0071
0,9793
0,8648
0,8561
1,3257
1,3108
0,97
0,86
0,88
1,00
0,1779
0,1844
0,2055
0,2087
0,2154
0,8480
0,8442
o,94136
1,2988
1,2801
1,2835
0,9372
0,9339
1,2772
1,01
0,9307
0,9222
1,2650
0,4335
0,3801
0,2362
0,2363
0,2405
0,2432
0,3138
0,4527
0,4507
0,4!3) 1
0,2474
0,2533
0,3164
0,3182
0,4504
0,4508
0,2638
0,2563
0,3204
0,3229
0,4514
0,2237
0,4648
0,2370
0,2640
1,02
0,5146
1,05
1,10
0,6026
0,6880
0,2629
0,4437
0,2715
0,3131
1,15
1,20
0,7443
0,7858
0,5984
0,6603
,0,4560
0,5798
0,7363
0,6605
1,30
1,40
1,50
0,6438
0,8827
0,8111
0,6585
0,6833
0,9180
0,7524
1,60
1,70
1,60
1,80
0,1705
0,1959
0,2801
0,9103
0,9308
0,8463
0,8367
0,7854
0,7138
0,7082
0,7052
0,7035
0,7018
‘
~
;,;::
;
1,6519
1,5729
1,5047
1,3843
1,3496
0,7004
0,3260
0,4522
0,4533
0,3297
0,4547
:698:
0,3452
0,3853
0,4604
0,4770
0:6850
0,4760
0,5605
0,5042
0,5425
0,6887
0,7069
0,9110
0,9033
0,8890
0,8256
0,6689
0,6808
0,7753
0,6328
0,6344
0,7202
0,8000
0,9234
0,8738
0,8043
0,7358
0,7761
0,6200
0,6617
0,8888
0,9112
0;9287
0,8518
0,6864
0,9745
0,8413
0,9275
0,8552
0,8M 4
0,8626
0,8456
0,8589
0,8806
0,8845
0,9287
0,9557
0,9772
1,0084
1,0313
0,8861
1,0157
1,0328
0,8835
0,9118
0,9359
0,9550
0,8827
1,0011
1,0463
1,0826
1,1792
1,0565
1,1016
1,1830
I
0,7667
0,8410
0,8609
0,6881
I
1,2710
1,2481
1,2232
1,2021
1,1644
1,1339
1,1320
1,1343
2,00
2,20
2,40
0,9715
0,8647
0,8836
2,60
2,80
0,8883
1,0031
0,8888
1,0042
1,0010
1,0063
1,0106
1,0137
1,0223
3,00
1,0057
1,0074
1,0101
1,0153
1,0284
1,0635
1,1075
1,1848
3,50
4,00
1,0Q87
1,0120
1,0140
1,0156
1,0221
1,0249
1,0368
1,0401
1,0723
1,0747
1,1138
1,1136
1,1834
1,1773
1,0179
1,0040
1,0600
1,0793
.
1,1560
1,1419
0,9663
0,8678
0,9754
0,8365
0,8841
1,0115
0,9511
0,8624
0,8526
0,8161
i
1,1381
1,1452
1,1516
1,1635
1,1728
35
.s
IS 14641:1999
ISO 9389:1992
Tabla A.2 – Valuas of correction term Z(l)
q
z(’)
p, = 0,010
pr = 0,050
p, = 0,100
p, = O,m
/Jr = 0,400
p, = 0,600
p, = 0,800
0,30
–O,ooo 8
–0,004 o
-0,0081
-0,0161
0,35
–0,000 9
-0,0046
-0,0048
–0,008 3
-0,0185
-0,0323
-0,0370
-0,0484
-0,0554
–0,038 o
– 0,0374
– 0,0570
-0,0560
- 0,C645
-0,0738
-0,0758
-0,0380
-0,0639
-0,0745
-0,0716
–0,064 6
0,40
-0,0010
0,45
0,50
– 0,0009
–O,ooo 9
-0,0047
-0,0085
–0,019 o
-0,0084
–0,008 o
– 0,0187
– 0,0181
-0,0043
-0,0041
-0,0086
-0,0172
-0,0164
-0,0343
-0,0082
-0,0326
–0,051 3
–0,048 7
-0,0045
0,55
– 0,0314
0,60
0,65
– 0,0205
–0,013 7
0,70
– 0,0083
-o,on 2
-0,0507
-0,0078
-0,1161
-0,0156
-0,0148
-0,0309
– 0,0284
– 0,0438
0,75
- O,m
-0,0339
-0,0744
-0,0143
-0,0282
-0,0417
0,80
0,85
0,80
0,83
-0,0228
– 0,0487
–0,0152
– 0,0089
-0,0319
-0,0205
-0,0154
-0,0126
-0,1160
-0,0715
-0,0442
-0,0326
-0,0262
– 0,0272
-0,0288
0,95
-0,0044
-0,0029
-0,0019
-0,0015
– 0,0012
0,97
0,88
-0,0010
–0,005 o
– 0,0009
–0,004 4
0,88
-0,0008
1,00
– 0,0007
1,01
-0,0006
4
– 0,0075
-0,0082
1
,
i
-0,010
?
-0,0335
-0,0285
-0,0531
-0,0435
-0,0120
-0,0240
-0,0351
– 0,0198
-0,0082
-0,0277
-0,0087
0,0038
0,0127
0,0190
0,0106
0,0237
0,0326
0,0287
0,0429
0,0477
-0,0080
– O,ooo 5
-0,0026
-0,0051
-0,0102
-0,0015
0,0000
0,0011
O,ml 9
-0,0029
0,0001
0,0023
0,0039
-0,0054
0,0007
0,0052
0,0084
1,30
1,40
0,0006
0,0007
0,0030
0,0125
0,0147
1,60
1,60
1,70
0,0008
0,0008
0,0008
0,0081
0,0072
0,0078
0,0306
0,0323
–0,078 6
-0,0588
-0:0429
-0,0303
–0,003 2
0,0236
0,0386
0,0489
0,0812
0,M6 1
0,0877
0,0158
0,0162
0,0163
0,0330
0,0329
0,0487
0,0501
0,0487
0,0162
0,0159
0,0155
0,0325
0,0318
0,0310
0,0488
0,0477
0,0484
0,0283
0,0276
0,0437
0,0617
0,0579
0,0411
0,0544
0,0280
0,0245
0,0232
0,0387
o,a385
0,0512
0,0483
0,0456
2,20
0,0008
0,0008
0,0007
0,0037
0,0078
0,0074
2,40
0,0007
0,0035
0,0070
0,0147
0,0139
0,0007
0,0033
0,0031
0,0086
0,0062
0,0131
0,0124
3,00
0,0006
0,0006
3,50
4,00
0,0005
o,oCO5
0,0029
0,0Q26
0,0059
0,0052
0,0117
0,0103
0,0023
0,0046
0,0081
2,84)
2,80
-0,0526
-0,0509
-0,0503
-0,0514
-0,0540
-0,0161
-0,0030
0,0081
0,0079
-0,0401
– 0,0381
-0,0386
-0,1562
-0,1110
–0,014 o
– 0,0079
-0,0089
0,0040
0,0040
0,003 @
–0,055 o
-0,1847
-0,0003
-0,0000
0,0002
0,0004
0,0008
-0,0811
-0,0579
–0,1100
1,02
1,80
1,80
2,00
‘
-0,0841
-0,0039
-0,0034
0,0080
0,0081
-0,0461
-o,on o
-0,0208
-0,0184
0,0036
0,0039
0,0040
0,0040
– 0,0589
– 0,0682
– 0,0450
-0,0380
-0,0080
1,05
1,10
1,15
1,20
~
–0,111 8
– 0,0763
I
,
0,0677
0,0887
0,0862
0,0835
0,0204
0,0345
0,0303
0,0401
0,0182
0,0270
0,0367
f—
,
..—.
IS 14641:1999
ISO 5389:1992
,d
Table A.2 – Valuas of correction term Z(l) (cone/uded)
—
z(l)
d
pr =
1,000
pr=
1,200
p, =
1,500
p, = Z,wm
p, = 3,000
p, = 5,000
pr = 7,000
-0,1608
–0,163 4
-0,1679
-0,2407
–0,273 8
– 0,2789
–0,273 4
-0,3886
-0,4523
-0,4603
-0,4475
-0,5572
-0,6279
-0,5355
-0,7915
-0,6653
-0,6836
-0,2511
-0,4253
-0,6162
-0,5631
-0,8606
-0,M)89
-0,2465
-0,2312
-0,3881
-0,3718
–0,544 6
–0,216 O
-0,2013
-0,1672
–0,344 7
-0,3184
– 0,2829
-0,7521
– 0,5828
-0,6346
-0,1736
-0,2682
pr = 10,OOO
—
0,45
-0,0606
-0,0821
-0,0846
-0,0829
–0,096 6
-0,1105
-0,1134
-0,1113
-0,1207
-0,1379
–0,141 4
-0,1367
0,50
-0,0683
-0,1069
-0,1330
-0,1640
-0,1762
0,55
0,65
-0,0649
-0,0603
-0,0759
-0,1015
– 0,0850
-0,0806
-0,1263
–0,1192
-0,1122
-0,1569
-0,1572
-0,1476
0,70
0,75
– 0,0718
-0,0661
–0,066 5
-0,0608
–0,1057
-0,0886
–0,1365
-0,1288
0,60
0,65
0,80
0,93
0,95
-0,0648
– 0,0767
– 0,0731
– 0,0840
–0,121 7
-0,1138
-0,0701
-0,0868
-0,0640
-0,1059
–0,1602
–0,1463
-0,0602
-0,0607
-0,0667
– 0,0678
–0,061 o
-0,0788
-0,1007
-0,0867
-0,1374
-0,1310
0,97
0,88
0,99
-0,0623
-0,0669
-0,0661
-0,0759
-0,0821
-0,0740
-0,0715
-0,0883
-0,0661
1,00
-0,0679
-0,0223
-0,0678
0,30
0,35
0,40
0,60
1,01
-0,0622
-0,0504
–0,054 1
-0,0580
–0,064 6
-0,0609
-0,5047
-0,4653
-0,4270
-0,3801
-0,5785
-0,2439
-0,3545
-0,3201
-0,4740
– 0,4254
-0,2195
-0,2862
– 0,3788
-0,2045
–0,184 3
-0,2651
-0,2526
-0,3516
-0,3339
–0,1240
-0,1202
–0,1162
-0,1637
-0,2381
-0,2322
–0,316 3
-0,3075
-0,2254
-0,0624
–0,077 8
-0,1118
–0,107 2
–0,167 2
-OZ185
– 0,2889
-0,29) 2
-0,1615
-0,2116
-0,2616
-0,0722
–0,102 1
- 0,~
8
–0,1556
–0,1370
– 0,2047
– 0,2731
-0,0373
0,0332
0,1085
-0,1021
-0,0611
-0,0141
-0,1635
–0,145 9
-0,1064
– 0,2476
– 0,2056
o,18pil
0,1684
0,2079
0,0875
0,2387
0,1737
0,0176
0,1008
–0,1763
-0,1728
-0,5250
-0,0473
-0,0521
-0,0062
0,0220
0,0227
0,1059
-0,0524
0,0451
0,0476
0,0525
0,0719
O,m 7
0,0843
0,0881
0,1630
0,1548
0,1477
1,30
O,CW 9
0,1048
0,1420
1,40
1,50
0,0857
0,1053
0,1363
0,1055
0,1035
0,2433
0,2309
0,1717
OSX350
tt,1058
1,70
0,0638
0,1008
0,1345
0;1303
0,1259
O,lMI 6
1,60
0,0664
O,(M65
0,1729
0,1658
0,2361
0,2305
0,2631
0,2768
0,2255
0,2528
0,2179
i ,60
1,80
0,0616
0,0782
0,0978
0,0847
0,1216
0,1583
0,2671
0,2576
0,0767
0,0719
0,0816
0,0657
0,2676
0,3096
2,40
0,0675
0,0603
0,1133
0,1057
0,0869
0,2648
0,2819
0,3017
2,00
2,20
0,1532
0,1476
0,1374
0,2224
0,2144
0,2646
0,1173
‘Q,1285
0,1812
2,60
0,0634
2,60
3,00
3,50
4,00
0,0588
0,0555
0,0487
0,0443
0,0754
0,0711
0,0829
0,0676
0,0828
0,1207
0,1138
0,1076
0,1706
0,1613
0,1529
0,0728
0,0551
0,0849
0,0649
0,1356
.0,1219
4,02
1,05
1,10
1,15
1,20
0,0672
0,0581
0,0527
-0,0432
O,
8
0,1r
7
0,1880
0,2069
0,1832
0,2720
0,2502
0,2464
0,2372
0,2268
0,2042
0,1657
-0,0578
0,3087
0,3135
0,3089
0,3009
0,2815
0,2817
0,2564
0,2378
–0,1642
-0,1231
-0,0423
..
0,1573
0,3355
0,3459
0,3475
0,3443
0,3365
0,3194
0,2884
37
IS 14641:1999
iSO 5389:1992
Figure Ala)
38
– Values of Z+o)as a function of p,
IS 14641:1999
IS() 5389:1992
z;)
.
““4;0
3/0
2;0
1;S
1,6
1,4
1,3
1,2
1,1
1,0 0,95
(39
0/65
0.,6
~
Figure A.1 b] – Values of Z#] as a function of Tr
39
.*
IS 14641:1999
ISO 5389:1992
,*
z;)
-0;1
0,2
0,3
0,4
0,s 0,6 0,70,8 QSI;0
2
34
56789
[0-
P,
Figure A.2a) – Valuas of Z~O~as a function of p,
IS 14641:1999
ISO 5389:1992
b“
%
m
I
41
. ._.
“’” ~
.
I,.
f,
IS 14641:1999
ISO 5389:1992
.1
i
A.4 Properties of gas mixtures and
gas-vapour mixtures, considered as perfect
gases
A.4.1
Gas mixtures
A.4.I.1
The ratio of the components is given by the formula
*i.
+$_=_
=
Zri Cpi
Cp~ =
qm,i
Zt?lj
Cpi
Cp =
1
CV=CD–
A.4.1.2
*- -.’
A.4.1.9
The mean specific heat of the mixture is determined
as follows:
qm
Emi
A.4.1.8
The mean molar specific heat of the mixture is determined as follows:
R
The molar proportion is given by the formula
A.4.1 .10
follows :
The mean isentropic exponent is determined as
Em, Cpi
A.4.I.3
formula
The volume ratio of the components is given by the
‘M
=
A.4.2
NOTE – For mixtures of perfect gases 6 represens tha mo~r Proportion.
A.4.1.4
The partial pressuresPi of the components are 9iven
by the formula
A.4.1.5
The mean molecular mass of the mixture is determined as follows:
ZVlj Cvj
,
1
.
/{
‘ -
~mj[Kj/(Ki
‘=
}
Gas-vapour mixtures
A.4.2.I
The vepour content is defined by one of the following
quantities.
A.4.2.I.1
The relative humidity, q, which is the ratio between
the partial vapour pressure and the saturation pressure at the
temperature of. the mixture is given by the formula
Pv
<,
‘=Psa
For rp >1 there is a formation of condensate.
A.4.1.6
The mean gas constant of the mixture is determined
as follows:
Rmd
RM=—=—
M
A14.2.1.2 The humidity content, x, which is the vapour mass
related to the mess of dry gas is given by the formula
x=
z’;.
qV-vG
_
qv w
R=
R=
Pv
—x—=—
Rv
P–PV
Rv
~
P Psst
P–PPsst
I
A.4.1.7 The following relationships exist:
In the particular case of humid air
9‘=t
x = 0,6221
P-
PPsst
mi
A.4.2.1.3 The mess ratio of vapour, mv, is given by the formula
pi = rjp
42
mv =
~=
q“vv
qVvG
qvvv
+ qvvG
_
x
1+X
f—
,
.—.
.
IS 14641:1999
ISO 5389:1992
A.4.2.1.4
formula
The volume ratio of vapour, rv. is given by the
It is defined as the flow,
mixture actualiy handled
directly from the flow-rate
~v = qm w &
=mv
qm R
Rv
—=
RPp
MM = Mvrv+A4G(l-rv)
It is defined as a flow-rate of dry~as qv&
A.&2.7.2
A.4.2.7.3
These two flow-rates are linked together by the
following relation:
= MG+—v‘=t (Mv– MG)
P
A.4.2.3 The mean gas constant, RM
... of the mixture is determined as follows:
-
mvRv+(l–mv)RG
q v, of a gaa-vapour
by the compressor and resuithg
measurement.
Pv
PP3at
—.=—
A.4.2.2 The mean molecular mass of the mixture, kfM, is
determined as follows:
R~=
A.4.2.7.I
=RG
1+4
1+x
[(
Rv
—
RG
)]
1
For the particular case of humid air
A.4.2.8
The condensate flow-rate separated in an intercooler
can be calculated as follows.
If between stage I and stage Ii of a compressor the gas is cooled
such that the relative humidity at the outlet of the intercooler
becomes greater than 1, a mass flow-rate qmc~ can be
extracted at this point of the circuit.
In this case it is assumed that after the extraction of the condensate the gas-vapour mixture is still saturated, i.e. that
9=1.
A.4.2.4
Tha mean molar specific heat is determined es
indicated in A.4.1 .8.
A.4.2.5
The mean isentroDic exDonent is determined as
indicated in A.4.1 .10.
‘
“
A.4.2.6
The viscosity of a gas-vapour mixture is determined
in the same manner as for a gas mixture by using the methods
indicated in annex B.
A.4.2.7
The volume flow-rate of a gas-vapour mixture can be
defined in two different ways, according to the contract
specifications, as given in A.4.2.7.1 and A.4.2.7.2.
The condensate flow-rate is determined as follows:
qmcd
=
f?mv,l
–
qmV,ll = qmG (Xl – ~sat,ll)
where
qmG
is the mSSS flow-rate
of dry 9as;
Xl is the humidity content at the inlet of the intercooler,
determined according to A.4.2.1 .2;
XW,II
is the humidity content of the saturated
the outlet conditions of the intercooler.
mixture at
43
,d
IS 14641:1999
ISO 5389:1992
Annex B
(normative)
“
“i
‘
Viscosity of gases and gas mixtures
B.1
Dynamic viscosity
S.1.1 Dynamic viscosity at atmospheric pressure
or at a pressure close to atmospheric pressure
If none can be found, it is adviaad for non-polar substances to
calculate the corresponding values by application of the
equations in [391:
~(-)
PCr “3
Tc,
B.1.l.l
Pure substances
Information is contained in [351, [361 and [371.
If the dynamic viscosity of a pure substance is to be aaaeaeedat
atmospheric pressure or at a pressure close to atmospheric
praasure, three methods can be used as follows:
= 2,3551
– 0,067 co
&
—
=0,7915+0,1693(.0
kTcr
where
k
is the Boltzmann constant (k = 1,3605
a)
the theory of Chapman – Enskog;
e
is the depth of potential energy minimum;
b)
the law of corresponding states;
u
is the collision diameter, “mangstroms;
c)
the method of VD1-Warmestlas.
o
is the acentric factor.
B.1.1.1.1
The theory of Chapman – Enskog
As a general rule the equation giving the value of dynamic
viscosity, p, expreaaad in paacal seconds, is as follows:
P=26693x10-3*T
~zQv
where
x 107 J/K);
In the case of polar gases, the calculation made and published
in [40] can be used.
kTcr
In the case of substances for which u and T* = ~
are not
given, it is recommended that the following equations be used
(see [411):
()
1,585 v~
u
=
1/3
1+1,36*
&
—.
k
1,18 (1 + 1,3d2) Tb
A4 is the molar maae, in grams;
C5=
T
is the temperature, in kelvins;
u
is the collision diameter, in angstrome;
f2v is the reduced integral of collision.
In the equation above, a and S2vare dependent on the potential
of interaction of the two molecules present.
The expressions for potential as given by Lennard – Jones for
non-polar substances and by Stockrnayer for polar substances
are adopted for the aaeeeament of quantities a and C2v.
1,84x lo31f:
VbTb
where subscript b indicates conditions at boiling point, with flp
expressed in debyaa 1) and ~ in cubic centimetres per mole
gram.
B.1.1.1.2 Method of the corresponding stataa
In the case of non-polar substances, the following relationships
have bean established (ace [431):
whercTheea quantities may also have been determined experimentally.
Numerical values for these quantities may be found, for
instance, in [61 or [381.
1) 1 dabye = 10-1* (dyn . cm4)1’2
. 10-= (10 N . m4)1’2
. 3,162 x 10-= (N . m4)1’2
2) 1 stm = 101326 Pa
44
< =
h
116M-112 per-213
and
PCr is expressed in atmospheres*).
4
f,
IS 14641:1999
ISO 6389:1992
The moat accurate
Chapman
method
is the appliition
of the thao~
of
Enskog using the reduced integral of colliiion as
–
defined previously.
In the case of polar substances with or without hydrogen bonding, the utmost caution is necessary.
Wti regard to the method of the corresponding states, either
the charts given in [471, or the dmgreme given in [481 or in [491,
or the followfng equation taken from [501, may be used:
APrv5
P
—=1+(1-o,45q)
Po
Bp, + (1+ C&)-l
-“
..ssi
..-.1.
i
B.1.1.I.3
Method
of VD1-W~rmeades
.
See [371.
666(@
9
PC,
%
B.1.1.2 Mixtures
exp a2 T, *3
A=?
r
For mixtures with n components, the kinetic theory of gases
gives the following equation, neglecting second-order effects:
c=+
;=l
j=l
/1
exp Y2 Tr ‘Y3
r
where
~i
are the viscosities of pure gases;
Um is the viscosity of the mixture;
are mole fractions;
yi and yj
al = 1,9624 x 10-3
a2 = 5,2663
@ij =
[l
+ @i/Uj)v2
2&[l
(Jk’i/Mj) -v412
+ (kf/Mj)l”2
a3 = 0,5767
)% = 1,6552
/9*= 1,2760
NOTE – Among the vsrious methods for assassing @u and @j/, that
given in [44] is currently preferred, even in the case of polar compounds. However, -the error which is usually lass then 2 % may
become very significant if ~ is markedly greeterthanMj and#i much
Y1 = 0,1319,
)’* = 3,7035
greeterthsnfl}
When hydrogenor heliumare presentin a proportionexceeding35 %
by volume, the more accurate, though more complex, method of
Raichenbergas givenin [45] may be considered.
The diegrenM given in figures B.1 and B.2 may be used in
determining the viscosity of gas mixtures; these diagrams are
based on the Bromley and Wilke method.
6.1.2
Dynamic viscosity at high pressure
B.1.2.1 Pure substencea
A dwgram in which the effect of pressure is shown has been
established in [461.
For any reduced pressure or temperature it can be determined
whether the gas is “dilute” or dense (sea f~ure B.3). The
boundary is such that the required correction is no greater
than 1 %.
Y3 = 78,6578
6, = 2,8486
62 = 2,9190
83 = 16,6169
In the formulae above, Up is expmaaad in dabyea, ~r in
atmoapherea and Tcr in kahrii, whiih leads to an error of leas
than 10 %.
The reduced vkoaity as recommended in [511 may also be
used, which leads to # g = 7,7.
The result may be obtained rapidly but is unfortunately approximate.
Among the moat recent data those published in [371 and [52]
may be mentioned.
45
IS 14641:1999
ISO 5389:1992
60
41
Ill
1
1
I
?()
40
30
M“;.......i
20
1 1 1
4-4
i
1
1
t
!
I 111
1
0,8
,
AL
U,o
!
Y
– -o,40,3r
“0,0050,01 oj)2
[!
,
0;2(j30,4
0;60,8
i
0,05 0;1
PIi
/Mk
Figure B.1 – Diagram for the determination
i
2
of the viscosity of gas mixtures
,-
6
{, -
4
3
Ill
II
1
I
I
I 1 1
2
1
0,8
~hot6
0,4
0,3
.
,
I
I
1
1
1
1
/
1 1 i
1
/
0,2
0,1 1 I 1 I 1
1
0,08
I
0,06
I
0,04
0,03
I
I
0,6 1
46
I
1
1
I
i
1 I
I
11
\
11
I 1111
I
1
I
1
1
I
1
2346810
Mi/Mk
Figure B.2 – Diagram for the determination
r
I
I
I
20 3040 6080100 200
of tha viscosity of gas mixtti~s
f,
——
IS 14641:1999
ISO 5389:1992
Dense gas
~
Dilute gas
I
0
I
23456789
Reduced temperature
Figure 6.3 – Diagram showing the effect of pressure
(see [461)
47
d
IS 14641:1999
ISO 5389:1992
B.1.2.2
Zcrm =
z
v~rm =
& Yi
Mixtures
Although its accuracy is questionable, the Dean and Stiel
method is the most frequently recommended:
Ofm-P%)
gm = 1,08 [exp(l,439 Q,J - exp(l,lll
Pml’m)l
where
Pcrm =
Zcrm
Yi Zcri
‘Crj
R Term
‘Crm
Am is the viscosityof the mixture at high pressure, in micr~
poises’);
from which Qcrmand ~m may be calculated.
E% is the viscosity of the mixture at low pressure, in
micropoiseslJ;
@m is the pseudo-reduced density of the mixture
Qrm = @m/Qcrm
In the case of non-polar mixtures with low molar masses, the
accuracy may be within 5 %.
In the case of non-polar mixtures with high molar masses or of
polar mixtures, the Dean and Stiel method may stiil be used but
with iesser accuracy.
where
Another general method is described in [37].
@m is the density of the mixture, in gram moles par
cubic centimetre;
@crm is the pseudo-criticaldensity of the mixture, in gram
moles per cubic centimatre (ecrm = Pcm/Zc~m R T&J;
the calculation of the mixture pseudo-critical parameter being
made according to the amended rules of Prausnitz and Gunn,
i.e.
B.2
The kinematic viscosity of a pure substance or of a mixture is
determined using the formula
where
p
Term =
Yj Tcri
z
i
1) 1 pP = 10–7Pa. s
48
Kinematic viscosity
is the dynamic viscosity;
Q=—
P
ZRT
f—
,
.—..
IS 14641:1999
ISO 5389:1992
..
,4?
,
‘
Annex C
(normative)
: -J
Conversion factors from non-Sl units to S1 units
Measurement
No.
Measurement
S1 unit
Term and symbol for non-Sl unit
Multiplication
symbol
factor
C.1
length
inch, in (“)
foot, ft
yard, yd
mm
m
m
25,4
0,3048
0,9144
(exact;
(exact]
(exact)
C.2
speed
foot par minute, ft/min
mls
0,00508
(exact)
C.3
area
square inch, inz
square foot, ftz
square yard, ydz
cd
d
rn2
6,4516
0,092803 w
0,838127
(exact)
(exact)
C.4
volume
cubic inch, ina
cubic foot, fts
cubic yard, yda
gallon, gal (UK)
gallon, gal (US)
ml
drn3
m3
(exact)
drd
dti
16,387084
28,3168
0,784555
4,548 (E3
3,78541
msl kg
0,082428
C.5
density
cubic foot per pound, ft3/ lb
C.6
flow
cubic foot per minute, fts/ min
1/s
0,47185
C.7
mass
grain, gr
ounce, 02
pound, lb
slug
hundredweight, cwt (UK)
ton (UK)
ton (US)
m9
9
kg
kg
kg
kg
kg
64,79891
28,3485
0,45358237
14,5839
50,8023
1016,05
807,185
—
—
—
(exact;
(exact)
C.8
density
pound per cubic foot, lb/fta
kglrrr3
16,0185
C.9
force
N
N
N
9,80885
4,44822
103
C.lo
——
pressure
kilogram-force, kgf
pound-force, Ibf
sthbne, st
bar
kilogram-force per square metre, kgf/@
Torr (mmHg O ‘C)
pibze, pz
pound-force per square inch, lbf/in2
technical atmosphere, at ( = kgf/cr@
physical atmosphere, atm
Pa
Pa
Pa
Pa
Pa
Pa
Pa
lW
9,80885
1,33322 x 102
103
6,88476 X 103
0,980865 x lW
1,01325 x 10s
(exact)
(exact)
(exact)
(exact)
(exact)
(exact)
C.11
work
kilowatt-hour, kW. h
kilogram-force metre, kgf. m
foot pound-force, ft oIbf
J
J
J
3,6 X 10s
9,80885
1,35582
(exac~
(exact)
C.12
quantity
of heat
15 ‘C calories, calls
I.T. calorie, callT
British thermal unit, Btu
metric horsepower hour, ch. h
horsepower hour, hp. h
thermie, th
J
J
J
MJ
MJ
MJ
4,1855
4,1888
1,05508 x 103
2,647 8)
2,88452
4,1855
(exact)
(exact)
C.13
internal energy
density
British thermal unit per pwnd,
kJ /kg
2,32601
(exact)
C.14
internal energy
volume
metric horsepower minute per cubic
metre,ch. rein/ rn3
J/l
44,1289
horsepower per hundred cubic feet per
minute, hp/100 cfm
J/l
15,&30 5
kilogram-force matre per second, kgf. m/s
metfic horsepower, ch
horsepower, hp
foot poundal per second, ft. pall/s
w
kW
kW
w
9,W885
0,735488
0,745700
0,0421401
power
C.15
I
I
Btu/lb
I
I
(exact)
.
