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D I S C U S S I O NT. E . Blehar1
1 Based on previously conducted gas property metho dcomparison
studies, i t has been my experience that workfactors that deviate
from 1.0 by more than 1.5 percent areindicative of erroneous or
inconsistent gas properties orequations of state in that particular
region. That is, byutil izing multiple gas property methods, i t
often becomesapparent that the gas method that yielded a 0.89 or
0.94 workfactor (as in Mr. Huntington's examples) was, in fact,
inconsistent with other more applicable gas methods. The
moreaccurate gas property methods resulted in work factors
nearer1.0, and in fact values of polytropic head and
efficiencynearer the design and expected values. The differences in
theseresults, then, were functions of the different gas
propertymethods and not the Schultz equations. For this reason, i
twould appear to be more beneficial to select examples withgas
property methods that resulted in work factors nearer 1.0for Mr.
Hunt ing ton 's comparisons. This may y ield a moreval id com
parison .2 The work factor deviations occur most frequently
overlarge compression paths. As Mr. Huntington has subdividedthe
compression path into shorter polytropic paths (which, infact, more
closely approach the isentropic path in the ex
treme), a more valid comparison would be to evaluate theSchultz
method over these same smaller intervals, and sum theresults. In
this ma nner the work factor should appro ach 1.00for each of the
shorter paths and yield more accurate resultsor minimally a more
valid comparison.3 The area of application and gas property
evaluationrelative to the "d om e " or crit ical point has a
significant effecton the long path of compression versus the short
pathevaluation due to large variations in gas properties in
thatregion. Therefore, the area of application and range of
gasprope rty accuracies for that area would be of value inassessing
the significance of the differences in calculationmethods. That is,
if the gas properties are highly inaccurate inthe area of
evaluation, then a 1.0 percent difference incalculation m ethods m
ay not be a significant value.In conclusion, I would like to
compliment Mr. Huntingtonon his efforts to identify a more accurate
method to evaluatecentrifugal compressor performance. The range of
pressure,temperature, and gas mixture applications and
requiredaccuracies has change d considerably since the original
Schultzpublication. It is a credit to Mr. Huntington that he
hasdevoted considerable t ime and effort to question,
investigateand improve those methods. As a final note, if
furthercomparisons are conducted relative to my above comments,
Iwould be interested in discussing those results with Mr.Hu n t in
g to n .
Author ' s Clos ureMr. Blehar's comments generally deal with two
areas ofconcern: firstly, the question of the use of appropriate
gas
property methods and data and secondly, the large deviationsof
the Schultz polytropic head factors from 1.0. While Mr.Blehar is
correct in stating that the use of inaccurate gasproperties may
result in significant errors in the/-factor, i t isnot clear that
deviations in /f r o m 1.0 are alone sufficient tocondemn a gas
property method as inaccurate. If this weret rue, our
thermodynamicist colleagues would have a simpleand efficient method
to evaluate equations of state. In addition, they would always
conclude that the perfect gasequations were best since they are
quaranteed to give/-factorsequal to 1.0. Realistically, one must
accept that some com-Senior Engineer, Compressor Design and
Development, General ElectricCompany , F i tchburg, MA 01420.
pression services, especially high-pressure services
wherecompressibili ty factor changes m ay be 30 percent or mo
rebetween inlet and discha rge, may have /-fac tors that de
viatesignificantly from 1.0. These deviations are simply an
indication of the nonide ality of the compressed gas for the
givencondi t ions.The scope of the paper has been limited to a
comparison ofthe three simple (i .e., hand calculable) polytropic
head/ef-ficiency calculation methods versus the precise
reference(numerical integration) method and did not include
anevaluation of the effects of various gas property
evaluationmethods. In fact, the use of a single accurate source for
gasproperties for all of the metho ds was intended to eliminate
gasproperty deviations as a source of comparative error betweenthe
methods evaluated and the reference method. However,preliminary
studies to this work were carried out usingeq u a t io n s o f s t
a t e (Red l i ch -Kwo n g an d Red l i ch -Kwong-Soave) that are
considered to be less accurate than theLee-Kesler equation of state
that was finally used. Thesepreliminary studies showed similar
relative comparisonsamong the methods as those given in the paper.
This validatedthe use of a single gas property source to eliminate
gasproperty deviations as a source of relative error between them
eth o d s .
Regarding the specific source of gas data for the examplescited
in the paper, each calculation method demonstrated (andthis
includes the reference method) used an identical equationof state
with identical basic gas data (crit ical pressure, tem-
l ' 1 PRESSURE (PSIA)Fig. 1 Specific volume versus pressure
along the constant efficiencypolytropic path calculated by the
reference method for case 4
Fig. 2 Percentage deviation from the reference of the specific
volumeversus pressure paths predicted by the three simple
methods
Journal of Engineering for Gas Turbines and Power OCTOBER 1985,
Vol . 1 07/877Copyright 1985 by ASME
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perature, specific heat function, etc.) for i ts calculations.