IS 14641:1999
ISO 5389:1992
Measurement
No.
Measurement
I,
heat flow
C.16
I.T. kilocalorie per hour, kcallT/h
British tharmal unit par hour, Btu/h
—
C.17
——
C.’I8
—..
—
c. “19
Pound-force second per square foot, lbf.s/ftZ
Pas
Pas
kinematic
viscosity
I
stokes, St
square foot per second, ftZ/s
Nr21s
dls
I
Temperature
T–To
(exact)
(axact)
10-4
(exact)
0,0929030
(exact)
1,163
I
0,14422s
W/(m. K)
I
1,73073
W/(m. K)
I
W/(m2K)
Wllm2. K\
1,163
I
(exact)
1 R7R %
I
If tin degrees Celsius, fF in degrees Fahrenheit, Tin kelvins and
T~ in Rankine degrees refer to one and the same physical state,
then the numerical values t,tF,T and T~ are related by the
following formulae:
t = 5/9 (~F – 32)
where
T
factor
0,1
W/(m. K)
I.T. kilocalorie per hour square metre kelvin,
kcal,T/(h. W. K)
British thermal unit per hour square foot degree
Fahrenheit. Btu/(h. ft2.°F)
The Celsius temperature t of a system is given by the expression
t=
47,BB0 3
poise, P
I
C.21
1,163
0,293072
I
heat transfer
coefficient
Multiplication
w
I
I.T. kilocalorie per hour metre kelvin,
kcallT/(h. m.K)
British thermal unit per hour square foot
degree Fahrenheit, Btu/(h. ft2°F)
British thermal unit per hour foot degree
Fahrenheit, Btu/(hft.° F)
I
w
dynamic
viscosity
heat transfer
C.20
S1 unit
symbol
Tarm and symbol for non-Sl unit
t = T – 273,15
k the absolute thermodynamic temperature, in kelvins;
t = 5/9 TR – 273,15
To = 273,15 K;
(in accordance with the International Temperature Scale of
1868).
The Fahrenheit temperature tF of a system is given by the
expression
tF=TR–
To
thermodynamic
temperature,
in
Rankine
To = 459,67 “R
NOTES
1 ‘R should not be mistakan for an abbreviation for the abandonad
degree R6aumur.
2
1“R=519K
Multiples of S1 units
.
To allow words and symbols of multir)lesand submultiple of S1
units to be formed, the following SI prefixes are usad.
Prefix
where
TR is the
degrees;
C.22
Symbol
Factor
1012
tara
T
gigs
G
109
mw
M
k
h
106
kilo
hecto
data
daci
centi
mini
micro
nano
pico
103
102
da
d
c
m
10
v
n
10-6
10-8
10-12
P
10-1
10-2
10-3
IS 14641:1999
ISO 5389:1992
Annex D
(normative)
Similarity of flow
(Similar velocity trianglea)
D.1
General
D.1.1.2 Equal isentropic exponents
The following theory strictly applies only to uncooled compressors or to sections of cooled compressors between intercoolers. However, it may be applied to cooled compressors,
provided that the conditions for similarity of flow are satisfied
simultaneously in all sections of the compressor.
The conversion of test results from the test conditions to the
specified conditions, assuming constant polytropic efficiency,
is generally only possible when similarity of flow is assured for
the conversion of a test point to specified conditions, i.e. when
the following main requirements are fulfilled:
a)
geometrical similarity;
b)
equal isentropic exponents;
c)
equal enthalpy rise coefficients and flow coefficients;
d)
equal Mach numbers;
e)
equal Reynolds numbers.
The change of state of the medium handled can only be kept
the same at all points within the compressor under test and
specified conditions when the isentropic exponents are equal.
D.1.1.3 Equal anthalpy rise and flow coefficients
equal Mach numbers
and
Strict similarity of flow at each point within the compressor can
only be achieved when the enthalpy rise and flow coefficients
and the peripheral Mach numbers are equal, i.e. when
~ .
9’1
1%
The above similarity requirements refer only to flow in the compressor, and not to any intercoolers which may possibly be fitted nor to the mechanical losses. Furthermore the heat transfer
from the compressed medium to the casing of uncooled compressors, the conduction of heat by the casing and the rediation of heat by the casing to the surrounding atmosphere are
not considered.
For proof of compliance with the guarantee, these factors shall
be dealt with separately, unless their effect can be shown to be
smell enough to be neglected.
D,.1.1
D.1.l.l
Mau =
&
are the same under both test and specified conditions.
However, it is quite sufficient for two of these three parameters
to be equal under both test and specified conditions. In that
case the third is bound to be equal too. From the measuring
point of view, the simplest and most accurate parameters to
maintain are the enthalpy rise coefficient, by adjusting the
discharge pressure of the compressor, and the peripheral Mach
number, by adjusting the speed or the intake temperature.
Essential conditions
Geometrical
similarity
In moat cases the machine for which the guarantee is given is
the same as the one tested, so that the condition of geometrical
similarity is automatically fulfilled. However, H the tests are
carried out with a model compressor, striit attention shall be
paid to the geometrical similarity, including the relative
roughness of swept surfaces. If the compressor contains
adjustable means of influencing the flow (for example, variable
stetor or rotor blades), conversion can only be carried out when
the position of these devices is unchanged.
Fulfillment of these conditions then ensures that the Mach
number and the ratios of density, velocity and temperature at
any point, as related to a reference point, are the same under
specified and test conditions.
If the process of compression is interrupted by one or more
intercoolers, the equality of the above dimensionless coefficients shall be fulfilled for each of the groups of stages
situated between successive coolers. This can be done by
adjusting the speed and by controlling the intercoolers to produce equal temperature ratios on the gas side, under test and
under specified conditions.
51
IS 14641:1999
ISO 5389:1992
D.1.1.4
In this case the ratio
Equal Reynolds numbers
in order that the relative thickness of the boundary layer and
the flow pattern influenced by it remain the same, the Reynolds
number and relative roughness shall be the same under
specified and test conditions.
D.1.2
Permissible approximations
to the theory of
similarity
D.1 .2.1 In most cases all the conditions specified in D. 1.1
cannot be complied with at the same time. Therefore, equality
of those parameters which are only of secondary importance is
dispensed
with,
efficiency having
conditions.
D.1 .2.2
the
magnitude
of
been established
The influence
their
influence
under
of the Reynolds number on efficiency
at higher values.
The influence of a deviation in the test Reynolds number from
the specified conditions is taken into account by an appropriate
correction method which shall be used in a certain range of application (see 7.3.3).
D.1 .2.3 The stipulation of equality for the enthalpy rise and
flow coefficients and for the Mach numbers and isentropic
exponents can generally be complied with merely by maintaining equality of the flow coefficients @Te = @’Gw provided that
of the isentropic
exponent
N
exponent n and the factor ——
D.1 .2.5 When fire * KGU, the requirement of equkl ratio of
volume rate of flows can only be fulfilled approximately,
because the maximum d“tierence in volume flows may occur
somewhere inside the compressor, the change of state following a different course.
on the
test and specified
is relatively larger at low values of Reynolds number and smaller
the deviation
is equal to the ratio of the peripheral Mach numbers.
K or the polytropic
A series of calculations has been made in which the limiting
values of the ratio of reduced speeds fVrhave been established
for the variation in the ratio of volume rate of flow not to
exceed limits of ? %, 2,5 ‘% and 5 %. The results of these
calculation< for various polytropic exponents and various
pressure ratios are presented in figure D.4.
When the isentropic exponents differ, the equal peripheral
Mach numbers no longer &ad to an equal ratio of volume rate
of flows; they are therefore abandoned, except for cases where
the performance may be directly affected by the local Mach
number.
D.1 .2.6 If the test conditions extend beyond the inner
tolerance limit, an additional uncertainty will be introduced (see
figure D.2) for the conversion to specified conditions.
do not exceed the limits
m
given in figures D.3 and D.4.
These limits are specified in such a manner that when
@’lTe= @Ir&yor
If the outer tolerance limit is still not sufficient, it will be
necessary to check whether there is any point in carrying out
the test under such circumstances. At any rate a higher additional uncertainty shall then be agreed for the conversion.
In the se of compressors operating with local velocities close
to the %
v ocity of sound, it is necessary to check whether the
deviation of Mach numbers on test from those at specified conditions is still permissible.
the velocity relationship and thus the volume flow relationships
in the compressor may differ up to a certain percentage during
the test, and under the conditions on which the guarantees are
based, without the efficiency qpOI (uncOOled cOmPre~O~) or
qT (cooled compressors) and the work input coefficient r being
noticeably affected.
The above limits are based on the fact that the maximum deviation of the ratio of volume rate of flows (q v,x/qv, 1) at any
point
within
tolerance
the
compressor
is not
more
than
1 %
For cooled compressors it maybe necessary to check the limits
of tolerance for the conversion separately for the cooled and
the uncooled sections.
(inner
limit) or 2,5 ‘Yoor 5 % (outer tolerance limits for com-
pressors with steep or flat characteristic respectively).
D.1 .2.4 When ~T~ = KG., the lar9eSt variations in volume
flow always occur at the end of the compression process. Consequently the permissible deviation is defined in respect to the
ratio q v,X/qv,1 (outlet to inlet) and can be represented through
N
the permissible deviation of
(see figure D.3).
~ZIR~,l
52
For this of course the local Mach number (ratio of local velocity
of flow to local velocity of sound) shall be taken into account
instead of the peripheral Mach number.
D.2 Additional uncertainties resulting from
deviations in the ratio of volume flows
Under test conditions the ratio of volume flows (qV,t,x/qV,t,l)Te
may differ from the specified value (qV,t,z/@,t,l)Gu by UP to
1 % without any additional uncertainty being applicable to the
result of the conversion to specified conditions (inner tolerance
limit, see D.1 .2.3).
.,
IS 14641:1999
ISO 5389:1992
If the conditions of the test do not allow the ratio of reduced
speeds
P
4=(J&)Te/(&)Gu
to be chosen within the inner tolerance limit (see figures D.3
and D.4), an additional uncertainty shall be applied to account
for the inaccuracies introduced when converting to specified
conditions.
\
This additional uncertainty is determined as follows.
For the given pressure ratio and polytropic eXPOnentS n&I,T~
and nM,Gu, read the upper and lower limits for the admissible
ratio of reduced speeds Nr from the corresponding charts in
clauaa D.3, at the inner and outer tolerance limits. When the
characteristic curve is flat (see 7.3.2), allowing a deviation of
5 % in the ratio of volutne flows at the outer tolerance limit, the
admissible values of Nr should be determined for the three tolerance limits + 1 %, i 2,5 % and + 5 %. These values are
plotted on a diagram as shown in figure D.1. This diagram,
which has to be drawn for each occasion, gives the deviation
A k’,from the specified ratio of volume flows corresponding to
the’ teat value of N,.
5*
NOTE – With tha valueof A V, obtained,the additionaluncertainty,radj,on tha volumeflow, energyconsumptionand pressureratiocan be taken
from figure 0.2.
Figure D.1 – Deviation,
A V,, as a function of N,
c
I
AVr, Yo
Figure D.2 – Additional uncartaintv.rtij
53
IS 14641:1999
ISO 5389:1992
D.3
Permissible limits for the conversion from test to guarantee
conditions
NOTE – When teat cond~ions are such that the range of th? diagrams in figures D.4 and D.5 isexceeded,usethe flow chartsin figuresD.6 and D.7
to calculateIV,,~d.
Figurea D.3 and D.4 are taken from [631.
Reynolds number corrections are not incorporated in figuras D.3 and D.4.
u
I
IA.
I
I
I
I
IIlllllllu
z
I
I
I
I
I
1 --
I z
I
I
1
I
II
-’c- - 11
I
I
I
I
I
I
I
[
Q
-
III
1
!
1
1
1
1
1
I
*
-t
Fw#3WFt
m
54
f,
. .-.=
IS 14641:1999
iso 5389:1992
upper limit
lower limit
——_——
1,0
“
w
t199<~”tol
0,8
,
Nr
,
I
0,7
0,6 —
P
451
to
a)
1 I 1 I i
1)2
I 1 I 1 I 1 1 1 I 1 I 1 I I I 1 I I I I I I 1 1 I 1 J
2,#
2$
2X
1,6
?,8
2,0
1,4
%. Gu
w
7,0
0,9
.
48
\
N,
0,7
\
Ofi
\
t
1
%0
I
I
T&\
b)
0,5 —
44 . 1
\
I
I
1,2
\
\
1
1
Z4
I
I
1,6
I
I
I
I
2,0
1,8
I
1
22
1
I
24
I
2,6
‘M, Gu
Figure D.4 – Permissible limits for the conversion from test to guarantee conditions (~te * KG.)
55’
IS 14641:1999
ISO 5389:1992
——— __
upper limit
lower limit
2,6
,’
Figure D.4 – Permissible limits for the conversion from test to guerantee conditions (~T~ * ~Gu) (CO~tih9d)
,
.--.f —
IS 14641:1999
ISO 5389:1992
“
.
upper limit
lower limit
—————
:Q
\\.
R
2,0
0,6
?,7
7,0
2,
0,9
Nr
0,8
\.
0,7 -
T
\
_\
ej
1~(f —
\ .
>
I
qo
I
I
1,2
t
1
t+
I
I
1,6
I
1
1,8
1
1
2,0
I
I
2,2
1
1
2,4
1
2,6
nM,Gu
Figure D.4 – Permissible limits for the convemion from test to guarentea conditions (KTe * KGU) (confinuedl
S7
Is 14641:1999
ISO 5389:1992
,
upper hmit
lower limit
————_
1,3
7,2
1,?
to
0,9
. .
<
\
4s
N\
>
‘“ ‘<’J
- .
+
\ ,
0,4 —
f)
\
A,
\<
0,3. 1
<0
1
1
&2
1
1
49
I
1
46
I
I
1,8
I
1
2J
I
I
2,2
I
i
2,4
1
2,6
‘M,Gu
Figure D.4 – Permissible limits for the conversion from test to guarantee conditions (KTe * KGU) (continued)
58
IS 14641:1999
ISO 5389:1992
upper limit
lower limit
–———_
1,3
1?2
0,975 <~<1,025
%0
0#9
N,
48
\
\
\.
47 ~
46 —
\ \
\
45;0 ‘
#
I
I
1,2
1
1
Z4
I
I
?,6
I
I
1
1
2,0
?,6
I
1
2,2
1
1
2,Y
I
2,6
‘M,Gu
Pigure D.4 – Permissible limits for the conversion from test to guerentee conditions (~1~ * ~&j) (corrfirrued)
59
t
IS 14641:1999
ISO 5389:1992
upper limit
Iower limit
—————
1,4
fa
1,2
0,95< ~< 1,05
nM,Te= v
1
1
\ 1
i~
))
;,
<1 >
\
1,0
\
03
Nr
48
\
\
.
o,7
\
o,6
\
\
\
\ .
\
\
\
.
\ .
0,s
4
\ \
\
\ <<2
\
o,3
to
\
j)
o##—
I
1
I
1,2
1
i
f,e
I
I
%6
I
I
?,8
I
1
2P
I
I
2,2
1
\
1
2,4
I
2,6
‘M,Gu
Figure D.4 – Permissible limits for the conversion from test to guerantae conditions (KT. * KGU) (confimm?d)
,$,
IS 14641:1999
ISO 5389:1992
—————
upper limit
lower limit
%LIIHIHO
,.
6
‘M,Gu
Figure D.4 – Permissible limits for the conversion from test to gUemntee Conditions (KTe * KGU) (continued
61
.,
IS 14641:1999
ISO 5389:1992
.—
upper limit
lower limit
___
1s
s
f,#
r~
RiK-rv
495<<<
‘\
1,2
+L\\
J
405
a
\
L
1,/
to
\
\
I
i\
\
\
~
\
,
.
.
\
Y .
\
\
\
\
\
O#s
.
\
o,#—
“31,0
\
n)
1
1
I
42
1
I
49
1
1
~6
I
1
t,8
I
1
Z,o
I
I
2,2
1
1
2,$
I
+
2,6
‘M,Gu
Figure D.4 - Permieeiblelimits for the conversionfrom test to guerenteeconditions (~T~# rcm)(continued)
62
IS 14641: “1999
ISO 5389:1992
11
L
I
-1,+
p)
. V*3
m
1
I
1
I
i
I
I
I
I
1
I
I
1
1
‘M-1-L—U
.d
upper limit
lower limit
—— ___
\
.
1
I
I
I f#2
‘“<y<’”
LLl
:1
N‘r
T
\
47
\
I
I oy7!r<lfqu25
I I I
I
1
I
I
I
I
..t-l
‘
0,7 —
.
1
I
1
1
.
I
I
I
w
.
1
1
1
1
t
I
I
I
I
I
I
I
hl=[<w%”hl
\
\
l-l
q)
v
\ \
\
46;0 ‘‘
#
I
1
42
I
1
~+
I
1
$6
I
1
?,8
I
I
z#O
1
I
2,2
I
1
2,4
I
2,6
‘M,Gu
Figure D.4 – Permissibleiimitafor the Conversion from test to guarantee conditions (KTe # KGU) (conti
Wed)
63
IS 14641 :1999
0%0 5389I :1992 ‘
upper limit
lower limit
—————
\
\
.
‘FFFRWFF’”
‘‘‘““
A
\
\
1
1
1
I
.
I
t
1
I
1
w’
I
1
i
1
1
P
I
1
I
I
I w
1
I
1
I
I
I
I
I
%7
I
I
I
1
1,2
1
I
1
I
$4
1
1
1
1 1 I
I&
\
\
I
1
i
7J?
1
I
1 1 I
2#
I
1
1
I
1
1 1 I
2#2
1
I
i
1
U
I
I
I
1
Z9
1
I
I
J
2&
‘M,Gu
Figure D.4 – Permissiblelimits for the conversionfrom test to guerenteeconditions (KTe * KGU) (confinu$d
64
1S 14641:1999
ISO 5389:1992
*
uppar limit
Iowar limit
——— __
{
..
\
. ...
[
‘ 1,3
;
I
s
I
I
I
I
I
I
t?
Sx
49
.U
I
I
I
I \l
l-l
I
I
I
l-l
I
I
I
Fill
N,
1
l\
l\
I
I
I
I
1-
-0,8
N“<’
\. ].\
1~
1 \ 1\
\
\,
49
I
I
I
*
‘
\
\
,
v
48
\
\
\
\
4~o ‘
#
-
t)
47 —
1
1
1,2
I
1
Z4
1
I
?,6
I
I
I
1
24
?,8
I
I
2,2
1
I
2,$
\
I
2A
‘M.Gu
Figure D.4 – PermiaaibleIimitafor the conversionfrom test to guarantee COditiOM
(KTe *
KGU) (confinuad)
85
IS 14641:1999
ISO 5389:1992
————_
upper limit
lower limit
f=H--tFllllllllll-wllml
-
6
‘M,Gu
FigUm D.4 66
Permissiblelimitsfor the conversion from test to guarantee conditions (KTe # KGU)(continued)
IS 14641:1999
ISO 5389:1992
upper limit
—_———
‘
lower limit
1
.. ..-.
%l.,,=z~
t-t-t-
1
1
I
I
11111+
gl
$0
48
1=
.
*2
\
N,
.
F
.
1-
%0 “
48
u
\
I
I
1
1
\
F
\
opn?<~<lyls
1i-
t-l
I
I
I
I
I
I
I
I
I
1
I-%’w”-l
‘M,Gu
Figure D.4 – Permissible limits for the conversion from test to guarentee conditions (KTe # K~U) (continued)
8?
IS 14641:1999
IS() 5389:1992
t7
.-
upper limit
lower limit
—_———
\ \
. ... ...
i
~6
\
oJ5<&<lJN
%5.
\
\
%3+
1,2
\
1,1‘
Nr
\
\
1,0 ‘
7
@
\
48
.
0,7,
\
\
T
7=
\
\
0,6.
\
\ ,
\
0$ —
44,,*’
~>
y)
I L
42
I
I
&4
1
1
?,6
I
1
1
1
Z#
7,8
1
I
2,2
1
1
2,4
.
\
I
2,6
‘M,Gu
Figure D.4 – Permissiblelimits for the conversionfrom teStto 9Uemnteeconditions (%
68
# ~Gu) (COnfi/?Ud)
f,
Is 14841: 1999
ISO 5389: 1992
...->
HI—4—u
K
-t--t-l
O?<’:?’
1
I
I
I
1
1
1
1
1#2
&+++—ti
‘r
f#4
w
Iu
I
I
1
‘Pi,Gu
Figura D.4 -
d
“
upper limit
lower limit
_———_
.
Permissible limits for the conversion from test to guarantee conditions (~T~ * K@) (continued)
89
Is 14841:1999
ISO 5389:1992
upper limit
_——
?,7
1 \
\l i
1,3
\I
d
\l
I I I
\
\l
i
lower limit
I I I I I
I
I
Iy
\\
I
t
t-l
I
l-l
Ivr
I
——
j\
I \l
I
1
-Q
l’\l\l
I
lsll\
I
I
I
l-l I
I
I
1
tot
t-l
I
1
I
l-l
t
l-l
48 I
FI
1
1
I
I
xl
L
x]
I\
l\
I \l
I
l\
1
1>
1
1
I
1
n
I
I
Xl
IIYI
1
I
I
I
I
1111
1
I
1111
I
I
1
1<
l”,
\l
1
I
1
v\
r.\l
\
l\
1
I
1
11111
\l\
-s
i\l
I
I
Y \
=1
\
1 . xl I
-1
I
1.
\
l-d
1
II
I
1
1
1
1
1
\
u
1
I
.
I
I
I
\
1
-
x
h
I
1
I
Iv
\
\
1 \
\
0,7‘
\
\
o# ‘
\
45 —
ab)
441~1
#
1, *’
8
?@
\ .
1
1
Z4
1
I
1#6
1
I
1
1
2,0
1,8
1
I
2,2
I
t
2,V
\
I
A
2J
‘M, Gu
Figure D.4 – Permissiblelimits for the ‘conversionfrom test to guarsnteeconditions (KT. # KGU) (con?inued)
70
IS 14641:1999
ISO 5389:1992
1- N
I
{
?. ’.P. ‘l’,{
I
1
1
I
_——
__
I
I
1
1
I
N,
f,2
1$
5 ,
%!
\
\
‘WQki
-t-H
z?
\
“
\
b
,“-
{
upper limit
lower limit
~2’
.
127
64
0,!7
1,3
Figure D.4 – Permissible limits for the conversion from test to guarsntee conditions (KT, # K~u) (continued)
71
Is 14641:1999
1s05389:1992
.
–—–
1,8~
u \
N\
I
I
i
I
I
I
I
I
I
upper limit
lower limit
__
I
I
I
I
1
4
1
I
1
I
I
I
I
I
I
495<
l\
l’,
1
. ..>’
1
I
i
vr~T,M
nNJe‘V
HI
s
\
k
Ii
t-\l
h
\l
N
L
l\8k\.1
+&k
\ .
\
1,2
\ ,
\
\
\
Nr
\
‘{’
\=
\J
l\
“~
\
Is
Y
..
I \
h
l\ \
\
Flll\l
I-111
I
I
I
‘r.
I
t
<1
I-1111
Y
L
09t
I
t-1
I
t
I
I>
I
l\
1
I
1
I
II
1
I
I
\
}.
.
l\ll
I1 11-.1
xl
I
i
I
I-1111
1
I
II
I
I
1
1w
l%.
1
xl
I
48
1
1
1~.1
\
I
N1
w
1
I’d m
1--1
ml. \
\
\
.
\
\
0,7
‘~&
-
\
\ .
146 —
\
ae)
\
\
4% ‘
I L
1,2
1
1
$4
1
1
$6
1
1
t
1
2#o
7#8
I
t
2#2
1
1
2,+
l<.
2/6
‘M,Gu
Figure 0.472
Permieeibb
Iimite for the conversion from tO$t to 9UWOntie condition
(KTe *
KGU) (corrckdedl
IS 14641:1999
HO 5389:1992
D.4
Permissible deviation of the peripheral Reynolds number
Figure D.5 (taken from [54]) shows the permissible deviations in the peripheral Reynolds number of centrifugal
application of the correction method (sea annex E).
compressors for the
Limit of
application
\\\\\\\’
/
Y//
/
//////2
104
105
106
107
108
ub
Guarantee Reynolds number /?eu,Gu= —
‘t,l, Gu
figure D.5 – Allowabla
ranga of application of tha correction mathod
73
.......
,
IS 14641:1999
ISO 5389:1992
D.5
Determination
of settings
Additional input for real gasas:
D.5.I
Input values for flow charts in figures D.6
and D.7
pcr, Te
critical pressure of test gas
‘Cr.Te
critical temperature of test gas
D.5.1.1
and, if available,
General
Unless otherwise agreed between manufacturer and customer
all pressures and temperatures refer to total conditions (see
6.1.1.3).
NOTE – For simplicity, the subscript t has been omitted when referring to total pressures and temperatures in figures D.6 to D. 11.
b
zTe = f(p, T)
‘M,Te
compressibility factor
compressibility
functions
YM,Te }
KTe = f(P,
T)
isentropic exponent
is the rotor reference outlet tip width.
D.5.1.3
A V, ~ ~01 is the permissible deviation of the ratio of the
volume rates of flow from 1.
()
Reu,Te
Specified values
Input for all stage groups:
= j’(Reu,Gu) (for centrifugal compressors) (see
Gu
Pt, 1,
inlet pressure
figure D.5), or any other agreement between manufacturer and
customer.
~, 1,Gu
inlet temperature
Pt, 2, Gu
discharge pressure
~, 2, Gu
discharge temperature
‘1,
Gu
isentropic exponent at inlet conditions
~ = ~(pr, ~ ) compressibility function
@l, Gu
relative humidity, inlet conditions
Y = ~(pr, ~ ) compressibility function
‘G.
gas constant
(See clause A.3. )
‘Gu
speed
Reynolds number corrections are not incorporated in the flow
charts and formulae.
Additional input for real gasas:
&?u,@ ‘0’
For real gases,
compressibility
‘M, GU
D.5.1.2
Test date
‘M, GU
At compressor inlet:
‘M, &
Pt, 1,Te
pressure
‘M, GU
~,1, Te
temperature
or
K,, Te
isentropic exponent
RTe
gas constant
Pl, Te
relative humidity
~Te = ~(PTe, TTe)
dynamic viscosity
N-
maximum adjustable speed
Nmin
minimum adjustable speed
For stages following intercoolera:
~, l,Te
74
temperature
at stage inlet
factor
compressibility functions
1
isentropic exponent
pCr, Gu
critical preesure of specified gas
‘Cr, G.
critical temperature of specified gas
D.5.2
Perfect or near-perfect gases
NOTE – See table 2 for suggested limits within which the gas maybe
considered to be near perfect.
D.5.2.I
Test gas
The compressibility factor 21, ~e = Z2, Te = 1.
,’,
!,,
...—
IS 14641:1999
ISO 5389:1992
Determination of the settings:
perfect and near-perfect
start
I
gases
Inputteq,T@ unit to L
betaken from input
tistor calculatedfrom
cnitlettemD.of
,,. orecedunit
1
lsentrcpi~O~ nent ~fQo
lK&J
,?
,ql
1
1]
Unlessotherwse qeed all pressL
and tem~atures referto bta( mm
I
Fii!iG1.
E@Gl
6
CE5i’-J
k.i+
%+--l
Yes
28
,,
vr2’1+’!ivrIb
(ytrop exp
No
Ih - rGWo2 22
J
1’
I
i
Skiz
r-----’
he @k3J.ar testgas?
I,
I@i-d
—
A
i
Yes
pii$gq
Wtb V,-fedt.frcm thiscalculation
CAcdate forevq section
Rl%i%$%’Y&:;-
1
-i
Is it possib(eto maintainduring
thetest the mlculatedspeeds
and inlet tefnperatures
of the units?
1
(3
*-
Erd
NOTE – The iaentropic exponent K is represented as K in this figure.
Figure D.6 – Flow chart for the determinetion
i
Erd
of settings in the case of perfect and near-perfect
gases
.-=
IS 14641:1999
ISO 5389:1992
d
.
Determination of the settings:
Real gases
k-putterrplmof unit to k
betaken from irput
stall
.
Unlessothemise ~
m
al~pressures
r
0
I
I1
m
I
t
1
f
I
I
m
$JL%$$’%W’W
I
I
f
M=IiP-l
Elm
I
I
“dw”k
I
.. I
I
!
~
tl-etest the caicuktedspeeds
and inlet temperatures
Print data for
executionof test
/
I
1
Choosenew sutdiiision
basedon i~ut H
@
49
aridprecedng
catculatii
I
T-
I%nt a staterrmt thst theCmprFSW
camot be tested acccfdii toISO5389.
dsbthegiwntes tcditkmsdti
~hn. pessibbs@ivisbns.
E.
I
NOTE – The iaentropic exponent rc is represented aa K in thisfigure.
Figure D.7 – Flow chart for the determination
76
of cattings in the case of real gasea
-----
/
‘- ..3’L_
IS 14641:1999
ISO 5389:1992
In many cases the isentropic exponent can be considered to be
constant, i.e.
D.5.3
d
Real gases
The test gas is a real gas.
w
~Te = K1, T~ = K2,Te
The settings may be determined
given in figure D.6.
by following
the flow chart
The settings may be determined by following the flow chart
given in figure D.7.
D.6
D.5.2.2
Specified gas
Conversion
uncooled
to guarantee
conditions
for
compressors
If the specified gas is a perfect or near-perfect gas and the
discharge temperature
~, Gu is not specified, the polytropic
efficiency can be calculated from the internal power figure
Reynolds number corrections are not incorporated in the formulae.
according to the following equation:
D.6.1
(K–l)M,
GUX
KM, @
The conversion formulae are given in figure D.8.
@ (@l)Gu
qpol,Gu =
log
1+
(p2/pl)Gu[(K-
l)/KIM,
Gu – 1
Vs, G“
{
NOTE – See table 2 for suggested limits within which the gas maybe
considered to be near perfect.
}
where q~ Gu is the isentropic efficiency given by the formula
~s,G”
=
D.6.2
()
applies
to step
Real gases
The conversion method in figure D.9 is used for Schultz’s
method of polytropic analysis (see [11).
q,rr,UtJ$’111,
s
q“
~u
The above
figure D.6.
Perfect or near-perfect gases
6 in the
flow
chart
given
in
The same formulae apply when gas properties are determined
from tables and/or charts and equations of state rather than
from generalized compressibilityfunctions as given in annex A.
77
.
Is 14841:1999
ISO 5389:1992
1
Pin,e
Test values
*
cpM, Te
1111+—J—+
I
I
~
I
I
Y
Y
.
In
n,e=
()
In
2.2
PI
Te
[n ——
P2 72
(1)P1 T1
22
PI
or =
[n
Te
()
!L
[()( PI
Te
)1“
Pi ~
+1
Te CpM”q Vl $
&
+
,:YEik
(-)
or.
In
k
() 11
‘n(*)Te
Pin
In
Te
[
cpM”qvl
●
El-
n-
I
b
Te
1
+,
+
d
Te
I
NGU
B
c ‘M,Gu
116”
(ZIRIGU
~
NOTES
I
Unless otherwise agreed all pressures and temperatures refer to totel conditions (P = Pt and ~ = ~).
2
The iaantropic exponent rc is represented aa K in this figure.
Figure D.8 – Conversion of test resulte for perfect or neer-perfect gases in the case of uncooled compressors
78
IS 14641:1999
ISO 5389:1992
.-!
-7
m
Y
I
II
1
I
1
I(+),,=‘-vM,7:mT.(l”xM,T.)
1-
Rle ~ZN.re
‘011’=(m.cpM)f*(R.~
7@m=
m-Trl
I JIm-—
I’ao’
II‘Wo=%”wwl
m
Pl,Gu
NOTE-
Unlesothe~iw
?
D
I
agr4all
‘in,CO*
p~r~and
‘l, Gu %co”~poi,co,O
T POI,TO
temWratur~
mfertoto@l
aco ‘ ‘L.CO
mndtions(p
a
=piand
Figure D.9 – Conversion of test results for real gases in the-ea~
T=
~).
of-tincoo~~pr~om
.
--i. L
‘IS 14641:1999
ISO 5389:1992
D.7 Conversion to guarantee conditions in
the case of cooled compressors
D.7.1
Perfect or neer-perfect gases
NOTE – See table 2 for suggested limits within which the gas maybe
considered to be near perfect.
D.7.1.1 For cooled compressors according to 8.2.4.1, where
the ratio of the gas inlet temperature of the stages or stage
groups following intercoolers to the inlet temperature of the
compressor is the same under test and guarantee conditions,
the conversion formulae are given in figure D. 10.
*
D.7.1.2 For cooled compressors according to 8.2.4.2, where
the ratio of the gas inlet temperature of the stages or stage
groups following intercoolers to the inlet temperature of the
compressor is different under test and guarantee conditions,
the conversion formulae are given in figure D. 11.
D.7.2
Real gases
In accordance with 3.5.3.8, the compressor sections between
intercoolers must be converted separately (see clause D.6) and
the results combined.
For this combination, figure D. 11 may be used where applicable (steps 14, 15 and 16).
IS 14641:1999
ISO 5389:1992
Pin Te
Test values
n
1
L
❑
El---ml
t
I
n=l
J%
-i
1
=(ZIRT1)~eln
‘ml,
Te
‘mT,
Co
~
T,
01
=W
‘T,
Te
( )1
NGU
—
2
N Te
@l--T-
4
1.
—
—
.
Imll
NOTE–
Unlesaothewise
agreed allpresur*
andtem~eratures refer totOtal conditiOns(p =ptand
T=
~).
Figure D.1O – Conversion of test results for perfect or near-perfect gasas in tha case of compressors cooled
in accordance with 8.2.4.1 (see D.7. I.1 )
---
!
IS 14641:1999
ISO 5389:1992
.-4
-
,
---1
-1@
z
a
4
“
—
-:-El
.
Z“ z
—
2’
-+M_
3,
—-
n
2’
-.
.
a
a-
n“
11
—
~
Qil
!Jlll
m-en-’
I ‘1
1
,
,
I
I
I
I
NOTES
1
Unlesothe~iw
agrwdall
2
IentK
The hWItrOpiCeXpOt
pr-ures
andtemperaturm refer tototal conditions(p = p,and T=
isrepreaentad as~in
Z).
this figure.
Figure D.11 – Conversion of test results for perfect or near-perfect
gases in tha case of compressors cooled in accordance
with 8.2.4.2 (see D.7. 1.2)
.
f,
.——
,1S 14641:1999
ISO 5389:1992
Annex E
(normative)
!.
.....
Correction method for the influence of the Reynolds number
on the performance of centrifugal compressors
(according
E.O
to the International
Compressed
Introduction
The method provides formulae for the efficiency, specific compressionwork and flow corrections necessitated by differences
in Reynolds number between the workshop test conditions and
the guarantee conditions.
Air and Allied Machinery
Committee)
value of the peripheral Reynolds number for the first stage of a
stage group is given by
ub
Reu = —
. . . (El)
Vt,
1
where Vt,1is the kinematic viscosity at the inlet tota I condition.
The total losses are divided into two portions. In the region of
the best et%ciencypoint, the portion of the losses independent
of the Reynolds number is represented by a constant fraction of
0,3. The lossesdue to friction are assumed to be dependent on
a representative value of the friction coefficient A according to
the Moody diagram for pipe friction. The representative value
of A is related to a reference Reynolds number and to a
reference relative roughness of the compressor. These corrections can be applied in an allowable range, taking into account
the inherent limitations for accurate testing at low Reynolds
numbers.
The method is the result of an investigation of a Working Group
of the Process Compressor Sub-committee of the International
Compressed Air and Allied Machinery Committee (lCAAMC),
issued on June 25, 1964. A brief description of the application
of this method is given herein.
The correction method applies only to the internal hydraulic
losses and, therefore, balancing piston losses and mechanical
losses must be accounted for separately.
In multistage compressors, the representative value of the
Reynolds number of the first stage is taken to represent each
stage group.
E.1.2
roughness Ra; centre-line average (CLA) IGBI;
arithmetical average (AA) lUSA/: Roughness average f!cm
the centre-line of the peaks. It is given by
R,=
+
@iX
. . . (E.2)
The reference roughness R, k the average roughness for the
impeller and its diffuser and can be either measured or taken
from the manufacturer’s drawing (with agreement between
manufacturer and customer). The roughness values are
measured inside the impeller on one blade, on the disc and on
the shroud near the outer diameter. The values for the diffuser
are measured on the side walls and in the middle of one blade
near the inlet diameter.
The representative relative roughness of the stage is given by
E.1
Definitions
R,
For the purposes of this annex, the following definitions apply.
E.1.1 Reynolds number Re: A dimensionless parameter
expressing the ratio between the inertia and the viscous forces
in a liquid. In this International Standard, the representative
T
in multistage compressors, the representative value of the
relative roughness of the first stage is taken to represent each
stage group.
a3
IS 14641:1999
1S0 5389:1992
E.2
Symbols
and subscripts
Table E.1 – Symbols
Symbols
S1 unit symbol
b
m
I
D
Definitions
end observations
Outlet width of the first impeller of the stage group
m
Outlet diameter of the first impeller of the stage group
e
m
Oeviation of the surface from the line of the mean surface height
A ht
J/kg
.—
1
Enthalpy rise of the stage group
m
Length of the line of the maan surface
m3/5
qv,t,l
Inlet volume rate of flow of the stage group
Ra
m
u
m/s
—
Peripheral velocity at reference diameter, i.e. the outlet
diameter of the first impeller of the stage group
J/kg
I Polytropic specific compression work of the stage group
w . rw,l
I
Average roughness
dimensionless
r = Ahtluz
,---
Vnnl
dimensionless
t
Work input coefficient of the stage group
1
Pipe flow friction factor
dimensionless
A
@ = qv,t,l/(Dz
m2/s
I
v+ ,
d
‘.01 = ‘m. rmliu2
Polytropic efficiency of the stage group
I Kinematic viscosity at the inlet total condition
dimensionless
Flow coefficient of the stage group
dimensionless
Polytropic work coefficient of the stage group
Table E.2 – Subscripts
Dafinitiona
Subscripts
E.3
Gu
Guarantee conditions
Te
Test condkions
w
At Reynolds numbar tending to infinity
for efficiency
Formula
for test conditions, from Colebrook,
correction
The formula for efficiency correction in the region of the best
efficiency point is given by
.
0,3 + 0,7 AGUIA.
. . . (E.3)
0,3 + 0,7 ATJA.
For calculation of the A values, the following generally
accepted equations are wad:
from von Karman
7+== ()
. . (E.41
1,74 – 210glo 2+
7%=
(
.
K
(
1,74 – 210g,~ 2*
+
18,7
Reu,Te&
. . . (E.6)
)
For rough estimations, the Moody diagram (figure E.1) can be
med.
E.4 Formulae for specific compression
work input and flow correction
work,
There is a definite increase in both work coefficient and flow
coefficient with an increase in Reynolds number.
In the neighborhood of the test efficiency point, roughly half
the increase in the efficiency appears as an increase in specific
compression work, and this leads to the following formula:
for guarantee conditions, from Colebrook,
1,74–210g,~ 2++
— 1
18,7
Re~,m&
. . . (E.51
)
Ypol G.
-.0,5+0,5=
~@,T~
. . . (E.7)
?pol,Te
+
IS 14641:1999
ISO 5389:1992
With a knowfedge of the efficiency and work coefficient corrections, the correction for the work input can be calculated from
the relationship ~n = WwI/qwI,
which gives the following
formula:
‘G.
g
b)
From this, the ratiOq@,Gu/vpol,Te is found.
c) Equation (E.7) is used to calculate the ratio
~@,Gu/ Y@,T@ equation (E.9) to calculate the ratio
@GUt@Te#and tWJatiOn (E.8) tO CdCUhte the ratio rG.f ‘Te
at the best efficiency
point.
. . . (E.8)
= 0,5 + 0,5~poI,Gu
The change in flow with increasing Reynolds number can be
approximated by
d) The ratios Vml,Gu/?/@ T~, YpoI,G”f~@,T& and rG.lrTe
calculated at the best effi&iency point are taken to be the
same at all pointa of the measured teat characteristic.
. . . (E.9)
e) The measured test points are now converted to the corrected characteristic using these fixed ratios [d)].
E.5
Application
of formulae
to test data
The equations given in clause E.4 define the influence of the
change in the best efficiency point on the performance
characteristics.
The change in other points can then be
calculated by noting that the shape of the characteristic curve
remains essentially the same.
The full correction procedure is illustrated in figure E.2 and is
summarized below.
a) At the best efficiency point on the test characteristic the
ratio
E.6
Allowable
range
The range of application of the correction formulae and the
selection of a suitable test Reynolds number are influenced by
two factors, i.e.
— the accuracy of the correction formulae at different
Reynolds numbers,
the reliability of teats carried out at reduced suction
pressures or low driving power.
1 – ~pol,Gu
1 – ~pol,Te
is calculated according to equation (E.3).
The limit of application of the ICAAMC formula is shown in
figure D.5.
65
, ,
A
I
Hydrsulicsllyroughpipes
111
I
I 11]
&
b
0,08
0,07
5/10-2
4/10-3
0,06
3/10-2
-,10-2
O*O5
0-2
0-2
0,04
0-3
0-3
–-
0,03
4/10-’
0,02
2/10-3
. ..- -3
m
J \ I
Ill
I
I
I
0,016
0,014
0,012
HI
.yclrdicsllysrncmth
pi=
I
0,01
0.008
.—
10”
2
4
6
104
2
4610s2
.4
6
10°
2
461012
4-6
@
Re,=*
Vt,l
Figure E.1 – Friction fector for turbulent flow in rough pipes
I.*
,.
IS 14641:1999
1s05369:1992
Work input
coefficient ratio
rGu/rT~
-Equation
(E.8)
q
8
J.
.
(E.7)
Reference polytropic
work coefficient ratio
Vpoi,Gu/Vpol,Te
Efficiency ratio
flpol,Gu/?pol,Te
1
1
1
Flow ratio @l, Gu/I#JI,Te
Figure E.2 –
Illustrationof correctionprocedure
87
IS 14641:1999
ISO 5389:1992
~
Annex F
(informative)
Examples
F.O
accounting separately for the dynamic pressure. The following
comparison of the results indicates the magnitude of the error
introduced and shows that the approximation in these two particular cases is acceptable.
Introduction
F.O.1 General
This annex gives examples to demonstrate the determination of
test settings and the conversion of test results to guarantee
conditions in typical cases.
Correct method
Approximate method
C** - ~12
2
w m,t =
NOTE – The examples given in this annax do not incorporate the
Reynolds number corrections because the ICAAMC method was not
available at the time when the examples were incorporated in this international Standard.
~1
(V
wm,~= Wm +
dp)t
2
Example 1:
Converted internal power at guaranteed pressure ratio:
F.O.2 Test conditions
Approximate method
Correct method
320,4 kW
320,5 kW
Table F.1 summarizes the test conditions covered by the diffarent examples regarding gas properties (perfect gas or reel
gas) and the approximation to strict similarity of flow.
NOTE 1 – Local Mach numbers at inlet and discharge are 0,043 and
0,071 respectively.
F.O.3 Computation of specific compression work
Example 4:
In all examples the specific compression work is computed on
the basis of total pressures and temperatures. The velocity
heeds at the standard inlet and discharge points therefore do
not appear as a separate tarm, which is the case when the computation is carried out according to the correct formulae baaed
on static pressures and Wmpereturaa (see 3.4).
Convertad internal power at guaranteed pressure ratio:
Approximate method
Correct method
7983,3 kW
7992,8 kW
NOTE2 – LocalMach numbersat inletand dwharge are 0,056 and
O,119respectively.
Ths method of calculation $ivee sufficient accuracy, because
the gas velocity in the inlet and discharge nozzles of turbocompressora is usually low (A4a < 0,2).
F.O.4
Accurecy of computation
Re-ceiculetion of thk numerical results of the examples may
reveal differences in the lest digits depending on the accuracy
and storage capacity of the computer used. -
In order to verify the validity of this approximation, examples 1
and 4 have also been calculated using the correct method of
Table F.1 – Synopsis of test conditions
Teat conditions
Similarityof flow
strict
Exemple
1
x
x
constant
4
5
6
x
x
x
x
x
KTe # K@
Iaentropic exponent
3
x
approximate
~Ts = ~@
2
x
x
x
x
x
x
x
x
x
not conatsnt
constant = 1
Compressibility factor
Test gas
spaed
x
x
x
x
x
not conatsnt
air
x
x
x
x
x
x
x
gas mixture
adjustable
x
not adjustable
no
Intercooling
x
yes
x
x
x
x
x
x
x
x
x
x
x
A 14641:1999
ISO 5389:1992
F.1
Example
isentropk
1 – Uncooled
eXpOnWIt
~Te
=
~@
turbocompressor,
speed
F.1.2
The purpose of the teats is to prove the guaranteed power requirement for the guarantee point.
adjustable
F.1.l
Purpose of tests
General
The conditions at the inlet on teat deviate from the guarantee
conditions. The same peripheral Mach number as given in the
guarantee conditions can be achieved by changing the speed.
F.1.3
The guarantee condfiions, guaranteed performance and other
design values are given in tables F.2 to F.4.
The installation consists of a three-stage turbocompreeaor for a
biatomic gas mixture, driven by a back-pressure turbine.
Design
of installation
Table F.2 – Guarantae conditions
Numarical
value
Symbol
Designation
m
GU
I Pt,l,
Inlet pressure (total)
1
0,9524
Inlet temperature(total)
I
‘t,l, Gu
I
Gas constant
I
R@
I 764,9
‘GU
1,4
I
Isentropic exponent
(Gas mixture, perfect gas ZGU = 1)
i
Kinematic viscosity
v, ~,,
30,16
I
3,27x 10-5
Unit
1
bar
I
‘JC
I N.ml(kg.K)
—
I rrWs
Table F.3 – Guamnteed perforrnanca
Symbol
Numerical
value
Volumetric flow atinlet
qV,t,l, Gu
9,715
dls
Discharge pressure
Pt,2, Gu
1,2203
bar
‘e, Gu
0,009297
kWh/ms
Specific power requirement at compressor coupling
Unit
qKt,Gu
Table F.4 -
Other dasign values
Designation
Compressor speed [due to variable-speed drive not
guaranteed)l)
Symbol
NGU
Outsida diameter of Stage 1 impeller
DI
Cross-section of inlet no2zleZ~
Al
Cross-section of discharge nozzlez)
A2
1)
The subscript Gu designates the design speed.
Numarical
value
I
Unit
4700
rl min
,0,9
m
0,3s
d
0,1926
d
1-
2) It is important that thase flow cross-sectionsbe given because of low pressure increase in this instance.
(Thus the static and dvnsmic components of the Dreasures can be determined.)
Is 14541:1999
ISO 5389:1992
F.1.4
Since it is impossible to test the machine set with gas on site,
the tests are carried out on the supplier’s test bad using air, the
compressor being driven by a variable-speed cradled electric
dynamometer, in such a way that the compressor shaft torque
can be measured directly.
N, =
m
Te
.-/
=1
N
() m
The test set-up is illustrated in figure F.1, and the test conditions are given in table F.5.
F.1.5
()
N
Test set-up
G“
2s9,3 x 3oly
NT, = 4700
. z ~1 r,min
i 764,9 x 303,37
Setting conditions
Since figure F. 1 is not required in fulfilling this condition,
h’mI,G. and ri’Gu do not need to be r=JcUlated.
The test conditions are set to achieve flow similarity in accordarwe with 8.2.3.2, i.e.
Ap
Cradled electric
dynamometer
Both cradled frames
mechanically interlocked
?
(D+q’1
‘(w?
Cradled gear
&
Figure F.1 -
Test set-up for example 1
Table F.5 Designation
Isentropic exponent (air)
Mean inlettemperature
Geeconstsnt
Test gas assumed parfect, therefore ZTa = 1
90
Test conditions
Ia
I
I
I
Symbol
I,
Numerical
valua
II
Unit
—
‘Te
1,4
‘t,l,
Te
2S,16
*C
RTe
2BB,30
N.rnl(kg. K)
I
I
4
-.....LL
IS 14641:1999
ISO 5389:1992
Alternatively the settings could be determined as follows by
using the flow chart given in figure D.6. The calculation
sequence is as follows (the numbers given are those
designating individual boxes in the flow chart):
1 –2–3–4–5–6–7–8–9–10
Since in this particular case Z and CPdo not vary within the
machine, the condition of26 is fulfilled.
A check as to whether the setting conditions determined can
be maintained in the testis made in 45. Since this is the case in
this instance, the calculation ends with 46 – 47.
–11–12–
13 – 21–22-23-24
Since strict similarity can beguaranteed here with rcTe= KGU
andwith variable speed, AVr,td = Oisinaertedinto 23.
The test was carried out maintaining the above test conditions.
F.1.6
A check as to whether the assumption made in 7 is true is
cerriedoutin25
– 26.
Test results
and conversion
See tables F.6 to F.8.
Table F.6 – Test results
Symbol
Numerical
value
Test number
—
1
Date of test
—
1964-08-26
–
Time of test
—.
12,50
h
Atmoepharic pressure
Ps
1,013
bar
Gas constant
Designation
Unit
—
‘Te
2s9,30
Nm/(kg. K)
Speed
NTe
2881
rlmin
Msee flow-j
qm,Tc
6,75278
kgls
Inlet pressure (total)
Pt, I, Te
1,00
bar
Inlet temperature (total)
‘t,l, Te
28
Oc
Dansity
@t,l,Te
1,150
kglti
Volumetric flow at iniat
(also usable inlet volume flow)
qKt,l, Te
5,8
I-rP/s
Discharge temperature
‘t.20Te
58,66
Oc
Diecharga pressure
1,2871
pt,Z Te
.. . .
.,
-..
.
..
- I LompuIeo worn me mass now wnlcn IS measured in accordance with ISO 5167-1.
Table F.7 Designation
.,
I
J---
– 44 (see the note to F.O.I).
Pass43
bar
Calculation results
Symbol
Numerical
value
Unit
Preseuraratio
(@pl)t, T~
1,2826
–-
Specificieantropiccompressionwork
w m,s,t,Te
23220
N.m/kg
Iaantropic compre~”on powar
‘s,t, Te
156,8
kW
Power at compressor coupling
‘e, Te
214,7
kW
Mechanical compressor power loss
‘f ,Te
3,0
kW
Internal power
‘in, Te
211,7
kW
intemai ieentropic efficiency (from Pin,Te)
?s,in,Te
74,07
%
htarna[ po~ropic efficienW (from tt,2,Te)
r/@,in, Te
75,05
%
Polytropic exponent
nTe
1,630
—
Specific polytropic compression work
‘m,rml,t,Te
23628
N.rnlkg
91
IS 14641:1999
ISO 5389:1992
Table F.8 – Conversion to guaranteaconditions (seefigure D.81
Designation
Symbol
1
Numerical
valua
Unit
Dasign speed
NGU
4,700
rlmin
Test speed
NT=
2681
rl min
Converted volumetric flow at inlet
qv,t,l,
9,5728
@/s
co
Converted specific compression work
w m,pol, t, Co
62617
N.mlkg
Converted pressure ratio calculated with rrco = nTe
because ~Gu = ~Te
(P2/Pl)t,
1,2927
—
Converted internal power
Pi”, co
327,87
kW
Converted mechanical power losses
Pf,co
6,3
kW
‘e, Co
334,17
kW
Converted power at coupling
co
NOTE – The conversion of mechanical losses is carried out according to the formula
NGU 1,5
‘f,Co
F.1.7
= ‘f,Te
~
()
Test uncertainty and comparison with guarantee
Tabla F.9 – Comparison with the guarantee (see 9.4)
Designation
Symbol
Numerical
valua
Unit
60,351
N.m/kg
Guaranteedspecificpolytropiccompressionwork
w m,rml,t,Gu
Conversionfactor
9 k’,t,GuWm,pol,t,Gu 0,97s 1
—
9v,t,co%r,pol,t,c0
Internalpowerabsorptionrelatedto (p#pl)t, @j
Pin, cO
320,7
kW
power at COU@hfj related tO (@~l)t,Gu
Ps, co
327,0
kW
Specific power at coupling related to (p2/pl)t, G“
Pa, co
0,00835
kWh/ms
o,a)8 287
kWh/rn3
+ 0.57
%
qv,t,l,co
Guaranteed specific power at coupling
‘e, Gu
q~t,l,Gu
Deviation in specific power at coupling from guarantee
value
The specific power at the coupling is exceeded by 0,57 % (see table F.9) but, since this is within the overall test uncertainty, the
guarantees are met accordingly.
The measuring errora are calculated in accordance with 9.2.
The test uncertainty for example 1 is ahown in table F.1O.
92
,.*,
.—.—
Is 14841:1999
ISO 5389:1992
Table F.1O– Resultingtaat unce~inty
Designation
Uncertainty in
volumetric flow
at inlet
Symbol
Numarical
value
rq “, Ts
1,1
‘N, Ta
0,35 %
Quality grade 0,2 final scale value 5 ~
Tpl,Ta
0,13 %
1 mmHg on absolutepressure
7T1,Te
0,33%
%
Uncertaintyin pressure
Uncertaintyin specific
F.1.8
Comparison
10 on absolutetemperature
‘rsc,qv
1,207 %
Nr
1,0
ln(p2/pl)
0,254
‘pz,Ta
0,43%
1 mmHg on absolutepressure
‘res,~lpl
0,4s %
See 9.2.6
C4
201,1
rff
10 %
Estimated
‘F
1,34 %
One scaledivisionaa assumederror
‘rea,Pe
1,740 %
See 9.2.7 and table 10
power at coupling
1
According to ISO 5167-1
Not applicebla,in accordancewith 5.9
7Z,
ratio
.... .!
{
Comments
See 9.2.5
of different calculation methods
A comparison of different calculation methods is given in table F.11.
93
Table F.11– Comparisonof different calculationmathods
Total
(
Total
(P,, I,)
~22 -
wm=wm*+—
Guaranteeconditions
Inlet pressure
PL1,@ = Q=
Inlet temperature
fcl,a
Gasconstant
ftm = 764,9 N.m/(kg.
Iaantropic exponent
K@ = 1,4
Compreaaibiiii factor
Za
Kinematic viscosity
v~ = 3,2678 X 10-s I&s
Dischargepressure
ptiti
Volumetric ftow et inlet
Specific power required
et conqxasaorcoupling
2
Suction side: total
=,2
Static
Discharge aide: static
)
0,9524 bar
0,9524 bar
pi,@ = o?~l 2 bar
30,16 ‘C
30.16 “C
t,,Gu
= 30 “c
Pt,z,ti = 1.2203 bar
~,Gu = 1,2160 bar
Pz,@ = 1,2160 bar
qv,tl,a = 9,715 */a
qV,t.l,Gu = 9,715 dls
f?v,t,l,(m = 9?715 ~ls
qv,l,ca = 9,7222 dla
P*a
—
= 0,008~
qv.tl
Pe ~
= 0,008287kWhlrn2
Pa&
= 0,009297 kWh/rn2
qv,t,l
P* Q
= O,U 297kWhlm2
4 ber
= 30,16 ‘C
K)
= 1,0
= le~3bar
Expectedcompressor
N& = 4700 rhnirr
Outsidediametar
of 1stimpeller
fl=0,9m
Area of inletnozzle
Al = 0,38rrP
Area of dischargenozzle
Az = 0,1828+
kWh/n@
qv,tl
qv,t,l
Teat conditions
Teat gas
Air
Iaantropic exponent
KTe =
Inlet temperature
ttl.Te = 26,16 ‘C
I,,Te = 26 “c
Gas cmnstant
RTe = 269,31 N. m/(kg. K)
RTe = 269,30 N ~m/(kg ‘K)
Compressibility factor
zTe = 1,0
ZT, = 1,0
Kinematic viscosity
V’re= 1,6401 x lo-=rr?ls
vT~ = 1,6401 X 10-5 r#/s
Air
1,4
KTe =
1,4
-
II
$
II
I?