Theequation of state used was the Lee-Kesler equation cited in
thepaper and recom mend ed by the Reid, Sherw ood, an dPrausnitz
text also cited. The source of basic gas data forRefrigerant-12 was
from Dupont l i terature on Freon while theother basic gas data for
carbon dioxide and ethylene weretaken from the Exxon proprietary
gas data l ibrary which hasbeen used and refined over the many
years of Exxon's gashandling experience. Finally, the equation of
state and basicdata were coded into a single gas property computer
subprogram to provide functionally continuous gas
propertyevaluations for each of the methods.Mr. Blehar also states
his belief that the comparison of theSchultz method to the
reference method is perhaps not validsince the reference subdivides
the polytropic path into manyshort paths while the Schultz method
is asked to negotiate theentire path in one step. It is clear that
subdividing thepolytropic path significantly reduces the gas
propertyvariation along each subpath and makes calculation
ofpolytropic head much more accurate. This is precisely the
ideabehind the reference calculation method. What is not clear
ishow Mr. Blehar would use this subdivision technique toimprove the
Schultz method without completely duplicatingthe calculation
procedures used by the reference method.There fore, since this
"subd ivid ed" S chultz metho d and thereference method would be
essentially identical, comparisonsbetween them would be
pointless.
Since it is clear from the discussion above that Mr.
Bleharagrees (at least in concept) with the reference method,
hiscomments do not address the major focus of the paper whichis
simply the order-of-magnitude accuracy improvementpossible with the
new polytropic calculation method (equation(22)) developed in the
paper over the previous "simple"methods in comparisons to the very
precise reference. Tounderstand the reasons for the better accuracy
of the newmethod, i t is best to look at the definition of
polytropic headgiven by equation (2). This equation simply
represents thearea under the curve of specific volume versus
pressure alongthe polytropic path. This functional curve as
produced by thereference method for example case 4 is shown in Fig.
1. Thearea under this curve is the reference head. The
simplepolytropic methods, through their assumptions and
basicequations, either explicit ly or implicit ly approximate
thiscurve in order to calculate head. Deviations between
theseapproximate curves and the true curve may lead to errors
inpolytropic head and efficiency. Figure 2 is a plot of
thesepercentage deviations for all three of the simple
methodspresented in the paper for example case 4. As can be
easilyseen, the Schultz and the M allen and Saville curves (labeled
asPTC and M&S) deviate significantly from the reference
curve(Fig. 1) in both bou nded area and curve shape. In c ontras t
,the new method (labeled as RAH) is barely discernible fromthe
zero-error axis and thus shows that i t best matches th e
truepolytropic path and will produce the most accurate resultswith
consistency.
A. A. Fozi2I would like to congratulate the author for his
contributionto better understanding of the polytropic analysis.
Themethod described in the paper as the "reference method" doesin
fact yield the most accurate evaluation of the polytropicvalues as
defined by the equation
ed h = VdP (e = const)John Schultz, in his original paper,
showed an approximateintegration method by use of auxiliary
polytropic constants in
an d n. Mr. Huntington proposes to do the same by
numericalmethods utilizing computers for achieving very high
accuracies. In this discussion I would like to point out that
suchaccuracies may not be necessary in view of the inherent
simplifying assumptions of the application of the polytropic
analysisto the evaluation of gas compressor test results.Volume
flow through a compressor is continually changing(decreasing) and,
therefore, the inlet stage of a multistagecompressor is larger
(higher specific speed) than the exit stage.This means that some
stages having optimum specific speedwill be more efficient than
other stages. Depending on wherethese efficient stages are located,
the actual path of compression will lie to the left (often) or to
the right (seldom) of thehypothetical polytropic path.A good
example is the ethylene compressor case number 3of Mr. Huntington's
paper. In this case a typical compressorwith six stages may
perform, on a per-stage basis, as follows:
Using an equation of state 3 the total polytropic head isequal
to 88,367 (ft-lb/lbm) compared to the value of 91,525obtained by
Mr. Hunt ing ton .Another compressor having a different number of
stages,different diameter, or of a different manufacture will
haveanother interstage characteristic and, therefore, a
differentpolytropic head and efficiency for the same inlet and
dischargeconditions.This result should not be surprising since the
path of compression lies to the left of the constant efficiency
path (i.e.,reference method) when plotted on a Mollier chart .The
significance of the foregoing is that a mathematicallyaccurate
polytropic analysis is no nearer to reality than thecalculations
based on the extra assumption of a polytropiccompression constant
(i .e., J. Schultz' method). Again, this isso because the typical
gas compressor does not follow a constant polytropic efficiency
path. Once a simplifying assumption such as constant e has been
introduced, the accuracy ofcalculations will be limited and may not
be arbitrarilyincreased.Any argum ent as to interpreta tion of test
results may be settled early if the parties involved agree between
themselveswhich method of polytropic analysis is acceptable to
both. Insuch a case, the "reference" method is only as valid as
anyother method. It should be noted that the isentropic
analysis
2Senior Engineer, Gas Compressor and Systems Dynamics, Solar
TurbinesIncorporated, San Diego, CA 92138-5376.3 The equ ation of
state used was a modified Soave-RK . The difference in
headcalculation is due largely to the "assumed" versus "actual"
compression pathrather than the choice for the equation of
state.