II
L-I
.-c
ii
E
2
L-4
II
II
II
il
l-’
m
IS 14641:1999
ISO 5389:1992
9S
~.,
——
Table
F.11 – Comparison
calculation
z
(continued
Suction aide: total
~22 – ~lz
W,,, = Wm,~~,i. +
(Pt, It)
methods
Total
(
Total
Example 1
of different
Static
~acherge aide: static
)
st calculation
Pl,Te
Inlet gas density
Pt,l ,Te
Pt,l,Te
,l,Te =
‘l’Te
=
Zl,Te~Te
~1 Te
1,(K)35X Id
= 1,0 x 269,3 x 301,41
= l,1508kg/ti
. l,lW8kg/~
qm
.
v,I,l,Te
.-
Te
V,t.1.Te =
@t,l,Te
.
dla
1,0022
1,Te
1,0035
KTe –
KTe– 1
~*[(*)--j
**[(3
_ 1,4 x 105 X1,0035X
1,1508
-vi
.4X14
0,4
[(1,2926) 0’=7
x
- 1]
l,4989kg/r@
= 5,6679 rolls
—
— 5,6725 @/s
t.le _ 1,~ 5
__—
1,0022
l,Te
= 1,2687
105 X1,OO22
-11+
%.%.[(*)=
,,
x
1,1499
[(1,2697)
–
‘m,s,Te =
KTe –
1
‘T*
0,2s57
X
.
_ 6,75276
1,1489
vm,=,Te
=
vm,s,t,Te=
vm,s,t,Te=
1,0022x NY
1,0X268,30X301,25
= 1,28660
= 1,2687
= 1,2826
.
_ 6,75276
1,1508
12825
‘2,Te
——. = _l._-.
l,Co35
[,l,Te
~–1,2925
Q==
t,l,Te
specific iaentropic
compression work
6,75276
1,1508
= 5,W79
= 5,6679 rrWa
, ~eRTe ~,,T:
qm,Te
,,l,Te = —
&?l,Te
qrn,Te
—
@t,l,Te
_
6,76276
1,1508
Te’z
Zl,T~R~~ 7’l,T=
1,(X)35 x I&’
= 1,0 x269,3 x 301,41
volumetric flow at inlet
Pressureratio
,,Te = 1,1508 kg/d
11+
KTe– 1
1
-q
,,
KTe PI Te P2,Te
—~Te– 1 &’,,T. [(-)
/%,Te
‘1
‘T’
_px
105 X1,0035X
_gx
1,1508
0,4
105 X1,OO22
1,1499
x
0,4
x
[(1,2660)0’=7 - 1]
x
[(1,2687 )0’=7
–
_ 1
11
+ @y342
- 15056972)
_2
=23223
. 23220 N.m/kg
Isentropiccomrm.saiOn
power
Power at compressor
coupling
—
— 23220
X 6,75278X
10-3
—
— 23223x6,75278x
= 156,8 kW
P.,Te = Torque. 2 n. NT,
P,,Te = Torque ~2 n. NT~
=10-3
x711,58
= 214,7 kW
x2xn
X2=
— 10-3 x711,56
64)
= 214,7 kW
10-3
— 22665 X6,7528
—
– 154,53 kW
= 156,8 kW
x2xnx2~
~~,Te = W~,=,t,TE.q~,T~
Ps,Te = ‘rn,s,Te q~,Te
P~,t,Te = Wm,S,~,Teqm,Te
%n,Te
f~,t,Te = Wm,$,t,h
. 228W$N. m/kg
. 22665 N.m/kg
Nm/kg
P=,T, = 2147 kW
X1 O-3
—
— Z996X 6,75276X10-3
= 155,3 kW
P,,T, = Torque”2 II” NT,
— 10-3 X711,56X
2x
n x 2+
= 214,7 kW
r’
II
II
:
c
&
II
,-
xx
LO (-4
II
II
II
—
-1
1
c1
I
o
—
.-,
g
I
I
—
Q~&
;
Al=
——
1
,
I
y.
II
x
ml
x
II
II
I
-
*I*
)
I
x
I
-1
x
0
.
x
0
II
IS 14641:1999
ISO 5389:1992.
.s
:
II
~
–.
.i
*
m
II
N
II
II
97
.
Table
F.11 –
of different
calculation
Total
I
Total
(Pt, t,)
Example 1
Comparison
methods
\
(continued)
Suction aide: total
Static
Discharga side: static
Conversion of test results
to guarantee conditions
Converted volumetric
flow at inlet
M-a
qV,f,l,Co = qV.l,Te ~
=5,6679x
qV.t,l,Co
=
NGU
qV,l,Te ~
.5=79X
~
av,,,l,co
%5728
=
NGU
@/s
qv,t,l,co = ~V,l,Te—
,NTe
.58725x~47~
~71JQ
2881
2861
= 9,5728 m’/S
Converted specific
polytropic compression
work
w m,pd,i,co = Wm ~,t,Te
= 9,5803 m3/s
= 9,5728 M’/S
–
NGU 2
—
()‘Te
NGU 2
()
wfwdt.CO— Wm.~ol,,,Te~
wm,rml.CO =
()
—
– 62617 N. m/kg
PI, l,Gu
“’”=”
Pt,l,Gu
=
ZtiRGUTt,., Gu
—
0,9524 x 1(F
1,0 x 764,9 x 303,31
‘t’l’G”
= 0,4105 kg/m3
Converted pressure
ratio
(f’c. = nT~
because KGU = KT,)
—.
n
n–1
~
)
+1
= 1,28269
pin,Te
‘t,l.Gu ‘Gu 3
()
@t,l,T. NT.
= 327,67 kW
= 62710
N.m/kg
(;)co
= [(+)co
x
H
w
m.pd.t,CO
x
470Q3
.
()2661
n–1
co
+1
Pin co = Pin T, !?!!.@ N!!!
()
@t, 1,Te ‘Te
x
—
—
= 327,87 kW
=
~
ZGURGUTI ,G.
2 x lW
— Q,851
—
1,0 x 764,9 x 303,15
= 0,4102 kg/ins
x
(;)co=
——
1
()
+1
n-l
TI,t,G.
co
x-
x
[(%-)co
n
(–)
n–1
wm,pd, CO
(
—
—
CO
+1
ZGURG. TI ,G.
0,6324 X 61710
—+
1,6324
x 1,0x764,9x 303,31
1
0,629 X 62006
i( 1,629X 1,0 x764,9 X303,15
l,a32 4
1,s29
0,6324
m
+1
)
)
=
1,266
Pin,co = Pin,TeQ!?!!
!&
()
3
1.2698
P,n,~. = P,n,TeQL~+!32
@!,l,Te NTe
47003
(–)
2661
2
()
P1,Gu
L%,G.
+1
=
3
Te
n
wmmoLCO
ZGURGU
(
:
()
= 62006 Nm/kg
0,9524 x 1(F’
1,0 x 764,9 x 303,31
[W-)co
Wm ~o,,Te
—
-23289
Pt, 1,Gu
ZGURGUT,~
(:)co=
1
g,629 x 62607
—
—
+
1,628 x 1,0x 764,9 x 303,31
_2117xo,4105x
—
1,1508
2
= 0,4105 kglm’
+1
)
= 1,28266
= 2117X0,4105X
—
1,1508
=
—
—
1,az
G
0,63
=
0,8524 x IF
1,0 x 764,9 x 303,31
ZGURGUTI ,G.
(
‘kt,CO
—
‘t’l’Gu
()
n
co
0,63x62617
_+
—
—
1,63 x 1,0 x 764,9 x 303,31
Converted internal power
~RGuT~, ,, Gu
= 0,4105 kglm’
(:).O
= [(%%
x
()
w
m,pOl.t.CO
—— +1
x———————
ZGU%U ‘I,GU
1
=
4700
2661
=23167—
N2
wm,$ml,co =
—
() ‘Te
Te
.23526~2
Gas density at inlet
under guarantee conditions
NGU ‘
Wm ~,Te
@l,Te
211,7x0~
= 211,7 x0fi
X 4$3
1,1!M8
()
=
= 327,87 kW
= 327,66 kW
()
3
NTe
1,2499
X
‘~
()
3
\.,
Table F.11 – Comparison of different calculation mathods (concluded)
Total
Total
(Pt, t,)
Exampla 1
C22 –
W,n= Wm,wtk + —
(
Suction sida: total
C12
2
Static
Diacharga side: static
)
Conversion of test results
to guarantee conditions
[continued)
Estimstad m~hanicsl
losses
6.3 kW
6,3 kW
6,3 kW
6,3 kW
Converted power at
compressor coupling
334,17 kW
334,17 kW
334,17 kW
334,18 kW
‘m,pd,t,G. =
wm,r)ol,t,Gu =
wm,pd,
Gu=
w mti,ti
n
n
Speeific polytropic
compression work at
guarantee conditions
assuming the same
polytropic efficiency as
on test
rr~o = rz~e
n
ZGURGU
Tt,l,Gu x
n–1
(–)
ZG”RGUT1,G”x
n-1
(–)
Co
co
n–1
n
n–1
2
A
x[(
(–)
n
co
–1
1)
A,
= ~
co
x
[(;)(-)
1
x 784,9 x 303,31 x
= 80351 N.m/kg
Corrected internal power
at guarantee pressure ratio
X
803t13N. m/kg
qV,t,l,Gu ‘m,pol,t,Gu
‘i.,CO
—327,~
9,715 x 80351
9,5728 X 62617
= 320,4 kW
Corrected power
rit coupling
X784,9
‘m,
327,87
= 320,5 kW
1
n
X3O3;31X
0,628
O.azs
x
(1,278 4} “-
‘1
qV,t,l,G”
‘m,pd,G.
Co,G. =
Pin,co
= 320,58 kW
320,58
qv,l ,G. ‘m,pol,Gu
q v,l,CO Wm,pol,co
q V,t,l ,Co ‘m,pOl,CO
9,715 x 58456
9,5728 X 61710
-1
= 59740 N.m/kg
‘e,
‘in,CO
. 327,~
1
_1628
– L
x 784,9 x 3a3,15 x
[
PoI,t,Gu
c“
[() P1 G.
= 5%456N.
m/kg
9,715 x 803a3
9,5728 x 82 W7
P2
x—
x[(yl’2:)==-1]
qv,t,l,cowm,~,t,co
.
-1
‘e, Co,Gu =
Pin,co qV,t,l,Gu
qV,t,l,CO ‘m,pOl,t,CO
n–1
co
O,azz4
(1,2784)
[
42412 – 28,042
2
‘., CO,GU
=
‘e, Co,Gu =
n–1
n
x
‘tGu
[( pl,t,Gu )
_18324
..-!.-0,8324
R%URGU
n–l co
(–)
(–) –1
TI.Gux
(–)
PQ?l@
x
-1 –1+
+
.
‘G”RGU
CO
0,s2s
1,s29
0,s3
l=ls)
n–1
~zz- =12
-1
+—
2
]
1629 x 784,9 x 303,15 x
—
— ~
0,629
m -1
1
(–)
=
n
—327,88
9.72222 x 58740
9,5803X82008
= 320,6 kW
320,7
~
320,5
6,3
EJ3_
320,6
6,3
327,0 kW
326,8 kW
328,88 kW
326,9 kW
Corfected specific
power at coupling
0,00835 kWh/ms
0,008344 kWh/rrt3
0,009348 kWh/ms
0,00934 kWh/ms
Deviation from guarantee
0,57 %
0,51 %
0.527%
0,538%
.. .4 .L.
IS 14641:1999
ISO 5389:1992
Example
1
qv,i,~e
=
587222
.-I
ZRTt,2,Te
qln
M%2,T’ = A@2,Te
K
i
fTr3Js
6,75278
Al
= 0,39m2
= 0,1928x1,2925x
5,87222
cl,Te =
= 0,071
= 15,05697 mls
o ~
Pt,2,Te = P2,Te 1 + ~ Ma~2
,, T,]
NGU
(
cl,@ = 15,05697 —
NTe = 24,5636 m/s
. 1,2925 X
6,75278
qV,2,Te -- -—
,,W
~
A2 = 0,1928
= 5,0233
1 + +
X 0,0712
)
= 1,2971 bar
1
Tt,2,Te =
T2,Te
K–1
—
K
( l–
= 26,04 m/s
= 332,35 x
NGU
CZ,GIJ= 26,04 —
NTe = 42,481 mls
qm
Mat,l,T~ = —
AIP1,Te
r
ZR Tt 1
-
F.2
K
(
1
1-0,2857
x 0,0712
)
105 ‘F
F.2.1
1 + :
2 –
Uncooled
exponent
turbocompressor,
~T~ = ~@
speed not
variable
General
The test conditions under inlet conditions deviate from the
guarantee conditions. The driver has a fixed spaad so that
similar flow conditions can only be approximated using
figure D.3.
+$Ma~l,Te)
1,0022
Example
isentropic
= 0,04311
~t,l,Te=~l,Te(l
Ma~T,
,)
= 332,83 K
6,75278
—
– 0,39X1,0022X
.
(
mz
5,021
—
c2rTe= 0.1928
105
x 0,043112
The guarantee conditions, guaranteed performance and other
design values are given in tables F.12 to F.14.
)
(
= 1,0035 bar
F.2.2
Tt,l,Te= T1,Te
The purpose of the test is to prove the guaranteed power requirement for the guarantee point and to determine the
pressure-volume curve at a constant spaad.
,_ —K–1 A,ja:Te
K
= 301,25
1
1 –0,2857
F.2.3
Design of installation
x 0,43112
The installation consists of a three-stage, uncooled turbocompraesor for air, driven by an electric motor.
= 301,41 K
Table
F.12 – Guarentaa conditions
Symbol
Numerical
valua
Inlet pressure(total)
Pt,l, cm
0,9s37
bar
inlet temperature (total)
‘t,l , Gu
30
Oc
Gas constant
RGU
288,32
N.m/(kg.
‘Gu
1,4
.
‘Gu
9500
rlmin
Designation
Isentropic exponent
Compressor speed
100
Purpose of test
1
Unit
K)
Is 14641:1999
1s0 5389:1992
Table F.13- Guamntaadperformance
Designation
Volumetricflow at inlet
I Discharge f.weesure
I
I
Power requirement at compressor coupling
I
Symbol
Numerkel
valua
Unit
q V,t,l, Gu
9,16067
dls
/+,2,r3u
I
bar
‘1
2065
kW
I
Symbol
Numerkal
valua
Unit
D,
0,63
m
‘e, Gu
3,9031
I
Table F.14 – Other design values
Designation
Outside dwmeter of Stage 1 impeller
F.2.4 Teat set-up
The test is carried out at the compressor sits undar atmospheric condtions.
The test set-up is shown in figure F.2, and the test conditions are given in table F.15.
Pt
(ij-
*
(iJ=D=rl==l@=E
e-l
Figure F.2 -
Test sat-up for example 2
101
-
IS 14641:1999
ISO 5389:1992
F.2.5
Setting
conditions
[see 8.2.3.2)
Since the speed cannot be varied, it is impossible to maintain
preciselythe flow conditions on which the guarantee was baaed,
()
N
d=
OJ
In determining the setting conditions in accordance with the
flow chart in figure D,6 the following calculation sequence is
usad (the numbers given are those designating individual boxes
in the flow chart):
9500
,,
~288,3
N=
x 1,0 x 283,2
95(MI
G.
2s8,3
figure D.3c)] and, therefore, conversion of the test results to
guarantee conditions is still possible. In accordance with
figure D.2, a supplementary tolerance of 1 % for the measured
power requirement can be used.
= 1,035
x 1,0x 303,2
1–2–3–4–5–6–7–8–9–
To determine the permissible deviations from figure D.3, it is
necessary to calculate the polytropic exponent from guarantee
conditions and guaranteed performance.
The deviation in the volumetric flow ratios shown in figure D.3
is leas than 5 ‘Yo with the calculated ratio 1,035, a pressure ratio
(@@t,G.
= 3,96, and a Poiytropic exponent n@ = 1,564.
The setting conditions are given in table F.16.
Since a centrifugal compressor with flat characteristic is involved, a maximuin deviation in the volumetric flow ratios of
* 5_~0 is acceptable in the optimum efficiency range [see
Table
I
10–11–12–
13–21–22-23-24
+ 0,05 is inserted in 23 in the first instance and
A Vr,tol = – 0,05 in the next sequence to determine the upper
and lower tolerance limits. The calculation ends with 25 –
26 – (43 – 44, but see the note to F.O.1) – 45 – 46 – 47.
A V,,~d =
Had the test shown in 45 that the setting conditions determined
could not be maintained in the test, the compressor would have
had to be split up into several units and the calculations recommenced at 3 through 48 – 49.
The deviation is within the permitted range. The test was
carried out maintaining the above test condkions.
F.15 – Test conditions
Designation
I
Symbol
Numerical
value
Isentropic exponent
‘Te
1,4
Unit
Mean inlet temperature [total)
‘t, t ,Te
10
Oc
Gas constant
RTe
2SS,3
N.m/(kg.
Speed (not variable)
NT.
95fll
rlmin
Table
F.16 – Setting
conditions
Symbol
Numarical
value
Mechanicalefficiency
Vf
0,9s5
Internalpower
pin,@
2.034
kW
14S 024
N.m/kg
1521
kW
Designation
Unit
(estimated)
= qfPe
Specificisentropiccompressionwork
w m.s,Gu
Isentropiccompressionpower
p~, Gu
Isentropicefficiency
0,74s
P~
.
pin, Gu
Pressureratio
PJ2_
3,s3
‘t,l, Gu
102
Polytropicefficiency
‘fPol,
Polytropicexponent
‘Gu
Gu
0,792
1,564
—
K)
4
*
IS 14641:.1999
ISO 5389:1992
F.2.6
Test results and conversion
SeetablesF,17to F.19.
Table
Designation
F.17 – Test results
Symbol
Numericel
Unit
Test No. 2
Test No. 3
1965-04-30
1965-04-30
1965-04-30
—
11,30
12,30
14,MI
h
.
Date of test
velue
Test No. 1
Time of teat
Pa
1,0091
1,0091
1,0091
bar
Gas constant
RTe
288,32
286,32
288,32
N.m/(kg.
Speed
Atmospheric pressure
We
9500
9500
9m
r/rein
Mass flow”}
qm,Te
11,5667
11,3417
10,2028
kgls
Inlet pressure
pt, 1,Te
0,9864
0,9973
0,9993
bar
Inlet temperature
‘t, 1,Te
Tt, 1,Te
9,8
283,0
10,0
263,2
10,3
263,5
“c
K
Density
@l,1,Te
1,221
1,221
1,223
kglms
Volumetric flow at inlet
(also usable volumetric flow at inlet)
qv,t,l,Te
9,47
9,289
8,342
rn3/s
Discharge pressure
Pt,2,Te
3,7658
4,1482
4,9033
bar
●) Calculated from themssflow
meawred inaccordance with lSO5l67-l.
Table F.18 – Celcuiation
Designation
Symbol
results
Numerical
(P2/Pl )t,Te
3,780
Specificisantropiccompressionwork
w rrr,s,Te
131 W5
power
‘s,Te
1527
Power at compressor coupling
con-rpreaaion
value
Test No. 1
Pressureratio
Isentropic
K)
Unit
Test No. 3
4,907
—
143640
164596
N. m/kg
1626
1679
kW
+
pe,Te
2107
2206
2234
kW
Mechanical compressor power dissipation
‘f,Ts
31
32
32
kW
Internal power
pin,Te
2076
2176
2202
kW
Internal isentropic efficiency
Vs,in,Te
0,734
0,748
0,763
—
Internal polytropic efficiency
rlpol,in,Te
0,779
0,792
0,608
—
Polytropic exponent
nTe
1578
1564
1547
—
Specific polytropic compression work
‘m,poi,Te
138880
162150
174462
Nm/kg
-
Teble F.19 – Conversion to guarantee condition (see figure D.8)
Designation
Symbol
—
Numerical
Test No. 1
value
Test No. 2
Test No. 3
I
Unit
Converted specific compression work
w m,pol,Co
139680
162150
174462
N.m/kg
Converted pressure ratio
(p2/pl )trco
3,521
3,660
4,528
—
Converted discharge pressure
Pt,2,co
3,453
3,786
4,44
bar
Convatied volumetric flow at inlet
qv,t,l,co
9,473
9,289
8,342
dls
Converted intarnal power
Pin,cO
1907
1886
2 om
kW
Convertad mechanical power dissipation
Pf,co
31
32
32
kW
Converted power at coupling
Pe,co
1836
2om
2052
kW
103
*
Is 14641:1999
ISO 5389:1992
<
-’
F.2.7 Test uncertainty and comparison with guarantee
--- .:.:d
The test uncertainties are calculated according to 9.2.
As can be seen in figures F.3 and F.4, the guarantees are met within the test uncertainty .(saa also 9.4).
The test uncertainty for example 2 is shown in table F.20.
Table F.20 – Resultingtest uncertainty
Designation
Symbol
Uncertainty
in volumetric
flow at inlet
rqm,Te
Uncertainty
in pressure
ratio
Uncertainty
in power
at coupling
104
Numericel
1,2
%
velue
Comments
In accordance with ISO 5167-1
‘N, Te
0,63 %
(luality grade 0,5, final scale value 10 O@l
‘pl,Te
0,13 %
1 mmHg on absolute pressure
‘T1,Te
0,33 %
1 0 on abeolute temperature
‘adj
1,0
rtot,qv,l
~=1,~%
Nr
1,035
%
See 9.2.5
ln(p2/pl)
1,33
‘fi,Te
0,s3 %
‘sdj
1,0 %
~tott~lpl
~=1187%
SSS 9.26
C4
m
Current transformer 0,5; voltage
transformer 0,5; wattmeter 0,2 (estimated)
~Pe
0,75%
~Pf
10 %
‘sdj
1,0%
rtot,Pe
~=w%
Cluality grade 0,6; final pressure gauge
value 4 atm gauge (relative)
S*
table 9
i
IS 14641:1999
ISO 5389:1992
2200
1000
5,0
9v,t,l,co m3/s
o Teat
X
Guarantea
Figure F.3 – Graphs for comparison with guarentae
14641:1999
ISO 5389:1992
IS
L
Guarantaa pointa
5,0
4,5
4,0
3,5
3/1
8
10
9
~~t,l,co
,
~ 200”
A
m3/s
.
,
A~qoo”
2000
1900
1800
1700
9
8
10
9v,t,l,co
Figurs F.4 -
Grephs for comparison with guarentee
t
Is 14841:1999
ISO 5389:1992
F.3
Example
isentropic
3 – Uncooled
exponent
F.3.2
turbocompressor,
KT~ # KGU, speed not
The purpose of the tests is to prove the guaranteed power
requirement for two guarantee points and to determine the
pressure-volume curve at constant speed.
‘ variable
F.3.1
Purpose of tests
General
No similar flow conditions can be set in accordance with the
similarity considerations given in 8.2.3.2. Approximation solutions are sought on the basis of figure D.4.
The guarantee conditions, guaranteed performance and other
design values are given in tables F.21 to F.23.
F.3.3
of installation
Design
The installation consists of a two-stage, uncooled turbocompressor for ethylene, driven by an electric motor.
Table F.21 – Guarantee conditions
Symbol
Numericel
velue
Inlet pressure
Pt,l, G(J
0,9s0
Inlet temperature
Designation
Unit
bar
‘t,l, Gu
32
Qc
Gas constant
RGU
296,G5
N.m/(kg.
Isenttopic exponent
‘Gu
1,25
–
Compressor speed
NGU
12700
rlmin
Table F.Z – Guaranteed
Designation
performance
Numerioal velue
Guarantee
Guarantee
point
point
(b)
la}
Symbol
K)
Unit
Volumetric flow at inlet
~V,t,l,Gu
15 CKX)
12 WI
rnslh
Discherge pressure
Pt,2, GU
1,766
1,S63
bar
Power requirement st compressor
coupling
Ps, Gu
335
310
kW
Numerioal
value
unit
0,4
m
Tebie F.23 – Other design values
Symbol
Designation
I
Outsidediameterof Stage”1 impeller
1
DI
I
I
107
f,
IS 14641:1999
ISO 5389:1992
F.3.4 Test set-up
Since it is not possible to carry out the acceptance test using ethylene, e teat is carried out on ~te using air.
The test eat-up is illustrated in figure F.5, and the teat conditions ara given in table F.24. The power at tha coupling is determined by
the motor rating and transmission losses.
Gear
‘1
t-o
tz,oil
o
9
Figure F.5 – Test set-up for example 3
Teble F.24 – Test conditions
Designation
108
Symbol
Numarioal
valua
Unit
Isentropic exponent (air)
KTe
1,4
—
Mesn%ilat temperature
t~,l
,Ts
5
Oc
Gasconstant
RTS
2s7,3
N. m/(kg. K)
* -L_
4,
..
IS 14641:1999
ISO 5389:1992
F.3.5
?
Setting conditions (see8.2.3.3)
It is expedient to draw an auxiliary diagram (see figures F.6 and
F.7) for each of the two guarantee pointa from fiiures D.4j),
D.4m) and D.4q) for better interpolation. Using theaa
diagrams, it was found that a teat could be carriid out on the
present compressor for conversion within the outer tolerance
limits 0,85 c V,< 1,05, in the case of guarantee point (a)
The speed cannot be varied.
Because the speed cannot be varied, it is impossible to
maintain the flow ratios presupposed on giving the guarantee.
‘qKt,l,Gu = 15 ~
()
m
i=xf
()
N
nWh) with
12700
-re
~287,3
N
X
1,0 X 278,2
12700
G“
J296,65
()
N
1,064
-T,
,m<
,
x 1,0 x 305,2
< 1,175
N
() -
In order to determine whether the calculated ratio is within the
permitted range (see 8.2.3.2), the polytropic exponenta are
required. The internal isentropic efficiency q~ required to
determine qPOl,GU
is determined here from the iaentropic compression power formed by the guarantee values and from the
guaranteed power at the coupling assuming a mechanical efficiency qf = 0,88.
G.
and in the case of guamntee point (b) (qv,t,l,GU = 12500 m3/h)
with
()m,.
N
,W<
lN\
According to figures D.4g) and D.4k), the deviation in the
volumetric flow ratio is so high that it is impossible to conduct
the test within the inner tolerance limits (0,99 to 1,01).
Consequently, a check must be made to find out whether the
test is possible within the outer tolerance limits (0,95 to 1,05)
whwh can be used in the case of the anticipated flat
characteristic of a centrifugal compressor in the range of the
guarantee points (see figure D.2).
< 1,180
The value determined at 1,(M4 in the above example for the two
guarantee pointa is within these limits.
The setting conditions are given in table F.25.
Table F.25 – Setting conditions
Numerical
Designation
Symbol
Guerentee
point
(a)
vehe
Guersntee
point
(b)
Unit
Wm,@u
56
6
N.m/kg
Density
L?t,l, Gu
1,m
1,063
kg/rrr3
Isentropic compression power
Ps,@
255
233
kW
Powerat the compressorcoupling
Specific isentropic compression work
Pe,Gu(qf= O,*)
335
310
kW
Isentropicefficiency
7s,in,Gu
0,777
0,767
–
Polytropicefficiency
?pol,in,
Gu
0,766
0,7s1 5
–
Specificpolytropiccompressionwork
Wm,pOl,Gu
57448
63214
N.m/kg
Converted guaranteed polytropic
exponent
nGu
1,34
1,344
–
Polytropic exponent calculated using
nWl,in,Gu in the test
nTe”)
1,567
1,567
–
‘)
I
Since there ere no other details available than thm
npoI,in,Gu.
9iven in the 9uarantee, nls is formed u~r?9
I
1
.
109
.,,
.;
.,...
..l
~
,
IS 14641:1999
ISO 5389:1992
1,3“
;uarantaapoint(a)
} = 1,801
1
1,2
/
L
A
1,175
1,1
1,033
1,0
1,567
0,9
.
1,6
1,8
‘Te
Figura F,6 – Graph for comparison with guarantaa
110
,’<
f,
-——
,
Is 14641:1999
1s0 5389:1992
. ...
{
1,3
harantaa point (b)
),95<ltf<l,05
~Gu
= 1,344
/
1,180
1#1
1,043
1,0
1,576
1,7
Figure F.7 -
1,8
~ Te
Gmphfor comparisonwith guamntoo
111
IS 14641:1999
ISO 5389:1992
In determining theeetting conditions in accordance with the
flow chart in fiiure D.6, the following calculation sequence is
used (the numbers given are those designating individual boxes
in the flow chart):
1–2–3–4–5–6–7–8–9–
10–11–12–
13–21–22-28-29
Had the calculated pressura ratio (P~~l)E, been within the
range of the compression sequence, the extreme value of the
daviation A V,,fi could have been determined by 31 and the limit
Vr,2would have had to be adapted by 32 – 37 in such a way that
at no point of the compression process A Vr,X> A Vr,tO1.
The test was carried out maintaining the above test conditions.
A V, ~d = + 0,05 or A Vr,t~ = – OJ05 is inserted into 28 to
determine the upper and lower tolerance limits. In the present
instance, the pressure ratio (p#pl)EX determined in 29 at which
the maximum deviation A Vr,& = A Vr,td occurs is outside the
range 1 to (~z/@@.
Consequently, the formula sequance continues through 30 –
38-24
-2526-(43
-44, butseethe noteto F.O.l)–
45-48-47.
F.3.6
Teat results and conversion
Seetables F.26 to F.28.
It was established after the tests that all 3 test points are within
the extreme tolerance
limits to figure D.R.
Table F.26 – Test results
Symbol
Designation
Taat No. 1
Numerical valua
Teat No. 2
1965-03-12
1865-03-12
1965-03-12
–
h
Unit
Test No. 3
Date of test
—
Time of test
—
16,30
18,45
19,00
Atmospheric pressure
Ps
1,0051
l,m
1,005
bar
Gas constant
RTe
267,33
287,33
287,33
N.m/(kg.
Compressor speed
NTe
12700
12700
12700
rlmin
Mass flow ●, (also usable mass flow)
qm,Te
19865
17304
147m
kglh
Inlet pressure
pt, 1,Te
0,8854
0,9873
0,8883
bar
Inlet temperature
‘t, 1,Te
Tt, 1,Te
4,7
277,9
5,1
278,3
5,3
278,5
“c
K
Qt,l ,Te
1,2466
1,2472
1,2488
kgIms
Volumetric flow at inlet
(also usable volumetric flow at inlet)
qV,t,l,Te
16032
13874
11787
dls
Diecharge pressure
pt,2,Ta
1,657
1,974
2,041
bar
Density
‘)
In accordance with ISO 5167-1.
Table
Designation
F.27 – Calculation
Symbol
results
Teat No. 1
Numarical value
Test No. 2
Test No. 3
Unit
Pressure ratio
(P21pl)t
1,866
1,978
2,042
—
Specific compression work
‘m,s,Te
!54524
602&9
66373
N.m/kg
Isentropic compression power
‘s,Ts
3412,5
2&,8
258,1
kW
Power at compressor coupling
‘s,Te
421,8
365,5
346,5
kW
Mechanical compressor power dissipation
Pf,Te
8
8
8
kW
Internal power
‘in,Te
413,8
377,5
340,5
kW
Internal ieentropic efficiency
?$,in,Ta
0,731
0,766
0,761
—
Internal polytropic efficiency
rlpol,in,Te
0,754
0,788
0,784
—
—
N.m/kg
Polytropic axponent
Specific polytropic compression work
112
nTe
1,611
1,566
1,573
‘rn,pol,Te
56185
61832
65246
K)
c,
~.,
IS 14641:1999
ISO 5389:1992
Table F.28 – Conversion to guarantee conditions (sea figure D.8)
Symbol
Designation
last No. 1
Numerical value
Test No. 2
Test No. 3
Unit
Converted specific polytropic compression
work
w m,pol,co
58195
61932
65246
N.m/kg
Converted polytropic exponent
nco
1,381
1,340
1,342
—
Converted prassure ratio
(P2/pl )t,co
1,777
1,679
1,837
—
Converted inlet volume
qV,t,l,Co = qV,t,l,Te
16032
13874
11787
m3/~
Converted internal power requirement
Pi”, co
358,6
327,9
295,3
kW
Converted mechanical power dissipation
Pf, co
8
8
8
kW
‘e, Co
387,6
335,9
303,3
kW
Converted power at coupling
F.3.7 Test uncertainty and comparison with
guarantee
The test uncertainties are calculated in accordance with 9.2.
The compressor in question having a flat performance curve,
the comparison will be made at the guaranteed inlet volume.
For this purpose the converted test results, i.e. specific
polytropic compression work, pressure ratio, internal polytropic
efficiency and power input at coupling, are plotted veraus the
converted usable inlet volume (see figure F.8). Taking into account the total resulting inaccuracies, the conclusions are as
follows (see figure F.9).
–
Guarantee point (b), q v,t,l,@ = 12500 mVh: the requirements of the guarantee are met for both pressure ratio
and power consumption.
–
Guarantee point (a), q ~,t,l,@ = 15000 ins/h: the
pressure ratio is higher than guaranteed, and accordingly,
so is the power input. For better comparison it is necessary
to apply the procedure outlined in 9.4. The converted test
results are read from the curves plotted
in figure F.8 and
defined by the three test points, at the guaranteed
volume flow qy,t,l,Gu = 15000 m3/h, i.e.
inlet
w~,pol,co = 58470 N. m/kg
P,, CO= 353,2 kW
–
the power at coupling reduced to guarantee conditions is
wm,Pol,Gu
Pe, co, Gu = ‘e, Co
x w
m,pol,Co
57448
= 353,2 X ~
= 341,2kW
and the guarantee value is 335 kW.
The converted power is thus slightly in excess, even if
the resulting total test uncertainty is taken into account.
The teat uncertainty for example 3 is shown in table F.29.
113
~~ J
IS
ISO
14641:1999
5389:1992
380
320
300
II
G
.-c2,0
3
(:)
*#
b
1,8
●
\
(a)
1
1,6
3
m
I
(b)
)(
(a) ‘
1
k
\
11
12
13
14
15
qK+J,cO
,103 m3/ h
O Guarantaapoint
~ Teat point
Figurs F.8 – Graphs for comparison with guarsntaa
16
17
IS 14641:1999
ISO 5389:1992
L
-—
I
Guarantee points
21
2,0
1,9
s.
-+
~“
1,8
Q“
1,7
1,6
10
11
12
13
14
~K+),Co
,103
m3/h
13
14
15
16
17
15
16
1
400
380
360
3
x
.
2. 340
Q,,
320
300
280
10
11
12
~t~,co
‘@m3/h
Figure F.9 – Graphs for comparison with guarantae
115
IS 14641:1999
ISO 5389:1992
*
Tabla F.29 – Resulting test uncefiainty
Designation
Uncertainty
in volumetric
flow at inlet
Uncertainty
in pressure
ratio
Uncertainty
n power
jt coupling
116
I
Svmbol
I
Numerical
value
I
Commants
r qm,Te
1,0
%
In accordance with ISO 5167-1
‘N, Te
0,06Y.
Digital measuring instrument –
1 rev on indicator
‘pl,Te
0,13 %
1 mmHg on absolute pressure
‘T1,Te
0,36 %
1 0 on absolute temperature
‘adj
0,9 Q/o
rtot,q y, 1
~=1~%
N,
1,064
ln(p2/pl )
0,623
‘p2,Te
0,16 %
‘ad;
0,9 %
rtot,p2/pl
~=o,~~
C3
2,191
[4
351,5
7P=
0,75 %
TPf
10 %
‘adj
0,9 %
rtOt, Pe
~=~zo%
see
See 5.9
}
925
1 mmHg on absolute pressure (see 5.9)
sea
926
Current transformer 0,5; voltage
transformer 0,5; wattmeter 0,2 [estimated)
see
927
and
table
9
IS 14641:1999
ISO 5389:1992
F.4
Example
isentropic
4 –
Cooled
exponent
turbocompressor,
~T~ = ~@,
variable
speed
and temperature ratios
F.4.1
F.4.2
Purpose of tests
Thepurpose of the teats is to prove the guaranteed power
requirement for the guarantee point.
General
The speed and temperature ratios can be varied so that similar
flow conditions can be used.
The guarantee conditions, guaranteed performance and other
design values are given in tables F.30 to F.32.
F.4.3 Design of installation
The installation consists of a five-stage turbocompressor of
centrifugal design for air with intermediate cooling after each
stage, driven by steam turbine.
Table F.W – Guarantee conditions
Designation
Numerical
value
Symbol
Unit
pt,l, G“
0,9635
bar
Temperature
‘t, 1,Gu
25,31
Oc
Relative humidity
qG”
70
%
‘Gu
269,5
N.m/(kg.
Pressure
Gas constant
Isentropic exponent
Volumetric tlow of cooling water
Inlet temperature of cooling water
I
‘Gu
\
I
qV,W,Gu
Im
I hvIG,,I
1,4
1m3/h
I
27
K)
I ‘C
Table F.31 – Guaranteed performance
Designation
Volumetric flow at inlat
Symbol
Numerical
value
qV,t,l, Gu
114626
Specific power requirement at compressor coupling
(-)
Ps
qV,t,l
m3/h
6,5321
Discharge pressure
Unit
0,071 a
Gu
bar
I
--J
kWh/rn3
Table F.32 – Other design values
Designation
Symbol
Numerical
value
Unit
Speed (Not a guarantee condition for variable-speed
driver 10
NGU
4650
rl min
Outside diameter of Stage 1 impeller
DI
1,12
m
Inlet temperature of air ahead of
Stage II
ft,l,ll,Gu
40
Oc
Stage Ill
tt,l,lll,Gu
42
Oc
Stage IV
ttrl,ll/,Gu
45
Oc
ft,l,v,Gu
46
Oc
Stage V
1)
The subscript Gu designatea the design apeed.
117
.“
,
IS 14641:1999
ISO 5389:1992
F.4.4
To guarantee similar flow conditions, i.e.
Test set-up
N
The compressor is subjected to trials on the test bed, driven by
avariable-speed electric motor. Since therating of thetest bed
motor is insufficient for operation at atmospheric intake
pressure, the compressor shall be run at diminished intake
pressure. Running in this way, itisnot possible to judge the
intercoolers as a reduced flow of cooling water must be admitted because of the reduction in the pressure level.
The test set-up
is illustrated
. ...
() –G,e=l
N
() m
G.
the teat shall be conducted at a speed reduced in the proportion
ditions are given in table F.33.
r
288,3 x 286,23 .0
‘Te
—=
in figure F.1O, and the test con-
NGU
~1
269,5 x 298,46
‘
1
The result is NTe = 4560 rl min.
F.4.5
Setting
conditions
In determining the setting conditions in accordance with the
flow chart in figure D.6, the following calculation sequence is
used (the numbers given are those designating individual boxes
in the flow chart):
(see 8.2.4)
1–2–3–4–5–39-40-41-42
see the note to F.O.1) – 45
By means of the flow of cooling water, the inlet temperatures
of the air into the individual stages (see table F.34) can be set
so that the temperature relationships
The test was carried out maintaining the above test conditions.
= 11,Ill, IV, V, agree with the design value.
Table F.33 – Test conditions
Designation
Im
Inlet pressure
I
Inlettemperature
I
Humidity of air
!
Gae constant
Symbol
I
Inlet temperature of cooling water
Table F.34 – Inlet air temperatures
‘t, 1,Te
I
Numerical
valua
Unit
0,2409
bar
15,08
Oc
I
9Te
\
70
]%
RTe
I
288,3
I
fwlTe
]
24,8
N.m/(kg.
K)
I ‘C
at differant stages
Valuesin degreeaCelsiue
Vslua to ba set
during tests
—
15
tt,l,ll
40
30
tt,l, ill
42
32
ft,l,lv
45
34
ft,l,v
48
37
4,1,1
118
Design valua
,
Pt,l,Te
I
Designation
but
Since the speeds and the inlet temperatures for the stages are
variable, the compressor can fulfil the setting conditions as a
unit. Accordingly, the calculation ends with 46 — 47.
Tf,l,j/Tt,l,l
wherej
–(43-44,
I
QNI
4
:
<--
“.
+!2
>
“r+
~
0
f
———
———
.—
.
—.
.
———
——
I
I
J
r
l-+
——
w=
-&
:-
———
———
0
+J.95
y9’{:]‘
~
QN-
7.
o
———
-9Q~,
E
I
i
Ii
I
i
=+-
1S 14641:1999
ISO 5389:1992
119
4,
IS 14641:1999
ISO 5389:1992
.~
F.4.6
Test results and conversion
%..
.
See tables F.35 to F.37.
{
Table F.% – Test results
Designation
Symbol
Test number
Unit
1
—
Date of test
—
1965-04-26
–
Atmospheric pressure
Ps
1,010
bar
Gas constant
RTe
2s6,3
Nm/(kg. K)
Speed
NTe
4560
rlmin
Mass flow’)
qv7,Te
33114
kglh
Inlet pressure
Pt,l,Te
0,2409
bar
Inlet temperature
‘t,l,Te
15,0s
Oc
‘t,l,Te
266,23
K
Density
@t,l,Te
0,2699
kgIms
Volumetric flow at inlet
(also usable volumetric flow at inlet)
qL’,t,l,Te
114226
m3/h
Discharge pressure
pt,2,Te
1,6055
bar
●) Calculated from the mass flow measured in accordance with ISO 5167-1.
—
120
Numerical
value
‘.
IS 14641:1999
ISO 5389:1992
Table F.36 – Calculation rasults
Symbol
Numerical
value
(P2/Pl)t,Te
6,6646
–
‘m, T,t,Te
157618
N.m/kg
mass flow
qrr],Te
33114
kglh
discharge temperature
tt,2,Te
76,62
Oc
inlet temperature
t~,l, Te
15,08
Oc
Att,Te
61,54
“c
‘in,t,l,Te
568,8
kW
flow of cooling water
q V,W,Te
166,7
m3/h
outlet temperature of cooling water
t!#/,28Te 31,04
Oc
inlet temperature of cooling water
h#/,l,Te
24,80
Oc
temperature difference
A@,Te
6,24
Oc
‘in,Te
1354,7
kW
qV, oil,Te
2,75
m3/h
inlet temperature of oil
~1,oil,Te
38,61
Oc
outlet temperature of oil
f2,0il,Te
46,86
Oc
temperature difference
Atoil,Te
7,25
Oc
kJ/(kg. K)
Designation
Pressure ratio
Specific isothermal compression work
Unit
Power absorbed by the gas (compression sections I -V)
temperature difference
power calculated with Cp = 1,0048 kJ/(kg. K)
Power absorbed by cooling water ( = power absorbed by
the gas in sections 11,Ill, IV)
power calculated with Cpw = 4,187 kJ/(kg. K)
Power absorbed by the bearing lubricating oil
– journal bearing: volumetric flow of oil
mean specific heat
cpM,oil,Te
1,9693
density
@l,oil,Te
0,866x 103
kglms
power
p f,Te
9,4
kW
qV,oil,Te
5,62
m3/ h
inlet temperature of oil
fl,oil,Te
39,19
“c
outlet temperature of oil
t2,dl,Te
50,07
“c
temperature difference
— thrust bearing: volumetric flow of oil
A1oil,Te
10,66
Oc
mean specific heat
cpM,oil,Te
1,978
kJ(/kg. K)
density
@l,oI,Te
0,866 x 103
kglms
power
‘f,Te
29,0
kW
‘f ,Te
36,4
kW
isothermal compression power
PT,Te
1449,8
kW
internal power
‘in,t,Ts
1923,5
kW
mechanical compressor power dissipation
‘f,Ta
38,4
kW
power at coupling
‘e,t,Te
1961,9
kW
isothermal coupling efficiency
ri’T,t,e,Te
73,9
%
total mechanical power dissipation
‘ower requirement
121
.
f
...—
IS 14641:1999
ISO 5389:1992
Table F.37 – Conversion to guarantee conditions (see 8.2.4.1)
Symbol
Designation
F.4.7
Numerical
value
Unit
Test speed
N~e
4560
rlmin
Design speed
NGU
4650
rl min
Converted volumetric flow at inlet
qv,t,l,co
116,480
m3/h
Converted isothermal delivery head
‘rn,T,t, Co
163,901
N.m/kg
Converted pressure ratio
(f@pl)~,co
6,6663
–
Converted internal power
Pin,t,cO
8006,8
kW
Convertad mechanical power dissipation
Pf,co
38,6
kW
Converted power at coupling
‘e, t,Co
8048,4
kW
Test uncertainty and comparison with guarantee
The teat uncertainties
are calculated
in accordance
with 9.2.
The converted inlet volume is slightly higher than guaranteed (see table F.38), even when taking into account the test uncertainties.
The converted specific power consumption is lower than guaranteed by about 2,96 % (see table F.38).
The guarantee
can be considered to be fulfilled.
NOTE – When calculating the power absorbed by the gas in compressor sections I and V, the leakage losseswere neglected. As the power consumption is well below the guarantee figure, MS simplification is justified.
The test uncertainty
for example 4 is shown in table F.38.
Table F.38 – Comparison with the guarantee (see 9.4)
Symbol
Numerical
value
Guaranteed pressure ratio
(P2/Pl)t,@
6,6408
–
Isothermal delivery head at (p2/Pl)t,@
‘m,T,Gu
163,583
N.mlkg
Conversion factor
a‘rn T Gu
‘nr,T,Co
0,9861
–
Internal power absorption related to (P2/pl)t,Gu
‘in, Co
7883,3
kW
Power at coupling
‘e, Co
8032,9
kW
Specific powerat couplingrelatedto {pz/pI)t,@
- ‘e Co
0,06686
kWh / ms
Guaranteed specific power at coupling
Pe Gu
-.
4v,t,l,Gu
0,07106
kWh/ms
– 2,86
%
Designation
Deviation from guarantee value of specific power
at coupling
122
~v,t,l,co
Unit
1
#,
IS 14641:1999
ISO 5389:1992
.....
!
Table F.39 – Resulting test uncertainty
Designation
Uncertainty in
volumetric flow at inlet
Uncertainty
in pressure ratio
Uncertainty
n power at coupling
F.4.8
Comparison
Symbol
Numerical
value
Comments
‘a,ntTe
1,0%
In accordance with ISO 5167-1
‘N, Te
0,22 %
Quality class 0,2; final scale
value 5 COO
‘p,, Te
0,56 %
1 mmHg on absolute pressure
‘Tl, Te
0,35 %
1 0 on absolute temperature
‘rss,q~,l
1,22 %
See 9.2.5
N,
1,0
ln(p2/pl )
1,e90
‘p2, Te
0,6490
‘res, p~lpl
1,555 %
See 9.2.6
rPin
1,5 %
Energy balance estimated
7Pf
10 %
Estimated
r T, ,j
0,33%
10 on absolute temperature (see 5.9)
‘res, Pe
1,55 %
See 9.2.7 and table 9
See 5.9
1
I Quality class 0,6; final value 10 atm gauge
of different calculation methods
A comparison of different calculation methods is given in table F.40.
123
Table F.40 – Comparison of different calculation
Total
(p,, t,)
Example 4
Guaranteeconditions
Inlet pressure
P~,l,G. = 0,=
Inlet temperature
tt,l,GU = 25,31 ‘C
Relativehumidity
@@ = 70 %
Gasconstant
RGU= 269,5 Nm3/(kg oK)
Iaentropicexponent
KGU
=
5 bar
Total
(
~22 Wm = Wm,‘tatic+ —
~12
2
)
methods
Suction side: total
Static
Discharga sida: static
P~,I,G. = 0,9635 bar
pt,l,Gu = 0?=
f~,l,G” = 25,31 ‘C
/t,l,G” = 25,31 ‘C
P1,Gu = Wfm bar
5 bar
tl,Gu = 25 “C
1,4
Volumetricflow of cooling
water
qV,w,Gu = 600 m3/h
Inlettemperatureof tiling
watar
tw,l,Gu = 27 “C
Objectof the guarantee
Volumetricflow at inlet
qv,~,l,G. = 114626 m3/h
qV,t,l,Gu = 114 ~
Dischargepressure
Pt,Z,@ = 6,5312 bar
PZ,G. = 6,472 bar
p2,G” = 6,472 bar
Specific pOwar
requirement at compressor
coupling
(–)
(–)
P,
—.
ql’,t,l
()
Speed (design)
NGU = 4650 rlmin
Outaide diameter
of Ist impeller
D, = l,12m
Density at inlet
Pe
9V,[,1
0,9635
= 0,07106 kWh/m3
Pe
qv,t,l
Gu
x IF
269,5 x 296,46
—
– 1,1363 kg/m3
m3/h
= 0,07106 KWh/m3
G.
0,9635 x lti
269,5 x 296,46
= 1,1363 kg/m3
qv,t,l,@ = 114 ~
m3/h
qv,,,Gu = 115 ~
P2,G. = 6.472 ber
(–)
Pe
—
-0,07106
GU
1,1363 kg/m3
m3/h
KWh/ti
qv,l
= 0,07096 kWh/ms
G.
0,961x 105
X T = 269,5x296,15
P1,Gu
‘l’G” = ZXR
= 1,1363 kg/m3
Inlet temperature of air
ahead of
Stage II
‘t,l,ll,Gu
=
@
Staga Ill
‘t,l.lll,Gu
=
42 ‘c
Staga IV
‘t,l,lV,Gu
=
45 ‘c
Stega V
rt,l,v,G”
=
46
‘c
“c
i%
,.
Table F.40– Compefisonof different calculationmethods[cof?finuad
Total
(Pt, It)
Example 4
Total
(
‘m
= ‘m, stetk+
=22 -
Clz
2
)
Suction side: totel
Test setting
NTe = 4580 r/rein
Static
Discharge side: stetic
NT, = 4 5@ r/rein
N~e = NGU
i
‘44===
.4850
_‘Te Tt Te
‘G.
‘LG.
283,3X237,95
i 2s8,5 x 298,15
= 4580 r/rein
= 4580 r/rein
Test rasdte
Test number
1
Date of test
1975-04-28
Atmospheric pfaSSUm
pa = 1,010 bar
Gas constant
R~e = 28S,3 N. m/(kg. K)
speed
N~O= 45W r/rein
Maea flow
q~,T. = 33114 kg/h
Inlst praeeura
pt,l,T~ = 0,2409 bar
~,,T~ = 0,2403 bar
Pt,l,Te
=
02@
Inlet temperature
tt,l.Te = 15,08“c
tcl,~a= 14,8‘C
rt,l,Te
=
15,0s Oc
Density at inlet
Pt.l#Te
QI,I,T. =
9 br
t?~l,T.= o,m 9 kgl+
P1,T. = or2a 3 Mr
I,,Te
= 14,0s ‘=’C
b?l,le=
‘RTeTt,l,Te
Volumam”c flow at inlet
?V,t,l,Te
=
114 ~
~lh
= O,24O9X1O5
288,3 x m8,23
= 0,2403 x 1(P
288,3 x 287,85
= 0,2888 kg/m2
= 0,2885 kg/rr@
Vv,t,t,To =-
q~ T.
@t,l,Te
qV,t,l.Te = l14228m31h
qV,l,Te =
_ 33,114
Discharge pressure
7t,2,Te= 1,8055 bar
pl,Te
ZRTCTl,Te
Ql,T@
0,2889
33,114
0,2885
= l14228rn21h
= l14383rn21n
~Te = 1,581 b
_
*
p2,Te = 1,581 bar
~,T,
=
1,581
bar
,
I’f
Table F.40 – Comparison of differant calculation
Total
(
Total
Example 4
~22 Wm = Wm ‘t,t~ + —
(P,, f,)
metnoas [cmrrmuedl
2
Suction aide: total
~,z
Static
Discharge side: static
)
Test calculation
Pressure ratio
~t,2,Te = 1,605-5
~2,Te _ 1,581
pt, 1.Te
Pl,Te
0,2409
= 6,64346
Specific isothermal
compression work
0,2403
()
wm,T,Te =
wm,T,Te =
Pt,l,Te
=
f?Te~l,Te
P2,Te
———
In
()
= 288,3 x 286,23 x In 6,6646
Pa
Pl,Te
0,2409
= 6,6044
= 6.6209
wm,T,Te= ‘Te~t,l,Te In %,2,Te
—
P2,T. = 1,581
pt,l,T,
1,581
0,2403
= 6,6209
()
P2,Te
‘T.
.
~t,l,Te In
+!?y
—
Pl,l,Te
wm.T,Te =
RTe~l,Te
P1 ,Te
= 266,3 x 287,85 x 95 x In 6,6209+
= 266,3 x 266,23 x In6,W44
= 266,3 x 287,95 x 95 x ln6,6209
= 156665 N.m/kg
= 156919 N.m/kg
+ 44,772 – 21,182
2
= 157618 N.m/kg
a)
= 157687 N.m/kg
Power abaorbed by gas
Discharge tampersture
total
t,,2,Te
= 76,62
ftr2,T8= 76,62
tt,2,Te = 752
f2,Te = 75,2
Temperature difference
A/ = 61,54K
At = 61,54K
AI = 61,54K
AI = 61,54K
Powercalculatedwith
CP= 1,0048 kJ/(kg. K)
Pin,Te = 566,8 kW
Pin,T, = 566,8 kW
Pin ~e = 566,8 kW
Pin T= = 566,8 kW
b) Power absorbed by
cooling water
Pin ~e =
Pin,Te =
c) Power absorbed by the
bearing oil
ff,~e = 36,4 kW
Pf,Te = 36,4 kW
Pf,Te = 36,4 kw
Internal
Pin,Te= 1823,5
kW
Pin T, =
Pin Te =
1923,5
kW
P m,Te = 1923,5
Power at coupling
Pe,Te= 1861,9
kW
P e,Te = 1 861,9kW
fe,~e =
1861,9
kW
P~,T~ =
1861,9
kW
Isothermal
PT,Te= 1448,8
kW
PT,Te =
PT,T~ = 1442,9 kW
PT,T, =
1443,4
kW
rlT,e,Te = 73,90 %
h’~,e\T. = 73,93 %
rlT,e,Te =
73$57 %
power
compression
1354,7
kW
1354,7
kW
1923,5
kW
1450,5
kW
Pin T, =
1354,7
kW
Pin T, =
1354,7
kW
Pf,T, = 36,4 kW
kW
power
Isothermal coupling
efficiency
()
P2,Te
In —
pI ,Te
VT,e.Te
=
73,55 %
.-c
E
2
g
v
II
.
2“
II
II
II
x
z
j
II
8.
&
II
II
x
x
Lclm
m
IS 14641:1999
ISO 5389:1992
m
II
127
.
___
.. 4
Table F.40– Comparisonof different catcukstion methods (carchdad)
(
Total
(Pt, l,)
Example 4
‘m
Total
~22 -
~t2
2
)
= ‘tn, stalk +
Suction side: total
Discharge side: static
Comparison with the
guarantee (corrtirrtred)
Isothermal specific
compression work
at {fi/PI )@
‘m.T,t,Gu = /?QTtl,@
Irr =
()
P2
wm,T,t@ = )?@ T,,@ In —
() Pt,l &l
= 268,5x 286,46x In6,6408
I%
= 268,5 x 296,15 x In 6,5873
()
wm,T,t,& = R@ Tt.l,@ In @Pt,l m
‘m,T.G. = %J~I,G.
+
= 268,5 x 286,46 x In 6,5606
= 268,5x
= 163563 N.m/kg
= 163664 N.m/kg
= 162786 Nm/kg
= 162646 N.m/kg
Internal power related
to (@P, )Gu
Prn,ti = 7883,3 kW
Pin,co = 7882,8 kW
Pin,co = 7882,9 kW
Ph,ti
Power at coupling
Pe4C0= 8032,9 kW
P,,cO = 8032,4 kW
Pe,co = 8032,5 kW
Pe,c- = 8028,6 kW
Specific power
at coupling refated
to (@PI )(j.
-.‘e Co
~v,t,l,co
-.‘e Co
-80329
qv.t,l,co
1164W
- ‘e Co .- 80325
116460
qv,t,l,co
P, ~
.- 80329
l16&10
qv,?rco
= 0,06686 kWh/rn3
= 0,06696 kWh/d
= 0,06686 kWh/ma
= 0,08664 kWh/rrP
– 2,86 %
– 2,%3 %
-2,96
– 2,88 %
Deviation from guarantee
%
In —
P1 G.
286,16 x In 6,5873
+ 45,f@ -21,612
2
-80329
l164&)
()
P2
+
Gu
= 78W kW
IS 14641:1999
ISO 5389:1992
Example 4
A1=l,5xl=l,5m2
0,4064XX
h
A2=
= 0,1297m2
qV,l,Te = 31,76 ‘713/S
C,,J=
=
31,78
qV,l,Te
= —
1,5
Al
‘G(J
= 21,19 m/s
C1,GU= 21,19—
‘Te
5,6062
C2,T, = qV,2,Te _ ——————
= 44,77 mls
A2
0,1297
9,,7,GU
ZRTt,l,Gu
A lP1,Gu i
‘at,2,G.