1st stage2nd stage3rd stage4th stage5th stage6th stage
Pressure (psia)362.5- 609.2609.2-
980.3980.3-1515.41515.4-2357.42357.4-3262.63262.6-4351.2
Temperature (F) Polytropic efficiency98.3-171.7
0.8098171.7-245.2 0.7593245.2-317.3 0.7159317.3-390.6
0.7309390.6-449.9 0.6402449.9-503.3 0.6368
878/ Vol . 107 , OC TOB ER 1985 Transact ions of the ASME
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(not to be confused by the isentropic perfect gas relations)
issuperior to the polytropic analysis since it is not a path
function and is not ambiguous. The special utility of the
polytropicanalysis is the correlation between test and field
measurementsand is another issue.There are other factors in the
PTC-10 code which introducea higher percentage of errors in the
calculations than themethod of polytropic analysis; for example,
the accuracy oftest measurements, the accuracy of gas property
evaluation,and the method for performance correction due to
Reynoldsnumber effects. With respect to revising the PTC-10 code,
webelieve that the method of Reynolds number correction introduces
largest errors, and thus is in greater need of revision.I would
like to conclude these remarks by, again,acknowledging the
analytical achievements in Mr. Huntington's paper.
1st stage2nd stage3rd stage4th stage5th stage6th stageNetTable
2A Results (Ref)
Au th o r ' s Clo su re
Mr. Fozi 's comments raise several important issues concerning
the evaluation and use of PTC-10 test results. Hecorrectly points
out that compressors generally do not exhibita constant efficiency
throughout the gas compression andtherefore the PTC-10 assumption
of a constant efficiency is asimplification. However, this
assumption is valid because thePTC-10 performance test is used as a
flange-to-flangeevaluation and seeks to find an average efficiency
thatrepresents the compressor as a whole. It is not concerned
withindividual stage performances but only their cumulativeopera
tion bo th on the test stand and in the field.
The advantages of the two methods introduced in the paperare
that they accurately and consistently represent the true(i .e.,
constant efficiency) polytropic compression path that isbasic to
PTC-10 and will provide a precise correlation of test
stand and field results for all gases. The other
calculationmethods discussed, including the Schultz method,
deviatefrom the true polytropic path for nonperfect gases
andtherefore cannot provide as good a correlation.Mr. Fozi also
suggests through his hypothetical stage-by-stage analysis of Case N
o. 3 that ma jor differences (roughly3.5 percent) in calculated
head may be attributed to thenonconstant nature of the actual
compression path efficiencyand not to gas property evaluation
errors. I must disagreewith this and state that the bulk of this
calculated head dif-ference is due to gas property errors. Using
Mr. Fozi 'spressure and temperature breakpoints for each stage and
theidentical gas property evaluation method used in the paper,the
following stage performances are found:
Polytrop ic head (ft) Polytrop ic efficiency (percent)14584
81.0814872 76.8815149 73.6717279 77.0214405 68.8714439 69.4290728
74.3491525 74.99
This shows a 0.9 percent difference in head and
averageefficiency due to the nonconstant efficiency but a 2.6
percentdifference due to the different gas property
evaluationmethods.In this example, the differences in calculated
head due tochanging versus constant efficiency are not unexpected
or ofany concern because of the intended use of the PTC-10
resultsas discussed above. However, i t is a major concern that
suchlarge discrepancies in gas property evaluations are possible
asthese may have a serious impact on the design and successfulfield
operation of a compressor.Finally, I would like to gratefully thank
both Mr. Bleharand Mr. Fozi for their excellent and
thought-provokingdiscussions. Both have pointed out significant
areas ofconcern in the evaluation of compressor performance tests.
Itis clear that all major areas of concern sh ould be addressed
byfuture PTC-10 revisions including the polytropic
calculationmethod as discussed in this paper, Reynolds number
effects,and updated gas proper ty evaluat ion methods and data.
Journ al of Engineer ing for Gas Turbines and Power OCTO BER 1 9
8 5 , Vo l. 1 0 7 /8 7 9
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