K
=
9,1963
Mat,, ,~, =
=
x
105 x 1,5 x 0,2403
v
qrn,Gu
=
‘RTt,2,Gu
A 1P2,Gu i
~nxj650
‘Gu
CZ,GU= 44,77 —
=
—
NTe
‘
4560
qm Te
1,0X286,3X266,15
1,4
= 0,0579
35,76
269,5 X 348,35
“1’3
Te
= 45,65 mls
35,76
105 x 1,5 x 0,961 x m=o”’
6,472 X 105 X 0,1297
K
YF=
A’fat,2,Te = Afll
= 21,61 m/s
‘T13/S
qV,2,Te = 5,8062
Mat, ,,Gu =
= 21,19 X ~
105 x 0,1297
x 1,591
x i
= 0,11434
1,4
Xi-=orll,h
“ITe=plTet+$Ma’
lTe)=0’2m3b+~x0
t&79)=082a’bar
Pt2G.=Pz,Gu~+~Ma~z,G)=6472~+~x0,f1432)=6,~12bar
pt,2,Te=p2,Te(l
‘t,l,Gu
=
+:Ma:2,Te)=,,~l~
=
y~x0,0&j32)=2%8&K=
1,4
25310c
Tl,Te
( l–— ‘~l’Ma~,,~=~’%x
,,
‘t,2,Te =
'~'
TI,GU
( l-— ‘;1’M&Gu)==’15x(
?,
‘t,l,Te
+~X0,f1412)=l,w~
T2,Te
( l–—
K;l’Ma:2Tj=w%x(1
,,
(1-~x0,05792)=maK=
I,4_;xo,11942)=
15@0c
w~K=76Q0c
1,4
129-
IS 14641:1999
ISO 5389:1992
F.5
Cooled
Example5–
isentropic
exponent
variable,
temperature
turbocompressor,
~7. = ~@
Purpose of tests
speed not
ratio of cooled
section
variable
F.5.1
F.5.2
The purpose of the tests is to prove the guaranteed power
requirement for three guarantee points at constant discharge
pressure.
General
The speed cannot be varied and the temperatures in the cooled
section are set by means of the flow of cooling water.
F.5.3
Design of installation
The conversion of uncooled and cooled sections of the com-
pressor is carried out separately.
The guarantee conditions, guaranteed performance and other
desig~ values are given in t~bles F.41 to F.43.
The installation comprises a four-stage turbocompressor for air
with three intercoolers, inlet guide vanes to Stage 1, driven by
electric motor and gear unit.
Table F.41 – Guarantee conditions
Symbol
Numerical
value
Inlet pressure
Pt, 1,Gu
0,9607
bar
Inlet temperature
Designation
Unit
‘t,l, Gu
20
Oc
Relative humidity
@lrG”
70
%
Gas constant
‘Gu
266,90
Nm/(kg. K)
Isentropic exponent
‘GU
1,4
Overall flow of cooling water
q V,W,Gu
0,056944
m3/s
Inlet temperature of cooling water
fw,l,Gu
27
“c
Npr, Gu
1490
rfmin
Motor speed
Table F.42 – Guaranteed performance
Numerical
Symbol
Designation
value
Guarantea
point
(a)
Gusrantaa
point
(b)
Guarantee
point
(c)
Unit
Volumetric flow at inlet
qV,t,l, Gu
7,20633
5,76369
4,66056
m3/s
Discharge pressure
Pt,2, GLI
6,S649
6,S649
6,6649
bar
Power requirement at coupling
‘e, G.
1970
1610
1390
kW
Discharge pressure, Stage I
Pt,2,1,G“
1,700
1,535
1,425
bar
Dk.charge temperature, Stage I
‘t,2, 1,Gu
356
351,2
3W,5
K
Table F.43 – Other design valuas
Symbol
Numerical
valua
Unit
Stage II
T1,II,GU
310,2
K
Stage Ill
‘l, III,Gu
310,2
K
Stage IV
Tl,lv, @
310,2
K
Daaignation
Inlet temperature
130
IS 14641:1999
ISO 5389:1992
.:
F.5.4
●
Unit I: Stage I (without intercooling)
Test set-up
The teat is carried out at the compressor site under atmospheric
conditions. In this test, it is not possible to judge the intercoolers since a flow of cooling water differing from that of the
guarantee is admitted because of the deviation in cooling water
inlet temperatures.
Unit Ilc: Stages II to IV (with intercooling)
The additional calculation sequence for Unit”1is as follows:
3–4–5–6–7–8–9–10-11-
Setting
12–13–21–
22 – 23 – 24 – 25 – 26 – (43 – 44, but see the note to
F.O.1) – 45 – 46
The teat set-up is shown in figure F.11, and the test conditions
are given in table F.44.
F.5.5
.J
The values A V,,td = + 0,05 or A Vr,td = – 0,05 are inserted
in 23.
conditions
Since the speed is not variable, the compressor is run so that
the air temperatures in the cooled section Ilc are set to correspond to the design value.
In determining the setting conditions in accordance with the
flow chart in figure D.6 the following calculation sequence is
used (the numbers given are those designating individual boxes
in the flow chart):
1–2–3–4–5–39-40-41-42
see the note to F.O.1) – 45
–(43-44,
but
Since it is not possibleto set the speed or the inlettemperature for
Stage 1,the compressorhasto be dividedinto two units: 48 – 49.
The setting conditions for Unit I were maintained in the test and
the calculation for Unit I ends with 46.
The additional calculation sequence for Unit Ilc is as follows:
3–4–5–38-40-41-42-(43
note to F.O.1) – 45
–44,
butseethe
Since the inlet temperature for the stages in Unit Ilc can be
varied through the intercoolers, it is possible to maintain the
setting conditions for Unit Ilc. The calculation ends with
46-i7.
-
Tabla F.44 – Test conditions
Symbol
Designation
Ieentropic exponent
F.5.6
Numerical
value
Unit
1,4
KTe
Inlet temperature
‘t,l,Te
13
Oc
Mean inlet pressure
Pt,l,Te
0,8807
bar
Cooling water temperature
tw,l,Te
19
Oc
Gae constant
RTS
287,63
Nm/(kgK)
Test results and conversion
Seetables F.45 to F.47.
Table F.45 – Tast results
Designation
Symbol
Numerical
Teet No. 1
velue
Teat No. 2
Unit
Tact No. 3
Date of test
—
1864-03-11
lW-03-11
1964-03-11
–
Atmospheric pressure
Pa
1,003
1,003
1,003
bar
Gaa conetant
RTe
287,8
287,8
287,8
N.m/(kg.
Motor speed
Npr, Te
1488
1490
1482
rlmin
Poeition of inlet guide vanes
d
+
10
+54
+84
degree
kgla
Mace flow (also usablemass flow since measured
on discharga side)
qm, Te
8,8LM 33
6,75558
5,88844
Inlet preaeure
pt, 1,Te
tt,l , Te
0,8889
0,8826
0,8885
bar
12,1
12,9
13,0
Oc
285,3
288,1
286,2
K
1,200
kglrr+
Inlet temperature
~,1, Te
@t,1,Te
1,180
1,183
Volumetric flow at inlet (also usable volumetric
flow at inlet)
4V,l,Ta
7,28528
5,88278
4,72444
~3/5
Discharge pressure
Pt,2, Ts
7,5315
7,5119
7,1196
bar
Deneity
K)
131
\/
/
IS 14641:1999
!S0 5389:1992
132
,
1
I!_ ———
I
——
“-
>
+!7
G
Z
4
-l——
4
-@-
-+
‘=’’!.4) au-
6
‘T’
.Y.
m
%
#’
IS 14641:1999
ISO 5389:1992
Table F.46 Designation
Calculationresults
Symbol
Pressure retio
(pzipl)~
Specific isothermal compression work
Tast No. 1
Numaricel valua
Tact No. 2
last
Unit
No. 3
7,773
7,645
7,202
—
‘m,T,Te
166341
167408
162614
N.m/kg
Terminal power of motor
‘un, Te
2168
1785
1548
kW
Motor efficiency
vPr, Te
85,4
85,3
95,0
%
Power at coupling
‘e, Te
2066
1711
1472
kW
Isothermal compression power
kW
f’T, Te
1448
1131
922
isothermal coupling efficiency
VT, e, Te
70,1
66,1
62,6
%
Mechanical Ioaaee
~, Ta
70
70
70
kW
Internal compression power
‘in,Te
1888
1641
1402
kW
Table
F.47 – Conversion
Daslgnation
A
to guarantee
Symbol
conditions
(eae figure D. 11)
Test No. 1
Numaricai value
Test No. 2
Test No. 3
7,28626
5,66276
4,72444
rn3/a
Unit
a) Unit I (uncooladStage 1)
Volumetricflow at inlet
~V,t,l,l, Te
Discharga prasaure
Pt,2, I,Te
1,6856
1,5544
1,4465
bar
Inlet pressure
pt,l,l, Te
0,8689
0,8826
0,W65
bar
Pressure ratio
(p2 /p! )t, 1,Te
1,750
1,582
1,463
—
Specific iaentropic compression work
w m,s,1,Te
48637
40354
33087
N.m/kg
5,66276
4,71806
m3/5
Converted volumetric flow at inlet
qv,t,l,l, co
7,30500
Converted specific compression work
‘m,s, 1,Co
48975
40354
32850
N.m/kg
Converted preaaura ratio
(P2/pl)t, 1,C.o
1,725
1,563
1,446
—
Discharge temperature
‘t,2, 1,Ta
74,6
71,8
70,1
Oc
‘t, 1,1,Ta
12,1
12,9
13,0
Oc
‘in,l, Te
542
401
326
kW
‘in,l, Co
534
388
313
kW
lniet~-perature
Internal compm”on
power
Convertad intarnal compression powar
b) Unit Ilc (cooled Stagas II to IV)
Inlat temperature
‘t,l, Ilc,Te
36,8
36,6
36,6
Oc
Inlet pressure
Pt, 1,IIC,TS
1,6856
1,5544
1,4465
bar
Density
@t,l, IIC,Te
1,800
1,743
1,622
kglma
3,87583
3,48526
f7’r3/5
3,67583
3,48056
m3/5
Volumetric flow at inlet
qV,t,l, Ilc,Te
4,53063
Convartad volumetric flow at inlet
~v,t,l, Ilc,co
4,53684
Discharge pressure of entire compressor
pt,2, Te
7,5315
7,5119
7,1196
bar
Pressure ratio
(p2 /,@t, 11~,
Te
4,442
4,633
4,922
—
Specific isothermal compression work
‘m,T, Ilc,Te
133076
140441
142138
N.m/kg
Converted specific iaotharmal compression
work
‘m,T, Ilc,Co
133438
140441
141657
N.mlkg
Converted pressure ratio 1~
(P2/pl)t, il~,co
4,431
4,785
4,662
—
Internal compraaaion powerz)
‘in, Ilc,Te
1456
1240
1076
kW
768
711
Ml
kW. ins/kg
Convarted power ralatad to density 1~
Pin
Pt,l lRZ~,I
()
Ilqco
133
IS 14641:1999
ISO 5389:1992
Table F.47 – Conversion
Designation
to guarantee conditions (see figure D. 11) (cofrc/uded)
Symbol
Test No. 1
Numerical value
Test No. 2
Test No. 3
Unit
c) Unit Ilcs} [seefigureD.Ill
Volumetricflow at inlet
~v,t,l, Ilc, co
4,4s028
3,83308
3,45194
~3/5
Appropriate pressure ratio
(P2 /pl)t, 11~,co
4,48
4,80
4,87
—
Converted internal powar
‘in, Ilc,Co
1444
1208
1037
kW
Volumetric flow at inlet
9v,t,l, co
7,30500
5,88278
4,71806
m3/s
Converted pressure ratio of Unit I
(P2/pl)t, 1,co
1,725
1,583
1,446
—
Converted pressure ratio of Unit Ilc
(P2/pl )~,llq c,~
4,480
4,820
4,895
—
d) Total compressor
Converted total pressure ratio
Converted internal power Unit I
7,894
7,5
7,0
‘in, 1,Co
534
389
313
kW
Converted internal power Unit Ilc
Pin,Ilc,co
1444
1208
1037
kW
Mechanical losses in test
Pf, Te
70
70
70
kW
Converted mechanical losses
Pf, (-0
70
70
70
kW
kW
‘e, Co
2048
1885
1 4m
‘m,T, CO
172837
171058
185828
N.m/kg
Converted isothermal compression power
PT, co
1483
1120
905,8
kW
Convertad isothermal coupling efficiency
VT, s, co
71,4
87,5
83,8
%
Convened power at coupling (see figure F.13)
Calculated specific isothermal compression
‘ work
1)
(P2/pl)~, co
—
The converted pressure ratio and converted power related to density are ehown over the converted volumetric flow at inlet Unit Ilc,
~v,t,l, Ilc,co.
2)
Tha internal compression power is given by
pin, Ilc,Ta = pin, Te – pin, 1,Ts
3) Taking the converted pressure ratio of the uncooled Unit I into account, the appropriate volumetric flows at inlet for the cooled Unit Ilc are
obtainad for the individual test points.
134
J
,4
.-.-i”L.
4
IS 14641:1999
ISO 5389:1992
F.5.7
Test uncertainty and comparison with guarantee
The test uncertainties
The comparison
are calculated
with the guarantee
in accordance
with clause 9.
is carried out as shown in table F.48 (see figure F.14).
Apart from the test values listed here and designated by the symbol “O’ in figures F.12 and F.13, additional test points were run at
each of the inlet guida vane positions, and these have been evaluated and converted in the same manner.
Ail those points have been plotted on figures F.12 and F.13. The power consumption
tained from figure F.14.
at the guaranteed
pressure ratio 7,0 can be ob-
The guarantees are met for two points. The third point shcwvs a alight excess, aven after taking into account the measuring
The test uncertainty
error.
for example 5 is shown in table F.49.
Table F.48 – Comparison with the guarantee
Symbol
Designation
Test No. 1
Numericel velue
Teet No. 2
Test No. 3
Unit
Volumetricflow at inlet
qv,tol,Gu
7,m 3
5,7639
4,6606
dls
Guaranteedpowerat coupling
Pe,@
1970
1610
13W
kW
Convertedpowerat coupling
‘etCo
1960
1635
1435
kw
Table F.49 – Resultingtest uncertainty
Designation
Uncertainty
in volumetric flow
at inlet
Uncertainty in pressure
ratio
Uncertainty in power
coupling
Symbol
Numerical
velue
‘qm, Ts
1,1 %
In accordance with ISO 5167-1
7N, Te
0,07 %
Dtgital maasuring instrument,
1 revolution on indicator
‘PI, Te
0,14 %
1 mmHg on absolute pressure
‘T1, Te
0,35 %
1 0 on absolute
‘ree,qv, 1
1,165 %
See 9.2.5
IVr
1,014
ln(p2/pl)
2,051
‘fi, Te
0,9 %
Quality grade 0,6 final value 10 atm gauge
(see 5.9)
‘res,@pl
1,184 %
See 9.2.6
~4
2954
rpe
0,67 %
7Pf
2,66 %
‘T1,llc,Te
0,323 %
10 on absolute temperature
‘Tl ,j,Te
0,32 %
1 0 on abeoluta temperature
rrss,Pe
1,042 %
See tabla 9
Comments
temperature
sea 5.9
t
at
Current transformer 0,5 voltage
transformer 0,5 wattmeter 0,5
>
sea 5.9
>
135
IS 14641:1999
ISO 5389:1992
0 Tests evaluated in present example
:
800
F
“2
%
650
L
3
‘
5,0 I
2
4,5
4,0
3,5
3,0
3,5
~o
4,5
5,0
%(t,l,IIc,Co’m3/s
Figure F,12 – Grephs for comparison with guarentee
136
5,5
IS 14641:1999
ISO 5389:1992
-
X
Guarantee points
O
Tests evaluated in present example
❑ Additional tests
8,0
5=+84”
2
\
7,0
w
u
a)
I
b) ~
I
I
I
I
I
I
I
0
u.
-“
&
6,0
I
I
I
I
I
5,0
2 100
I
I
I
I
1
I
I
I
-1
I
I
I
~1 900
x.
5
ci?1700
I
I
I
I
I
1 500
I
I
.
I
f
3
6=+ 84°
1 300
4,0
4,5
5,0
5,5
6,0
6,5
7,0
7,5
8,0
9yf,1,co,m3/s
Figure F.13 – Graphs for comparison with guarantee
137
--L
d
IS 14641:1999
ISO 5389:1992
{
4’---
L
Guarantaa pointa
2000
P
1900
1800
1700
3
x
.
E
Q..
1600
1500
1400
1300
4,5
5
5,5
~vt,l,co
6
6,5
t ~3/s
Figure F.14 – Greph for comparison with guarentee
7
7,5
,>
--k
IS 14641:1999
ISO 5389:1992
F.6
Cooled
Example6–
turbocompressor,
isentropic
exponent
KTe *
KG.,
real
9=
(variable
compressibilityfactor),variablespeed, inlet temperatureof cooledsectionadjustable(within limits)
F.6.1 General
The following
example applies Schultz’s
The guarantee
conditions,
F.6.2
guaranteed
method of polytropic analysis.
performance
and other design values are given in tables F.50 to F.52.
Purpose of tests
The purpose of the teats is to prove the power requirement
F.6.3
guaranteed
for the specified point.
Design of installation
The installation consists of an eight-stage
centrifugal
compressor for a hydrocarbon
gas mixture and an external intercooler between
stages IV and V.
There is a gas turbine drive through speed-increasing
gear.
The specifed gas shall be considered as a real gas and therefore the necessary numerical values are given in table F.53 (notably the
input values for the flow chart in figure D.7, and the mean values of specifii heat cpM).
Table F.60 – Guarantaa conditions
Symbol
Designation
Numerical
value
Unit
ri
Gashandled,volumetricproportion
carbondioxideCOZ
0,01
.
mathsneCH4
0,30
—
ethaneCZHG
0,20
—
propaneC3HS
0,35
—
n-butanerr-C4H10
0,08
.
i-butanai-C4H10
O,w
—
Inlet pressure,abaoiuta
Pt,l, Go
3,0
bar
Inlet temperature
‘t,l, Gu
311,2
K
Gas temperature after interceder
Tt,2, IC,GU
318,2
K
Speed
‘Gu
11000
rlmin
Numerical
valua
Unit
Table F.51 -
Guarentead performance
Designation
Symbol
qrrr,ut, GU
10,0
kgls
Dkcharge pressure, absolute
Pt,2, GU
34
bar
Power at coupling including speed-inweeaing gear
p, Gu
2820
kW
Uaablamassflow
.
,....
!!
.,
‘IS 14641:1999
ISO 5389:1992
Table F.52 – Other design values
I
Symbol
Numericel
valua
Unit
Stage IV discharge pressure, absolute
P},2, IV,Gu
10,3
bar
Stage IV discharge temperature
~t,2, Iv G“
377,4
K
Compressor discharge temperature
Tt,2, Gu
400,9
K
Stage I
DI
0,4
m
Stage V
Dv
0,4
m
inlet
0,4
m
Designation
““”
Impeller diameters
Compressor flange sizes
outlet to intercooler
0,3
m
inlet from intercooler
0,3
m
discharge
0,2
m
Table F.53 – Numerical values of gas specified
Symbol
Unit
RGU
236,66
236,66
N.m/(kg. K)
CPM, Gu
2021,6
2243,75
J/(kg. K)
Z1, GU
0,9753
0,9175
—
XM, G~
0,1296
0,4433
—
yM, Gu
1,0393
1,1320
—
Gu
1,1323
1,0676
—
Upol,Gu
0,605
0,63
—
‘Gu
1,1591
1,1726
—
KI,
F.6.4
Numerical valua
Staga group
Staga group
I
II
Test set-up
The test is carried out at the compressor site, but with a gas differing from the specified gas in both composition
and pressure level.
In this test it is not possible to judge the intercooler, because the cooling water flow must be reduced (the heat flow extracted from
the gas is much lower than the design value owing to a reduced gas pressure level).
The test arrangement is shown in figure F. 15, which also indicates the type of instruments used. The test conditions are given in
table F.54.
The split shaft gas turbine drive allows the spaad to be varied within the following limits:
NT,
0,7 < —
< 1,05
NGU
140
al
.-c
n
LO
5
z
-h
G
1$ 14641:1999
[S0 5389:1992
kI
I
In
L“
141
,
..—f -_
.
‘
IS 14641:1999
ISO 5389:1992
1
Table F.64 – Tast conditions
Test gas, volumetricproportion
F.6.5
methane
CH4
propane
C3H8
t
0,9
1,1
bar
Inlet temperature
Tt,l, Te
30s,2
K
Lowest oossible aas temperature after intercooler
Tt2 lC.Te. min
315,2
K
to be made bafore tha tast
Ghs properties
c)
Mechanical losses:
— compressor bearings and floating seal oil rings,
56 kW at 11000 r/rein, proportional to N1,5;
—
— the condensation of hydrocarbons in the intercooler
shall be checked according to [551.
No condensation is expected for the specified conditions.
Analysis of teat gas composition
Samples taken during trial runs before the teat have shown
only negligible variations in gas composition.
Gas samples shall be taken before and after the test. Pending the results of laboratory analysis, the gas composition is
considered to be constant. No condensation of hydrocarbons is expected in the intercooler.
There being only two components, calculation of the
specific heat CPcan be carried out easily with a (progmmmable) pocket calculator. Graphic interpolation of the functions given in [61 is used.
The re$ult is shown in figures F.16 and F.17.
step-up gear efficiency, 0,974;
— compressor internal leakage, 0,5 kg/s at 34 bar
absolute discharge pressure, proportional to discharge
pressure (radiation losses neglected).
—
other numerical values, e.g. critical data and
viscosity of the components, shall be taken from [61,
which will also be used as a source for all information not
available in this International Standard;
Power input
The power input shall be determined by energy balance.
— the specific heat CP shall be calculated on site
according to the recommendations given in [61, P. 135;
142
—
0,1
Pt,l, Te
Agreements
. ... ..
fi
The gas properties shall be evaluated as follows:
b)
S1 unit
—
Inlet pressure, absolute
Before the test, the following agreements shall be made.
a)
Numer!cal
valua
Symbol
Designation
d) Computation of
guarantee conditions
teat
results and
conversion to
Theaa shall be baaed on total pressures and temperatures.
Specific compression work: aimplifiad calculation baaad on
total conditions, with no separate term accounting for
dynamic heads at inlet and outlet, is accepted.
F.6.6
Datarmination
of tha settings
F.6.6.1 Compressor defined as one unit
F.6.6.1.1 In the first place, whether the gas mixtures in
question can be considered as perfect or near-perfect gases,
according to table 2, shall be checked.
The specified gas being a real gas, the necessary information is
available from design calculations.
For the test gas, determination of y, ~ and Y at inlet and
discharge conditions is required. Therefore the pseudo-critical
conditions of the mixture, i.e. the criiical pressure and
temperature as wall as the acentric factor of the mixture, must
be calculated to check whether simple linear mixing rules, as
given in A.1 .5, can be applied.
IS 14641:1999
1S() 5389:1992
..
2,20
G
0
g
\
:
1b<
2,15
2,10
2,05
2,00
1,95
IT
1,90
1,85
1,80
1,75
1,70
20
40
60
80
100
120
140
Temperature, ‘C
Figura F.16 – Graph for determination
of test gas specific heat capacity, cP,T~
143
%
+
I
4,
IS 14641:1999
ISO 5389:1992
G
0
Xm
2
z
~ti
Y
Absolute I
aaure: bal
2,40
2,35
2,30
8
\
———
2,25
2,20
15
\
2,15
2,10
L
2,05
2,00
E
20
40
60
80
100
120
140
Temperature, “C
Figure F.17 – Graph for determinetion
144
of teat gas epecific heat capacity, c~,T~
)
IS 14641:1999
ISO 5389:1992
F.6.6.1.2 The pseudo-critical
conditionsof thetest gesas are
givenin tableF.55.
The following maximum/minimum ratios are thus obtained:
Tcr,i,maX_ , ~
,
Tcr,i,min
PCr,i,max
—=
The knowledgeof thespecificheatCp, comwaasib~ty factor Z
and derivative compressibility factors X and Y is essential for
use in the following calculations.
With the above characteristic data of the teat gas mixture and
the anticipated test conditions given in table F.54, the following results are obtainad.
1,0634
PCr,i,min
Vcr,j,~~~
—=
Vc~,j,min
F.6.6.1.4 For the specificvaluesof the teatgas at the compressorinlet,thefollowingresultsareobtainad.
1,341
P = Pt,l,Te = 1,1 ~r (absolute)
T = Tt,l,Te = =,2
The respective limits for simple Iineer mixing (see A. 1.5) which
these ratios must satisfy are
Pr = (pt,l/pcr)T~ = o,~
Tcr, max < *
23
Tr = (Tt,l/Tcr)~e = 0,6759
Tcr, Min
In accordance w“th clause A.3 and figure F.18, the following
values are obtained:
end either
PCr, max or (vCrM)max
PCr, min
K
is ~lom to uni~
z(o) = (-y&j 9
(VCJ’f)min
z(l) = _ 0,)83
Since the maximum/minimum
ratios calculated do not satisfy
the limits for simple linear mixing, the more complex mixing
rules given in [6] shall be usad, because under theaa conditions
ZT(0) = 1,@cJ
the limits of validity are respected.
ZTIII = ()
The mixing rules used are
2$0) = 1,~
Tcr = ~riTcr,i
2:1) = o
Rmol(
Zrizc,,j)Tcr
PCr =
~ fivcr,iMi
In accordance with figure F.16,
CP = 1766 J/(kg. °C)
where
z = Zm + @z(l) = 0,9782
R is the gas constant of the mixture, calculated using the
simple linear mixing rule (perfect gas rule);
ZT = ZT(0) + coZT(l) = 1,043
are considered to be the critical data of the
2P = 2P(0)+ (UZJ1) = 1,006
Tcr and Pcr
mixture;
w
is the acentric factor of the mixture.
x=y–
F.6.6.1.3 For the mixture critical data, gas constant and
acentric factor, the following results are obtained:
z~
2P
Y=—=
z
1 = 0,06624
1,02842
J/(kg. “C)
RTe = 201,36
pcr,~e = 42,79 bar
F.6.6.1.5 An estimation of the test discharge conditions is
necessary in order to calculate the derivative compressibility
factors Xand Yand the ratio of specific heats y for comparison
with table 2.
Tcr,~e = 351,66 K
coTe= 0,1376
Table F.66 – Pseudo-critical
Component
i
Mi
conditions of the mixture
PCr, i
Tcr, i
‘Cr, i
bar
K
rnVkg X 10-3
Zcr, j
Ui
CH4
16,043
46,00
190,6
6,171
0,286
0,006
C3H*
44,097
42,46
369,8
4,603
0,281
0,152
145
IS 14641:1999
[S0 5389:1992
The basis of the estimation is as follows.
The pressure ratios and polytropic efficiencies of both sections
of the compressor are assumed to be the same for test and
specified conditions (i.e. guarantaa point).
F.6.6.1.8 According to the anticipated test data and following
the indications given in F.6.6. 1.6, the inlet and discharge conditions are:
Temperature: Tt,l,ll,Te = 315,2 K (minimum possible value)
pressure: ~t,l,ll,Te
= ~t,l,l,Te (~2/~l)t,l,Gu
As defined in 8.2.4.2, the inlet conditions for section II are the
following:
–
= 1,1 x3,4333
= 3,7767
bar (absolute)
Discharge pressure: ~t,2,11,Te = ~t,l,ll,Te (~2/~l)t,Il,G”
pressure = pressure upstream of intercooler
= 3,7767 X 3,30097
= 12,467 bar (absolute)
= discharge pressure of section I
— temperature = temperature after intarcooler
F.6.6.1.9
The determination
illustrated in table F.56.
The discharge conditions therefore become
of the discharge temperature
is
The values of the critical data Tc, and PC,, and the gas constant
~t,2,11,Te= ~t,2,1,Te(~2/~l)t,l,Gu
R and acentric factor w usad are those determined in F.6.6. 1.3.
~
‘t,2,11,Te = ~t,2,1C,Te
() ~1
The polytropic efficiency qWI = q@,,,,@ is known from design
calculations.
‘ll,Te
t,ll,Gu
The resultsfor T2 show good “convergence”; between the 2nd
and 3rd approximations the difference in discharge temperature
is leas than 0,1 ‘C.
where
~t,2,1,Te= ~t,l,l,Te (~2/~l)t,l,Gu
and, anticipating that the test gas follows real gas equations,
The formula for the polytropic exponent n is given by Schultz
(sea 3.5.3.3).
The results are as follows:
mll,Te =
[%(k+xM)],,,Te
bar (absolute)
‘t,2 = Tt,2,11,Te = 386,17 K
in which
F.6.6.1 .10 The data computed for compressor inlet conditions (see F.6.6. 1.4) now make it possible to decide whether
the test gas can be considered as near perfect.
?pol,ll,Te = qpol,ll,Gu
The above real gas equation
polytropic analysis).
is given
in 3.5.3.3
The determination of Tt,2,11,Te
therefore can only be achieved by
a ttial-and-error method, i.e.
let approximation: put m~ = ml, giving T;
– 2nd approximation: calculate mM with T2 = T; and
compare the result T; with the assumed value T;;
– 3rd approximation: calculate mM with T2 = T; and
compare the result, T;’, with the aeeuwd T;, and so on.
What remains to be done is the calculation of the ratio of
specific heats (see table F.57).
Since a negative answer to the above question is anticipat~
Schultz’s formulae for the iaantropic exponent K and the ratio
of specific heata y will be used.
The admissible limits for the gas mixture to be considered
as a perfect gas (see table 2)1 for the given pressure ratio
(~z/~l)T~ = 12,467/ 1,1 = 11,333, are as follows:
Ymax
= 1,075
(-)Ymin :~1
,.
x mex,tcd= ‘.~
Y I’lla,t., = l,m
5
The actual values are as follows:
All numarkal values refer to compressor section Il.
Ymgx
—
= 1,01
Ytin
F.6.6.1.7 For the Specified gas (see table F.53), the following
relationship is valid:
x max= 0,3139
F.6.6.1.6
Y~rxJl,ll,Gu = o@
146
“d
(Schultz’s
The polytropic temperature exponent mTe is calculated with the
average values of the compressibility factors ZM and ~.,
and
the average specific heat cPM, the computation of which requires the knowledge of T2,Te.
–
Pt,2 = ~t,2,11,Te = 1M67
= 1,0869
IS 14641:1999
ISO 5389:1992
... -
1
,
Table F.66 – Determinationof dischergetemperature
Numerical valua
Symbols and formulaa
Unit
Inlat (1, 11,Te)
Dis larga (2, II ‘e)
1st
2nd
3rd
approxi- approxi- approximation
mation
mation
K
315,2
392,72”)
365,32”)
366,17°)
Pt,
abs
bar
3,7767
12,46
—
12,467
~ = ~lTc,
—
0,6958
1,1161
1,0956
1,0975
Pr = PtlPcr
—
0,09007
0,2973
—
0,2973
z(o)
—
0,9570
0,9246
0,92U8
0,9212
—
-0,019
0,0038
0,0014
0,0016
—
1,106
1,166
1,196
1,195
z(l)
1
Zp
Sea dauae A.3 and figure F.18
z;”
2;0)
z;’ )
t
J
—
0,15
0,107
0,115
0,114
—
1,010
1,005
1,0055
1,0055
—
- 0,C4)2
–0,032
–0,029
–0,029
/(kg.°C)
1645
2254
2231
2232
z = z(o) + ~zll)
—
0,9544
0,9251
0,9210
0,9214
ZT = Z;’J’ + OJz+”
—
1,1266
1,2007
1,2118
1,2107
1,0097
1,0006
1,0015
1,0015
Cp (ace figure F.18)
Zp = z;? + O.)z; J
ZT
X= z-l
—
0,1605
0,2979
0,3158
0,3139
Y=+
—
1,057*
1,0616
1,0674
l,rm69
—
CPM
m=—
ZMR
~
CPM
()
1
_
+ XM
?pol
P2 m
Reault:T=T1x
~
0,9544
= Z1
0,9398
0,9377
0,9379
o,l&)5
= xl
0,2392
0,2461
0,2472
—
1,05786
= Y1
1,1M98
1,0717
1,0725
—
1645 = Cpl
2049,5
2a36
2036
—
0,16413
0,1666
o,lm 1
o,lm o
K
392,72
385,52
366,17
366,13
382,72
385,52
366,17
1,1617
1,1622
1,1621
= ml
.
()
Assumed :
K
T
1
n=
YM-m(l+XM)
—
1,1696 = nl
●) Assumed value.
147
. .AL
.4
IS 14641:1999
ISO 5389:1992
Table F.67 – Calculationof mass thermal capacities
Symbols and formulaa
Pt
Unit
Numerical value
Inlat (1,Te)
bar
1,1
12,467
q
K
306,2
386,17
z
—
0,9782
0,9214
x
—
0,06621
Y
—
1,02639
1,0669
Cp
J/(kg.°C)
1766
2232
—
1,1082
1,0600
—
1,1406
1,1521
K .
.
0,3139
Y-:1(1+X)2
y=Kk’
The conclusion is, therefore, that the test gas cannot be treated
as a perfect gas if the compressor is to be considered as one
unit.
The determination of the settings therefore has to follow the
flow chart given in figure D.7.
F.6.6.2.1.2 The specific values of the test gas at the inlet are
given in F.6.6. 1.8.
F.6.6.2.1.3
An estimation of section I test discharge conditions may follow the guiding principles given in F.6.6. 1.5, i.e.
/%,2,1,Te = ~t,l,l,Te (~2/~l)t,l,Gu
F.6.6.I .11 The design (specification) and test data available,
together with the above calculations, combine ail information
necessary, i.e.
a)
gas constant,
b) isantropic exponent of specified gas and test gas, at
inlet, and
c) compressibility factors of specified gas and test gas, at
inlet,
to check whether the compressor can be teeted as one unit.
~pol,l,Ts = ~@,l,Gu
These assumptions lead to the determination of the test
discharge pressure and, by the trial-and-error method
demonstrated in F.6.6. 1.9, of the test discharge temperature (it
being anticipated that the calculation will have to follow real
gas equations).
In accordance with F.6.6.1 .5,
~t,2,1,Ts = 1~1 x 3@33
= 3,7767 bar (absolute)
The sequence of calculations starts at step 41 in the flowchart
in figure D.7:
The critical gas data and acentric factor are given in F.6.6.1 .3.
~~,Te = 1,1082
The result is
K1,GU = 1,1323
Kl,Te – K1,GU = 0,0231
> 0,01
J@ = ~t,2,1,Te = 3,7767 ~r (absoiuta)
Tt,2 = Tt,zl,Te = 364,70 K
It is concluded that the compressor cannot be tested as one
unit, and therefore further subdivision is necessary.
This means that the determination of the settings must be
carried out separately for the two stage groups (or sections) of
the compressor.
F.6.6.2 Compressor subdivided into two uncooled
sections
F.6.6.2.1 SectionI (StagesI to IV)
F.6.6.2.1.4 All datarequiredfor comparisonwithtable2 are
nowavailable,exceptthe ratioY of specific heats at discharge
conditions which can be calculated as demonstrated in
table F.58 (sss also table F.57).
The pressure ratio is 3,4333.
The admissible limits for the given pressure ratio (see table 2)
are
(-) =
Ynlex
1,0%8
F.6.6.2.1.1 Forthe sakeof completeness
the same check as
carried out above for the compressor as a whole has to be
repeated here for section I alone.
x mex,tol = ‘~~
The specified gas is to be considered as a real gas.
Y -,,01
148
Ymin t~l
=
1,018
“
-+,..3
Discharga (2,Te)
>.
‘,
1s 14841:1999
ISO 5389:1992
Table F.58 -
Datarminationof dischargetamparatura
Numerical value
Discharga (2,1,Te)
I
I
Symbols and formulae
q
bar
Pt, *g
i
I 3,7767
1,1
I -
13,7767
1766
2067
2042,5
2046
z
.
0,9782
0,8731
0,9720
0,9721
x
—
0,06621
0,08735
0,08883
0,08867
Y
—
1,02638
1,0303
l,a3265
1,03223
zM
—
0,97s2 = ZJ
0,9757
0,9751
0,9752
J/(kg.°C)
Cp (sea figure F.16)
—
CPM
()
~=ZMRx
—.
~
Cp M
Result: Tt,2 = 7’t,l x
Assumed:
—
+ )(M
rlpol
Tt
()
P2 m
—
PI t
K
1766 = Cpl
I
1916,5
I
1806,81$K17
I 366,88364,37
0,14584 = ml
0,13573
I
K
0,13646
I
0,13645
364,71
364,70
368,88
364,37
364,71
I 1,13308
I 1,13266
I 1,13310
I
1
rr=
I
-
I
1,14576=
n,
yM-t?r(l+xM)
●)
Assumed value.
The actual figures (see table F.59) are
Ymax
—
F.6.6.2.I.5
The above calculations, which are necessary for
the decision whether a gas mixture suspected of follo~ng
real gas equations can be considered as near perfect, have been
ahown in some detail. The object is to demonstrate
the method. The main difficulty is the interpolation (and
extrapolation, for small values of reduced pressure pr) of the
tables and charts given in annex A. This is beat done graphically.
= 1,0129
Ymjn
x max = 0,09987
Y msx = 1,03223
It may be concluded that the test gas cannot be treetad as a
perfect or near-perfect gas.
The determination of the settings therefore has to follow the
flow chart in figure D.7, because the curves which cover the
range n~e =
Therefore the compressibility factors given in table A. 1 were
plotted in figure F.18.
1 to 1,2 do not reach beyond a pressure ratio
(p2ip1)~ 2.
Tabla F.59 – Calculationof mass tharmal capacities
Symbol
Unit
Numerical valua
Discharge
Inlat
(l,l,Ta)
(2,1,Ta)
I
bar
1,1
3,7767
II
Pt
Tt
K
306,2
364,70
z
—
0,9782
0,9721
x
—
0,06621
0,08867
Y
—
1,02638
1,03223
CP
J/(kg.°C)
1766
2046
—
1,1082
1,08084
—
1,14068
1,1261
K
Y
F.6.6.2.1.6 Follow”ngD.5.1, all values necessaryfor the
determination
of the settings for section I of the compressor
are listed hereafter.
An exception is information regarding the viscosity, as the
Reynolds number W-II be checked after an attempt has been
made to find a common teat speed for both compressor
sections.
The input values for the flow chart in figure D.7 which are not
known already can be easily computed from the fiiuraa already
available.
The praaaure-vcrlurna curve of the compressor section is
expected to be steep.
149
o-
IS 14641:1999
ISO 5389:1992
150
+
0
m-
+
1’
I
i
—.
—.
—.
0-
-4 —
I
I
I
J“ —a
I
!
/
/
q
1. o
I
/
[ .—
I
I
I
,——
CQ
o-
IS 14641:1999
ISO 5389:1992
Theinput liatfor the flow chart in figure D.7, referred toaection I of the compressor, isas followa.
The results are
~pol,Gu = 0r&15 (from input list)
+
General:
p2/pl= 3,433
D=0,4m
AVr,X,td = *0,01
AVr,X,td = ~0,025(outer
tolerance limit)
Test data:
= 1,1 bar (absolute)
‘t,l,l,Te
= 3W,2 K
= 1,1082
RTe = 201,3 J/(kg, “C)
T2,Te= 388,88 K
(step 10)
lz2,Te-zl,Te/
= 0,00508<0,01
btep 12)
= 11000 x l,05r/min
Nmin = 11000 x 0,7 r/rein
~Cr,Te = 41,=
(R (l/Cp, -1 /cp2) I = 0,0166>0,01
(Step 12)
The calculation tharefora follows steps 14 – 20:
??tTe= 0,12888
(stap 19)
lmTe-ml
(step 20)
= 0,01895>0,01
Returning through step 21 to stap 10 we obtain
Pl,l,Te = O
N-
[step8)
but
Pt,lJ,Te
‘l,l,Te
m = 0,14584
(inner tolerance limit)
bar
‘Cr,Te = 351,86 K
cP,Te = f(p, T) (see figure F. 17)
UTe = 0,1376
SpecMiad values:
~~,,,@
= 3 bar (abeoluta)
‘t,l,l,Gu
= 311,2 K
TzTe = 384,37 K
(step 10)
Here again, because the condition regarding the difference in
specific heeta (step 12) is not fulfilled, the calculation leading to
stap 20 must be repeated.
Ths time we obtain
l~Te-tnl= 10,12830-
(),126881 = 0,00131<0,01
and tha calculation continues through etaps 22 and 23 to
step 24:
ttGu = 1,1591 (from input list)
nTe =
1,13288
ltrTe
- ?rGul= 0,0262>0,002
(step 24)
~t,2,1,G. = 10#3 bar
‘t,Zl,Gu = 377,4 K
Kl,l,Gu =
1,1323
f%,l,Gu = O
‘Gu
= 238,66 J/(kg. ‘C)
NGU = 11000 r/rein
Z,,,tGu = 0,9753
Since the condition for the differwwe in polytropic exponent
(Step24) is not met, it is not po~”ble to calculeta P/r,td directIy.
Therefore, after the assumption of a value for A Vr,X,tOl(step
30), the calculation follows steps 31 to 40 in order to check
whether the pressure ratio assumed (step 7) is in accordance
with the requiremanta regarding the tolerable ratio of volume
\
rate of flow ratios V,.
A Vr,x,td will be chosen at both the inner and outar tOkSnCC?
limits, i.e.
\
A Vr,X,td = + 0,01
?poI,I,Gu= Q=
‘1,Gu = 1,1581
F.6.6.2.1.7 Thecalculation
startsatstep3 of theflowchartin
figure D.7.
A Vr,X,td = * 0,025
The aim is to find a common teat speed for both compressor
sections. Otherwise, since the speed is adjustable, strict
similarity of flow could be attempted, putting A vr,~,td = O.
The following results are obtained:
Then follows tha determination of the mean poiytropic
exponent of the teet gas, assuming that tha test pressure ratio
and test polytropic efficiency have the same values as for
specified conditions. This calculation is done through steps
6 – 22. It is a trial-and-arror method, the result of which, as
regards discharge temperature, has already been anticipated in
F.6.6.2.1.3.
,
A Vr,x,td + 0,01 + 0,025
-0,01
I 1,01
vr,~
()
Px
—
PI
1,208
-0,025
-l
1,025 0,8806
0,975
(step30)
0,627
5,028
(stap31)
2,708
En
151
.—
IS 14641:1999
ISO 5389:1992
Except for A Vr,x,tOl= A 0,025 the anawar to etep 32 is “yea” and the calculation continues through steps 33 – 40 to steps 27 – 28.
wth
(P2/pI) = 3,433 = (P2/pI)Guwe obtain
v
N
A V,,X,lOI
N,= () mn
+ 0,025
+ 0,01
0,8885
M,ttj
-0,025
-0,01
0,8837
0,9769
–
0,9680
(step 40)
(step 27)
(step 28)
‘&)Gu
‘&:@)
~
PI
()()
——P2
Te
PI
< 0,01?
‘:
‘m
‘:
no
yea
no
;
no
(step 26)
Note that for A Vr,x,ml = – 0,01 and following step 37, Vr,2had to be increased above 1 + A V,,x,tOl = 0,89, according to step 38.
ForA Vr,x,tol
= A 0,025 the calculation sequence jumps directly from step 32 to step 40.
The conclusion is that except for A Vr,x,tol = + (),()25 it is naceaaary to repeat the above calculation, starting at step 9 of the flow
chart, and assuming that
P2
—=
PI
()
&
PI
Te
The following results are obtained:
A Vr,x,tol
I
+ 0,01
-0,01
- O,&
(P21PJ
3,377
3,303
3,244
P2 [in bar (absolute)]
3,715
3,633
3,568
(step 9)
T2 (in kelvins)
388,11
368,83
385,97
(step 10)
IZ2-Z,I
0,0048
0,00452
0,00423
(step 12)
0,0164
0,0162
0,0159
(step 12)
0,01006
0,008 s
0,00883
(step 20)
IR(*-$)
lm~e-ml
Only for A Vr,x,ml = + 0,01 does the above first approximation not fulfill the condition ImT. – m I <0,01, therefore requiring a second
approximation aterting again at step 10.
Finally we obtain
I nTg
I
1,13046
1,13176
1,13313
I
3,366
3.3)0
3245
O,(XI8
0,003
0,001
l(:)T.-&)
I
0,9648
0,9782
NOTE – Following etep 37, Vr,2 hastobeincreasedto0,8907
1!52
I
I
I
(%+)‘0’01’ ‘y-w
N,,&
(step 22)
0,8691
for A vr,~,~d = -0,01.
I
-G.&
IS 14641:1999
ISO 5389:1992
It is now possible to calculate the test speeds for the inner and
outer tolerance limits (step 26):
NTe
—
NGU
=
RTezl,Te
N,,td
Test data: the lowest possible inlet temperature is chosen, so
as to obtain a test speed as close as possible to that found for
section 1.
Tt,l,Te
Pt,l,ll,Te = 3,7767 bar(absolute)
%iu%dt.~,c+u
Tt,l,ll,Te = 315,2 K
The numerical results are
~l,ll,Ta = 1,~
= 201,36 x 0,9782
x 308,2 J/kg
RGJ1,GuTt,l,Gu = 238,66 X 0,9753
X 311,2 .JIkg
‘Tezl,TeTt,l,Te
5
Other data: see F.6.6.2. 1.6
Specified values:
A Vr,x,tol
0,01
+ 0,025
0,9848
0,8837
0,9762
0,9691
0,8015
0,9097
0,8837
0,8872
+
Nr,tol,l
(-)
‘Te
‘G.
– 0,01
-0,025
Pt,l,ll,Gu = 10J3bar(absolute)
-
Tt,l,ll,Gu= 318,2K
~t,2,11,Gu = 34 bsr (absolute)
I
F.6.6.2.2
Tt,z,li,Gu = 4oo~9 K
KI, II,GU = 1,0876
Section II (Stages V to Vlll)
Z,,ll,GU = 0,9175
NOTE – Determination of the settings is to follow the same pattern as
used for section 1. Therefore mostly numerical results w“ll be given
heraafter,
with
only
a minimum
of explanatory
remarks.
qPoI,ll,Gu= Q=
nll,Gu = 1,1726
F.6.6,2.2.1
As regards the specified gas, from design calculations, the gas is to be considered as a real gas.
Other date: see F.6.6.2. 1.6
F.6.6.2.2.5
figure D.7.
F.6.6.2.2.2 Datealreadyavailable
for the test gas are given in
F.6.6.1.9 and F.6.6.1. 10. The additional data to be determined
here are the isentropic exponent K and the ratio of specific
heats y at section II inlet.
The results are
I
Symbols
lx
I
(l,ll,Te)
I
Discharge
(2,11,Te)
I
0,1805
I
0,3139
I
1,05788
I
l,m882
I
I-Y]
Inlet
K
1,0955
1,0600
Y=KY
1,1580
1,1521
The calculation starts at step 3 of the flow chart in
The results are
r?pc)l= 0,63 = qpol,GI.I
(step 6)
pzlp~ = 3,301
(step 7)
m = ml = 0,18413
(step 8)
(step 10)
I
T2,Te = 382,72 K
lzz,Te -Z1rTel=0,02827
(step 12)
The calculation continues with step 14, ending at step 22.
mTe
=
0,18684
lt?rTa
- ml = 0,01548>
F.6.6.2.2.3 Thepressureratiop21pj being 3,301 = (@Pl)Gu#
from table 2, the derivate compressibility factors X and Y
preclude the use of perfect gas equations.
>0,01
(step 19)
f),ol
(step 20)
The above calculation is then repeated,
m = mTe~
assuming that
T2,Te = 385,52 K
lz~Te - Z,,Tel= 0,03338>0,01
F.6.6.2.2.4 All datefor the flow chart in figure D.7 necessary
to complete a list similar to that computed in F.6.6.2.1.6 for
section I are already known.
Here too the pressure-volume curve of the compressor section
is expected to be steep.
The input list for the flow chart in figure D.7 referred to section
II of the compressor, is as follows.
General: see F.6.6.2.1.6
mTe = 0,17005
(step 19)
lmTe -ml
(step 20)
= ()#@l 41< (),()1
This time we can proceed through step 22 to step 24:
nTe = 1,16216
(step 22)
InTe - n@l = 0,01044>0,002
(Step 24)
NOTE – rraUistakenfromthe inputlist.
153
.,
.
IS 14641:1999
ISO 5389:1992
“
As for section 1,the calculation has to follow steps 30 – 40 of the flow chart in figure D.7. Here again, A Vr,X,tOlwill be chosen at both
the inner and the outer tolerance limits.
&_31
The results are
I
A Vr,x,tOl
..—
[
+ 0,01
+ 0,025
-0,01
-0,025
1,01
1,075
0,99
0,975
(step 30)
0,553
0,0624
5,071
19,58
Lstep31)
V,,2
I
()
Px
—
PI Ex
The answer to step 32 being “no” in all cases, the calculation continues (to ste~ 41 I with step 27:
Nr,tOl
0,9981
1,0058
0,9875
0,9794
(Pz/Pl )T~
(step 401
(step 27)
(step 28)
- (~),e-(~)
~:
~:
~:
‘:
(step 28)
b F)T.-E)
‘0’01’
‘es
‘0
‘0
‘0
Except for A Vr,x,td = + 0,01, the above calculation shall be repeated, assuming that
~=~
PI
() PI
Te
The results are
A Vr,x,tol
+ 0,01
+ 0,025
-0,01
– 0,025
p#pl
3,361
3,226
3,?71
m=ml
0,164
?
0,1841
0,1841
T2,~e(in kelvins)
384,03
381,11
388,63
jzz,~e - z~,~el
0,0287
0,02758
0,02709
> 0,01
> 0,01
> 0,01
mTe
0,1664
0,1688
0,1680
lm~e-ml
0,0157
0,0153
0,151
> 0,01
>0,01
> 0,01
.,
154
IS 14641:1999
ISO 5389:1992
In order to stay within the inner tolerance limit, the following
minimal inlet temperature to section I would be necessary:
For the second approximation, with m = mTe,#the followin9
results are obtained:
I + 0,01+ 0,025
A Vr,x,td
366,58
I
-0,01
– 0,025
384,12
383,07
I
f “~z,~e(in kelvins)
I
-
I I%h- %Tel
,I
-
>0,01
>0,01
>0,01 I
—
0,1700
0,1702
0,1704
I
mTe
1,16460
1-
InTe - n~ul
–
1,16363
1,16383
,
This is a considerable increase and the corresponding higher
discharge temperature of section I might render it impossible to
keep the inlet temperature to section II at the chosen level
(because of the intercooler capacity).
I
in all cases
>0,002
‘l,t,Te = a#2
0,0144
5,917
28,087
I
-
1,0075
0,8865
0,9W5 I
(p2Jpl)Te
—
3,370
3,233
3,177
I
()() I
PJ
P2
Te -G
x
2 = ~113K
Tt,l,l,Te
= 3152 K = Tt,l,ll,Te
I
—
—
0,008 0,005 0,006
<0,01 <0,01
<0,01
F.6.6.2.2.6
Determination of the settings must now be
repeated for section 1, but only at the outer tolerance limit
A Vr,x,to[
The answer to step 28 being “yes”, we can now calculate the
test speed.
The numerical results ere
+ 0,025
=
With the increased test gas inlet temperature, the correction of
the input list for the flow chart in figure D.7 is obtained as
follows.
Inlet conditions:
= 201,38 x 0,85448
X 315,2 J/kg
pt,l,l,~e
RGJl,GuTt,l,Gu = 238,66 X 0,9175
X 318,2J/kg
Tt,l,l,Te
= 3152 K
RTeZ1,Te Tt,l,Te
()
0,9142
~
,
In order to provide for a safety margin, the same test gas inlet
temperature will be used for both compressor sections, i.e.
Ex
I M,td
PI
()
2=W2K
Within the outer tolerance limit the required inlet temperature
to section I is much lower:
I ‘Te
Px
—
()PI
Tt,l,T~ = 303,2 x
0,9217
~
,
=
1,1bar (absolute)
~l,l,T.g = 1,11666
A vr,,y,t~
+
N,,td,ll
l(-) I
NTe
0,01
+ 0,025
– 0,01
– 0,025
0,8881
1,0075
0,8885
0,8805
0,8306
0,8384
0,9217
0,9142
Additional values:
zl,Te = 0,8871
NGU II
I
Xl,Te = 0,05314
Y,,Te = 1,01814
Comparison with the test speeds found for section I shows that
there exieta no common test speed for both sections, for the
test gas inlet temperature chosen.
From the flow chart in figure D.7, the following is valid:
rlwl = 0,63
As the inlet gas temperature to section II cannot be reduced,
the only way to achieve a common test speed is to increase the
inlet gas temperature to section I.
Assuming that N,,td and the compressibility factor Z1 remain
unchanged, the test apeed varies with the square root of the
absolute gas inlet temperature, i.e.
T1-—
p2/p,
= 3,433
m=
ml
= 0,1432
T2,Te = 376,10 K
lz2,Te - ZI,T81 = 0,0122>0,01
NTe 2
()
‘G.
lmTe -ml
= 0,01, not <0,01
as required
155
,...
(
-L
IS 14641:1999
ISO 5389:1992
.
Theabove calculation isthenrepeated within = mTe:
With comparison of the Reynolds numbet for the test and
specified conditions still to be performed, the speed chosen is
T2,~e = 371,48 K
!XE =0925
mT~ = 0,13403
[m~e-ml
NGU
‘
= 0,00083<0,01
= 10175 r/rein
‘Te
nTe = 1,13661
in~e - %ul
=
This test speed lies within the outer tolerance limit for section I
and within the inner tolerance limit for section Il.
0,02252>0,002
Additional values:
F.6.7
Test results
= 0,0835
‘2,Te
F.6.7.1 Compressor section 1
yzTe = 1,0292
z2,Te= 0,9739
F.6.7.1.1
cp2,Te = 2077,6 J/(kg. °C)
The test results are shown in table F.60.
Comparison with F.6.6.2.1.4 shows that here too the test gas
must be considered as a real gas.
We now continue with steps 30 and 31 of the flow chart:
I + 0,025
A Vr,x,tol
I ‘r,2
I
1()
Px
—
F.6.7.1.2
General
Evaluation of test results
Following clause 8, in particular 8.2.3 .3,8.2.3.4 and figure D.9,
the next steps will be
+ 0,0237
I
1,025
1,0237
I
0,5159
0,5531
PI Ex
a)
calculation of inlet and discharge total pressure;
b) determination of compressibilityfunctions required for
tha application of figure D.9.
I
F.6.7.1.3
3,447
~)Te-(?)
3,442
0,014
0,008
> 0,01
<0,01
I
Calculation of total inlet pressure (see table F.61 )
According to 8.1.3 the following approximation can be used:
Pt
—=l+;
P
Mtf
where
Note that in order to fulfill the condition
(qTe.~)
<0,01
A Vr,x,td had to be chosen somewhat smaller than the outer
tolerance limit, i.e. + 0,0237 instead of + 0,025.
(Condition: ~
C 1,05)
Gas constant: RTe = 201,36 J/(kg. ‘C)
Flange size: D = 0,4 m
The test speed now becomes
NTe
-‘G.
I
‘o=4zniiEz=-l
F.6.6.2.3 Choiceof testspeed
Comparison with the requirements for section II shows that it is
now possible to choose a common test speed for both compressor sections.
156
A = 0,126mz
Since the measured pressures and temperatures are not very
dtierent from the conditions assumed for the determination of
the settings (1, 1 bar; 315,2 K), the compressibility factor Z1
and ieentropic exponent K1 shall be taken in accordance with
F.6.6.2.2.6 :
z, = 0,8671
= z,,,,Te
K1 = 1,11666
= Kl,l,T@
-d
.
.-.LL
IS 14641:1999
ISO 5389:1992
Table F.60 – Test results
Numerical value
Symbol
Designation
Unit
Gasconstant
RTe
J/(kg. °C)
Spaed
NTS
r/rein
Massflow (usable)
7
in accordancewith ISO 5167-1
qm,ut,Ta
Inlet and discharge conditions
Inlet pressure (static)
Pl,l,Te
Inlet temperature (total)
Tt,l,l,Te
Discharge pressure (static)
p2,1,Te
Discharge temperature [total)
Tt,2,1,Te
a
4,0828
4,02s 1
3,9388
4,1533
m
kgls
bar
K
bar
K
Teble F.61 – Celculetion of total inlet pressure
Numerical
Symbol
valua
Unit
Teat No. 1
Teat No. 2
Teat No. 3
Taat No. 4
Mat
0,0665
0,08s 1
0,0700
0,0711
—
Pt,l/Pl
1,00248
1,00284
1,00274
1,00283
—
pt,l = pt,l,l,Te
1,1127
1,1049
1,1020
1,1001
bar
Teble F.S2 – CaIculetion of total discherge pressure
b
Numarical
Symbol
last
No. 1
0,0350
Mat
value
Unit
Tast No. 2
Test No. 3
Test No. 4
0,0377
0,0388
0,0420
—
—
l,ooom
1,000776
1,000S64
1,000883
4,12s
3,912
3,783
3,613
F.6.7.I.4 Calculationof total dischargepressure(seatable
F.62)
F.6.7.1.5
Pt,2/P2
Pt,2 = Pt,2,1,Ts
Flange size: D = 0,3 m
A = 0,0707
Here the same simplificaticrraa used for inlet pressure shall be
used.
The compressibility functions Z and rccan be derived from the
calculation already completed in F.6.6.2.2.6, with
K=
1
Z@
Y2 - —(1
CP2
+ X2)2
Z = 0,9739 = zz,l,Te
K=l,Wl
S=
K21Te
,,
A subsequent check will ahow whether this simplification is
admissible.
Calculation results
Table F.63 givea the following results:
a)
mz
bar (absolute)
reduced pressurePr and reduced temperature Tr;
b) compressibility factors Z(o) and Z(l) and derivative
~mpre88ibility factom ‘T(0), ZT(1)?‘p(0)and z~~~as a fun~ion
of reduced pressureand temperature, according to annex A
and figure F.18
c) compressibility factor Z and derivate compressibility
factors ZT and ZP resulting from the above fi9ur* in combination with the acentric factor of the test gaa (see
annex A);
d)
compressibility functions ~ and Y (see annex A);
e)
specific heat
CP
=
cp,Te
(see figures F.16 and F.17).
All the above values shall be determined for inlet and discharge
conditions.
157
.,
IS 14641:1999
ISO 5389:1992
Table F.63 – Calculationresults
Designation
Symbol
Inlet
(subscript to all symbols: 1, l,Te)
Numerical
Test No. 3
Test No. 4
Pr
0,02664
0,02635
0,026 2S
0,02624
T,
0,6843
0,8955
0,6863
0,s86o
K
z(l)
2+0)
bar
0,8679
0,8679
0,9679
—
– 0,0051
-0,0051
-0,0050
– 0,0050
—
1,038
1,039
1,039
1,038
—
—
0,8678
z~l )
0,046
0,046
0,045
0,04
2;0)
1,005
1,005
1,005
1,005
Zy)
o
0
0
0
z
0,9671
0,8872
0,8s72
0,M72
zT
1,0453
1,0453
1,0452
1,0045
2P
1,(N)5
1,005
1,005
1,006
—
x
0,05805
0,05683
0,05673
0,05s 03
–
Y
1,01819
1,01808
1,01802
1,01802
—
CP
1796,0
1797,0
1788,0
1788,5
J/(kg. °C)
Pr
0,08845
0,08330
O,m 75
0,0s617
bar
‘r
z (0)
1,0629
1,0688
1,0578
1,0546
K
0,9722
0,9734
0,9743
0,9752
—
– 0,0021
-0,0020
-0,0021
z(l)
-0,002
2+0)
1,057
1,056
1,0575
1,0558
z+’)
0,043
0,048
0,048
0,045
Zjo)
1,002
Zjl)
F.6.7.I.6
Unit
Tast No. 2
z(o)
Discharge
(subscript to all symbols: 2,1, Te)
value
Test No. 1
-0,004
1,002
l,m
1,002
0
0
+ 0,002
z
0,9719
0,9732
0,9740
0,8749
zT
1,W29
1,0647
1,W42
I,mo
—
2P
1,00145
1,002
1,002
1,0028
—
x
0,0836
0,09411
0,08262
0,068 3s
-
Y
1,03Q3S
1,02863
1,02872
1,02s 12
CP
2 @2,6
2065,5
2060,1
2075,5
J/(kg . ‘C)
Verification of inlet and discharge total pressure
With the data from table F.83, the exact value of the iserttropicexponent can now be calculated, according to Schultz’s formula (see
table F.64):
K =
Y-
:’(1
+W
Table F.64 – Values of isentropicexponent
Symbol
158
Numerical
value
Test No. 1
Test No. 2
Test No. 3
Test No. 4
~l,l,T@
1,1185
1,1185
1,1184
1,1182
K2, I,Je
1,0667
1,0803
1,0815
1,0818
Unit
-e
“’
..ti
IS 14641:1999
ISO 5389:1992
‘-,
F.6.7.1.8
It is now possible to check the calculation of absolute pressure
made in F.6.7. 1.3 and F,6.7.1 .4, notably for discharge conditions.
The ratiopt/p being small, considerably below 1,06, no relevant
numerical difference can be found. The above total pressures
and the compressibilityfunctions in table F.63 will therefore be
used in the following.
F.6.7.1.7
Calculation according to figure D.9
The calculation continues with the computation of the test
values to be converted to specified conditions in accordance
with figure D.9 (Schultz’s method of polytropic analysis).
[
‘These values are
a)
the inlet VOIUr’nf3triCflow q r/,t,l,Tegiven by
‘vtlrTe=(qm’”z;T’’’)T
Input values for figure D.9
Evaluation of the test resultscontinues with the computation of
the mean compressibility functions required for the application
of the formulae given in the calculation flow chart in figure D.9.
b)
the pressure ratio (pt,z/Pt, l)T~
c)
the polytropic temperature
d)
the polytropic exponent nTe given by
mTe given by
exponent
The values to be calculated are
a)
the compressibility factor
z, + Z2
~
z~=
1
t?Te=
b)
x~=
\
[
the compressibility functions
x,
yM–t?r(l+xM)
1Te
e) the specific polytropic compression work ~m,wl,Te
given by
+ X*
~
n-1
Y, + Y2
~
Y~=
c)
‘m’’0’’Te=~z1RT[(3
the specific heat
f)
[(3
n
-
‘IT.
the polytropic efficiency q@,Te given by
RZ~
Cpl + cp2
CPM =
Vpol,Te =
2
(
The input values calculated are given in table F.65.
rncPM – RZMX~
)
T,
The calculation results are given in table F.66.
Table F.65 – Input values for figure D.9
hlumericei velue
Symbol
Unit
Test No. 1
Test No. 2
Test No. 3
Test No. 4
‘M,l,Te
0,97848
0,88016
0,88062
0,88104
—
‘M,I,T.
0,07633
0,07652
0,07588
0,07371
.
‘M,I,T.
1,02428
1,02368
1,02337
1,02307
—
cpM,l,Te
1844,3
1841,3
1838,6
1837,0
J/(kg. °C)
Table F.66 – Calculation results according to figure D.9
Designation
Volume flow
Numarical
Symbol
qV,t,l,l,Te
- ,<.
value
Unit
Test No. 1
Test No. 2
Test No. 3
Test No. 4
2,2129
2,2634
2,3285
2,3683
rr+ls
3,4147
3,2643
—
Preesura ratio
(P,,2/P’,1 )l,Te
3,7087
3,5406
Polytropic temperature exponent
ml,Te
0,13161
0,13315
0,13481
0,13884
—
Polytropic exponent
nl,Te
1,13288
1,13588
1,13648
1,141 %
—
Specific work
w m,pol,l,Te
86642
& 481
83045
80305
J/kg
Polytropic efficiency
Vpol,l,Te
0,819
0,811
0,801
0,786
—
I
159
IS 14641:1999
ISO 5389:1992
F.6.7.2
F.6.7.2.I
Compressor section II
General
The test results are shown in table F.87.
The inlet pressure is the discharge pressure of section I (see
8.2.4.2).
As a first approximation of the compressibility factor Zz and
ieentropic exponent rc2, the values resulting from the above
calculations made for the det~rmination of the settings will be
used. Since tha test speed corresponds to the inner tolerance
limit, the arithmetical mean of the values found for A Vr,X,td =
+ 0,01 and A Vr,x,td = – 0,01 is chosen. The results are
The usable mass flow, compressor speed and gas constant are
the same as for section 1 (see table F.80).
A Vr,x,tOl
Computation of the test results shall follow the same pattern as
for section 1. In the following subclauses therefore, only the
results are given.
Z2
F.6.7.2.2 Calculationof total discharge pressure (see table
F.68)
– 0,01
+ 0,01
Tt,2 (in kelvins)
I
i K2
*-P .-,
385,52
384,12
0,92099
0,92190
1,0599
1,08231
I
which gives the mean values
Z2 = 0,9214
Flange size: D = 0,2 m
1,0611
K2 =
A=0,0314m2
Table F.87 – Test results
Numerical
Symbol
Designation
velue
Test No. 1
Test No. 2
Test No. 3
Test No. 4
Unit
Inlet and discharge conditions
Inlet pressure (total)
Pt,l,ll,Te
4, i2s
3,912
3,763
3,613
bar
Inlet temperature (total)
~t,l,ll,Te
314,8
315,1
315,5
315,3
K
Discharge pressure (static)
P2,11,Ts
14,466
13,045
11,445
9,5336
bar
Discharge temperature (total)
~t,2,11,Te
369,37
3s6,0
361,66
377,18
K
4
,,
.
Table F.88 – Calculationof total dischargepressure
Symbol
Mat
160
Numerical
value
Unit
Teat No. 1
Teat No. 2
Test No. 3
Test No. 4
0,0226
0,0255
0,02s4
0,0356
—
Pt,2/P2
1,0027
l,otxJ35
1,00046
l,oa)66
—
pt,2= pt,2,11,T~
14,47
13,06
11,46
9,54
bar
...
--A.
IS 14641:1999
ISO 5389:1992
.
F.6.7.2.3 Calculation
results
.
TableF.69 showa the calculation results for reduced pressures and temperatures, compressibility factors, compressibilityfunctions ~
and Y, and specific heat.
-“
‘
F.6.7.2.4
Verification of total discharge pressure
The calculation of the iaentropic exponent at discharge conditions resulting from the date given above gives the results shown in
table F.70.
Here again, the recalculation of total discharge pressure using the abova exact valuea of 22 and K2 showa no significant corrections,
as the ratio pt,2/p2 is low. The above total pressures and compressibility functions will therefore be used in the following.
Tabie F.69 – Calculation results
A
Symbol
Designation
Inlet
(subscript to all symbols: 1, lLTe)
valua
Teet No. 3
Teet No. 2
bar
0,08645
0,08330
0,08875
0,06617
0,6846
0,6855
0,6966
0,6860
K
0,8590
—
‘z(o)
0,8527
z(l)
-0,0123
2+0)
1,113
0,8553
0,8574
-0,020
1,111
-0,0188
-0,0182
1,110
lrlw
—
—
Z+l )
0,165
0,17
0,144
0,145
2;0)
1,010
1,010
1,008
1,008
– 0,002
-0,0025
0,8526
0,8548
-0,002
0,8488
-0,002
0,8565
—
.z~
1,1365
1,1344
1,1288
1,1200
—
2P
1,0089
1,0087
1,0067
1,0097
—
x
0,18867
0,18080
0,16326
0,17068
-
Y
1,06327
1,06003
1,05638
1,05460
—
Cp
1652,6
1647,5
1647,0
1845,0
J/(kg. °C)
Pr
0,3451
0,3112
0,2731
0,2275
bar
Tr
1,1068
1,0871
1,0655
1,0720
K
z (0)
0,9109
0,9178
0,9250
0,8358
—
z(l)
-0,0005
– 0,0025
0,0045
0,0018
2+0)
1,226
1,205
1,1805
1,151
2+1)
0,122
0,121
0,111
0,?03
2:0)
1,0055
1,0061
1,0045
1,004
z~)
-0,026
-0,016
-0,025
0,9115
0,9181
0,8249
0,8355
zT
1,2428
1,2217
1,1853
1,1652
1,00165
1,00266
1,0023
1,0031
0,24557
x
0,36342
0,33070
0,28228
Y
1,08668
1,08217
1,06365
1,07254
CP
2267,5
2240,3
2206,7
2168,5
labia F.70 -
Isentropicexponent valuee
Test No. 1
Test No. 2
Test No. 3
Teet No. 4
1,0544
1,0570
1,0608
1,0664
Numerical value
—
-0,005
z
2P
‘2,11,Te
Unit
Tr
i!
Symbol
Teat No. 4
Pr
Z$t
Discharge
(subscript to all symbols: 2,11,Te)
Numerical
Tact No. 1
—
–
J/(kg . ‘C)
Unit
—
l,,tij
IS 14641:1999
ISO 5389:1992
F.6.7.3
Conversion toguarantea
conditions
is the internal leakage loss in cubic metres per second, with
Qt,l,Guin kilograms per cubic metre.
F.6.7.3. I
-,
General
The results for compressor sections I and II shall be converted
to guarantee conditions separately, in accordance with
figure D.9.
(There is no noticeable
seals. )
external
leakage
This formula is baaed on the agreement
The input values for figure D.9 are given in table F.71 and the
calculation raaults aregiven intable F.72.
Performance curves are then to be plottad for each section
separately and the steepness of the pressure-volume curves as
defined in this International Standard shall be checked. (The
curves are assumed to be steep. )
The converted performance curves of sections I and II will then
be combined to give the performance curve of the compressor.
loss because
of oil
made before the teat
of the converted discharge
pressure of section II. As the two sections will be converted
separately, a problem arises for section 1. The difficulty can be
overcome by adding the loss to the total compressor power
after combination of the performance curves of both sections.
and
raquires
the
knowledge
As a consequence, the following modified conversion formulae
for internal compressor power will be used and plotted for use
according to figure D. 11 (combined performance of both compressor sections).
This combination follows figure D. 11 inasmuch as it is applicable to real gases and Schultz’s polytropic analysis.
a)
F.6.7.3.2
Compressor section:
Conversion formulae (sea figure D.9)
‘in,Co
Some comments are necessary regarding calculation of
converted internal power, especially regarding consideration of
leakage Ioaaaa.
1+
‘in,Co
=
@t,l,Gu
x
b)
qV,t,l,CO x ‘m,pol,Co
~pol,Te
, + ‘gV,t,l,L,Co
qv,t,l,co
(
qv,t,l,co
(
The following formula will be used:
)
‘(
qv,t,l,co
)
~ Pt,2,11,co
Pt,2,11,Gu
@t,l,Gu
where qm,ut,cois expressed in kilograms per second.
Table F.71 – Input values for figure D.9
Numericel velue
Symbol
Test No. 1
Test No. 2
last No. 3
Test No. 4
‘M,ll,Te
0,8306
0,9353
0,9399
0,9460
‘M,ll,Te
0,2811
0,2608
0,2378
0,2062
‘M,ll,Te
1,0810
1,0781
1,0700
1,0638
cpM,ll, Te
2060,1
2043,9
2026,9
2 IXM,8
Unit
—
J/(kg. °C)
Tabla F.72 – Test valuas to be convertedto specified conditions
Numerical
Symbol
162
~p@Te
Compressor:
(
fiqv,t,l,L,co=
qv,t,l,CO x ‘m,pol,Co
p, co _ (pin,l,c~ + Pin f\,cJ , +
0,5
~ p~,z,ll,co
m, qln,ut,co
, + ‘qV,t,l,L,Co
‘t,2,11,Gu)
)
where
0,5
= @t,l,Gu x
‘q V,t,l,L,Co
Test No. 1
Test No. 2
qV,t,l,ll,Te
0,6742
‘~t,2/~t,l )ll,Te
3,5063
‘?lll,Te
veiue
Unit
last No. 3
I Test No. 4
0,6223
0,6587
0,6961
3,3369
3,0428
2,6405
0,16949
0,16846
0,17160
0,16456
—
‘ll,Ts
1,15756
1,1578)
1,16602
1,16965
—
w m,pol,ll,Te
82346
79131
73140
qpol,ll,Te
0,632
0,638
0,825
I
dts
J/kg
0,576
—
E
IS 14641:1999
ISO 5389:1992
F.6.7.3.3 Sectionl numericalresults
Input data for figure D.9 which correspond to specified conditions are already known, except for the gas density, from the input list to
figure D.7 (determination of the settings, see F.6.6.2.1 .6).
The gas density is
3 x 105
I,Gu
Pt, 1,
@t,l,l,Gu= RGUZt , , ~uTt 1I G. =
236,66 X 0,9753X
,,,
,,,
= 4,142 kglms
311,2
The calculation results are given in table F.73 and are plotted in figure F.19
Table F.73 – Calculation results – Saction I
Symbols
and formulae
Numerical
Teet No. 1
value
Teat No. 2
Teet No. 3
Teet No. 4
Unit
qv,t,l,l,co
2,3823
2,4865
2,5173
2,5582
@/s
w m,pol,l,Co
103588
99804
97058
83s55
J/kg
ml,co
0,15392
0,15528
0,15705
0,15839
—
nl,co
1,1554s
1,15756
1,16023
1,16378
—
(/J@p~,l )I,co
3,688
3,538
3,419
3,2s8
—
302,6
304,1
3’4,1
3G4,7
kW . mVkg
Pin,l,cO
‘tld’+-)l,co
For comparison, valuea corresponding to the specified point are as follows:
f?V,t,l,l,Gu = W5
(Pt,2/Pt,l)l,’u
rn3/s
= 3,433
[Qtll~;:~:lllGu=a2
The pressure-volume curve is steep.
F.6.7.3.4 SectionII numericalresults
Input data for figure D.9 corresponding to specified conditions ‘are given in F.6,6.2.2.4
The gas density is
Pt,l,ll,Gu
10,3 x IN
, II GUTt , II ‘u = 238,86X
‘t’l’ll’Gu = RGuZt ,,,
,,,
0,9175X
318,2
= 14,78 kglms
The calculation results are given in table F.74 and are plotted in figure F.20.
Table F.74 – Calculationresults – Section II
Symbols
and formulae
Numerical
last
No. 1
value
Teat No. 2 I Teat No. 3
Unit
TaatNo. 4
4v,t,l,ll,co
0,6207
0,6278
0,7132
0,7547
rn31s
w m,pol,ll,Co
86240
92483
854s1
74532
J/kg
mll,co
0,19284
0,19152
0,18463
0,20758
—
nll,co
1,17167
1,16888
1,17504
1,20146
.
(pt,2/pt,l )Il,co
3,67s
3,36s
3,096
2,675
.
97.52
97,55
97.85
‘W. rrWkg
Pin II co
84,52
‘t’’’Gu+*),Lcoco
163
IS 14641:1999
ISO 5389:1992
ValIJes
corresponding
to the specifiedpointareas follows:
~P’,t,l,lI,Gu
=
Q~65m3/s
@t,2/~t,~)ll,Gu
=
3,301
Pi
= 97,68 kW. m3/kg
f.iqv,t,l,L
al
[(”i
1 +
II,Gu
qv,t,l
The pmsure-voiuma curve is steep.
The test results therefore confirm the assumption made when determining the settings.
F.6.7.4
Total compressor performance
F.6.7.4.1
General
The conversion formulae are based on figure D. 11.
For a chosen value of converted inlet volume flow of section 1,the combination of the performance curves of both sections is carried
out as described below.
F.6.7.4.2
Section I
F.6.7.4.2.1
Choose the inlet volume flow qv,t,l,l,co.
F.6.7.4.2.2
Read (pt,2/pt,l)l,c0 from the performance curve in figure F.19 and
r
l@tl~+*)Jl,co
Pin
F.6.7.4.2.3
1
Calculate
()
Pin
~ + Aq~t,l,L
qv,t,l
Lco
and
Pt,l,l
&?t,l,l,Co = @t,l,l,Gu =
[1
(.z#7’t,l)l
Gu
F.6.7.4.3 SectionII
F.6.7.4.3.I Calculate
the inletvolumeflow
1
flv,t,l,ll,co
F.6.7.4.3.2
= qv,t,l,l,co
(Pt,2/Pt,l)I,Co
[( )1
164
(Zl R Tt,l)I
@
Read (pt,2/pt,l)ll,co from the performance curve in figure F.20 and
Pi.
Qt,l
(Z,lwtr,)ll
[1
Aq},t,l,L
1 + ~
,,
11,
co
IS 14641:1999
ISO 5389:1992
L
4
.s
\
Specified points
O
Test points
310
‘E
3
305
p1
2
I
I
300
295
L
290
I
#
m
Steetmess
A(ji2iq )Q9K1 0,278”2,511
1
A q~dP2
/P1 )
3,7
1
0,10.3,433—
=
2,033>1
KT
d
<1
3,6
2
(P2@t,I,co
3,5
I
3,4,
3,3
3,2 I
2,35
i
I
lln’
2,40
I
I I
I
2,45
2,50
2,55
qvtj,l,co’
m3/s
Figure F.19 – Compressor section I performance cunfes
2,60
&
IS 14641:1999
ISO 5389:1992
O Test points
L
— Specified points
99
.5?
>
E
98
2~
L
u i
3’
,
k
97
d
4
[( )1
Pin
‘qVtl,
9~,
96
L
I+*
Kt,l
l,CO
95
(
94
1=
I
I
Steepness
A@/q 1“qtil
0,535.0,683
Aq@2
0,08.3,301
3,6
1
/P1 )
1,384 >1
k
@2 /PI
lt,ll,co
–
3,4
-—-.
-——
I
I
3,2
I
I
I
\
3
b
I
3,0
I
E
I
2,8 L
I
I
2,6 L
0,62
i
I
0,64
0,66
0,68
~v,tJ,II,
Figure F.20 -
4
0,70
co’m3/s
Compressor section II performancecutves
0,72
0,74
0,76
IS 14641:1999
1S0 5389:1992
F.6.7.4.3.3 Calculate
F.6.7.4.4
Total compressor performance characteristics
The total compressor performance characteristics are as follows:
a)
usable mass flow
~m,ut,co = qv,l,l,co
b)
x @t,l,l,Gu
discharge pressure
“21’cO=pt’’Gux(~),co
x(~)lc0
c)
internal power
Pifl,~O =
[(l+-)c:(l+-).Jxi+*)’cO
where
0,5
Pt,2,11,co
.—
~V,t,l,L,l,Co – ~1 , , ~u x
Pt,2,11,Gu
,,,
is in cubic metres per second, and &’t,l,l,@ is in kilograms Per cubic metre;
d)
power at coupling including gear losses
Pe,co =
(pin,co
+ Pf,~l,Gu) X &
where
~f,Oil,@ = 58 kW
0,974 is the step-up gear efficiency [see F.6.5).
F.6.7.4.5 N~rnerical
results
NOTE — The following point numbers bear no relation to the test numbers used previous!v.,
%,l,l,G.
= 4142
Wrn3
(Z+?
rt,l)ll=
u
(s*
F.6.7.3.3)
0,9175
X 236,66 X 318,2
= o WI
0,9753
X 238,66 X 311,2
‘
..
~, ZIRTt,
i)l
GU
Pt,l,l,Gu
=
3 bar (absolute)
~
Pt,l,ll,Gu = 34 bar (absolute)
Pt,l,l,Gu
= 4,3056 kglms
(i?@~t,l)ll,Gu
A synopsis of the numerical results is given in table F.75.
167
, ,@
IS 14641:1999
ISO 5389:1992
Table F.75 – Synopsis of numericel results
Symbols
and formulae
Designation
Numerical
value
Point 1
Point 2
Point 3
Point 4
Unit
Section I (see figure F.19)
Volume flow
qv,t,l,l,co
2,40
2,45
2,50
2,54
m3/~
Pressure ratio
(P~,2/pt,l )I,co
3,664
3,563
3,46i)
3,347
–
Pin
302,75
303,60
304,60
304,95
kW. ins/kg
1253,9
1 2%,2
1262,4
1263,0
kW
Internal power, specific
Qt,l
[(
Internal power
Aql, tl L
1+ ~
.,
II I,co
Pin
, + Aqv,t,l, L
()
qv,t,l
I,co
Section II (see figure F.20)
Volume flow
~v,t,l,ll,co
0,6266
0,6577
0,6950
0,7300
rn3/~
Pressure ratio
(/J~,2/pt,l)ll,co
3,570
3,432
3,226
2,930
–
Pi”
95,m
97,07
97,55
97,66
kW. m3/kg
1520,1
1497,5
1453,2
1407,4
kW
10,52
kgls
Internal power, specific
Qt,l
[(
Aqv,t,l,L
1+ —
co
9V,!,1 i 11,
Pi”
Internal power
, + AqV,t,l,L
()
qv,t,l
11,
co
Totsl compressor performance
(see figure F.21 )
Usable mass flow
qm,”t,co
994
10,15
10,35
Discharge pressure
Pt,z,ll,co
36,79
36,69
33,49
29,42
bar
Relative leakage loss
Aqvtl
0,0675
0,0535
0,0476
0,040:
–
-
L
qv,t,l
Internal power
Pi”,c~
2922,9
2903,1
2644,9
2779,6
kW
Power at coupling, including gear Ioas
‘e<Co
3,060,5
3040,1
2960,4
2913,3
kW
F.6.7.5
Test uncertainty
F.6.7.5.1
specified point. The polytropic compression work was taken
from a plot against converted inlet volume flow:
Resulting test uncertainty
The additional
tolerance
Twj is found in accordance
w.m,pol,l,co = 101050 J/kg
with the
graph shown in figure D.2.
wrn,poi,ll,co = 94 ~
J/kg
Section I
Z Wm,Wl,co = 101050 + 94 OiM = 195050 J/kg
A V&o, = 0,025
?Aj=l%
Section II
The test uncertainty in the internal power of a compressor section was estimatad as the result of the uncertainties in usable
mess flow and in the gas temperature difference between
outlet and inlet, again for the conditions of point 2.
A Vr,tOl= 0,01
~~~i= O
The resulting test uncerteintias were calculated separately for
both compressor sections and then combined in accordance
with 9.2.7.
The uncertainty in the combined pressure ratio was calculated
for the conditions of point 2, which are closest to those of the
168
The uncertainty in the combined internal power was calculated
for the conditions of point 2
Pin,l,co = 1,0535X 1256,2
= 1325,5 kW
Pin,ll,co = lt~ 5 X 1 W,5
= 157,6
Zpin,co = 1 325,5+
kW
1577,6 = 2903,1 kW
%-
IS 14641:1999
ISO 5389:1992
Pin,ll,co = 1577,6 kW
The uncertainty in the combined power at coupling is
calculated in accordance with the method of power measurement 1 for a cooled compressor (see 8.2.4.2) given in table 9.
Pf,cO = 137 kW
F
F.6.7.5.2
Comparison with auarantee
For point 2 we obtain
Pin,CO = 29WI
According to 9.3.2 the guarantee is not fulfilled as regards mass
flow, which is slightly higher than that specified, even taking
into account the test uncertainties. See also figure F.21.
1 kW
l-’e,co = 3040,1 kW
F.6.7.5.3
Synopsis
(p2/pl)l,co
given in table F.76.
A synopsis of the resulting test uncertainty
= 3,583
for example
6 is
Table F.76 – Resulting test uncertainty
Numerical
Symbol
Designation
Uncertainty in volumetric
flow at inlet
r
value
Section II
Comments
Section I
2,1 %
2,1
q,,, .Te
‘pl,Te
0,14 %
‘T1,Te
0,35 %
‘Z1,Te
0,5 %
‘res
See ISO 5167-1
Yo
0,1 %
0,1 %
‘N,Te
Comments
0,95 %
(U-tube) (mmHg)
Quality grade 0,6;
final value 5 bar gauge
0,35%
0,5 %
[Estimated)
2,19 %
2,38 %
See 9.2.5
‘adj
1%
o
‘tot, qv,l,Te = rtot,qm,ut,co
2,41 %
2,39 %
[Estimated)
See 9.2.9
Sea 9.2.8.1
~ (1 + 0,2) x (2,41 + 2,39) = 2,86 %
‘comb,q,n,ut,Co
with z = 2
Uncertainty in pressure ratio
Nr
0,995
0,992
ln(p2/pl )
1,234
1,194
(P2/pl)Gu
‘~,Te
0,85 %
1,20 %
Cluality grade 0,6;
final value 25 bar gauge
See 9.2.6
See Tpl,Te, Section II
Trea
1,75 %
2,09 %
‘adj
1%
o
‘tot, @pl,Te
2,02 %
2,08 %
‘comb,
(1+0,2) 2,02 x*+
p2/pl,Co
(
Uncertainty in power
at coupling
with z = 2’
SW 9.2.8.2
—
4%
4%
‘adj
1%
o
‘tot, Pin,Ts
4,1 %
m
(1+ 0,2)
4,1
(
Pi.
=09wg
Pe
‘
Pf
—
Pe
?Comb,pe,co= [(0,8549x
= 0,04506
x =
For point2 conditions,
=2%%
)
7Pin,Te
‘comb,Pin,Co
Uncertainty in combined
power at coupling
(sea table 9)
2,08 x*
(Estimated)
4%
+ 4 x H
= 4,85%
2W3,1
)
with Z = 2
Cp= 0,543
For point 2 conditions,
see 9.2.8.3
,n &
()
.12762
P1l’
4,85)’ + (0,04506x 10)2+ (1,864x 0,1)2+ (0,15x 0,35)2 + (0,15x 0,5)2 +
+ (0,543 x 0,35)2 + (0,543 x 0,5)2] 1/2 = 4,67 %
assuming that rpf = 10 %
169
IS 14641:1999
ISO 5389:1992
L
3400
—
3200
—
Specified points
o
Points resulting from combination
of converted test performance curves
3
x.
0
J-
3000
—
2800
~;
L
2
40
—
1
2.
j
38
—
36
—
34
—
—.
32
30
1
28
9,6
9,8
10,0
10,2
10,4
q~u,,,,k9/s
,,
Figure F.21 – Totel compressor performance curves
10,6
10,8
IS 14641:1999
ISO 5389:1992
Annex G
(informative)
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Data Book, Gas Process Suppliers Associ-
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