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Hindawi Publishing CorporationInternational Journal of Rotating MachineryVolume 2013 Article ID 293486 12 pageshttpdxdoiorg1011552013293486
Research ArticleDesign and Performance Evaluation of a Very Low FlowCoefficient Centrifugal Compressor
Yongsheng Wang12 Feng Lin1 Chaoqun Nie1 and Abraham Engeda3
1 Key Laboratory of Advanced Energy and Power Chinese Academy of Sciences Institute of Engineering ThermophysicsChinese Academy of Sciences Beijing 100190 China
2Graduate University of Chinese Academy of Sciences Beijing 100190 China3Department of Mechanical Engineering Michigan State University East Lansing MA 48823 USA
Correspondence should be addressed to Yongsheng Wang wangyongshengietcn
Received 1 August 2013 Accepted 16 September 2013
Academic Editor Masaru Ishizuka
Copyright copy 2013 Yongsheng Wang et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
Very low flow coefficient centrifugal compressors are often applied as the last stages of multistage compressors Due to the lowervolume flow rate the flow channels in the impeller and diffuser are so narrow that friction loss becomes the main factor whichleads to lower efficiency than that of other stages in the same compressors In addition most of design methods are generally basedon medium flow coefficient centrifugal compressors Taking on researches on the low flow coefficient centrifugal compressors issignificant and necessary One-dimensional (1D) code consisting of design and analysis parts is developed in this study to providebasic geometric data and predict the entire performance of centrifugal compressor Three-dimensional geometry of the impelleris built CFD simulation is carried out as well to be compared with 1D prediction With the continuous geometry adjustment thefinal performance of the centrifugal compressor will be fixed once the performance discrepancy betweenCFD and one-dimensionalcode is acceptable The details on the flow field within impeller will be presented through CFD
1 Introduction
Centrifugal compressors are usually designed in the flowcoefficient range 120593 = 001 to 016 Often the need arises todesign very low or high flow coefficient 120593 radial stagesbut the aerodynamic challenges are not easy to satisfytherefore a designer usually has to make certain criticaldecisions Figure 1 shows the typical application area ofvarious compressor impellers and the typical areas wheremost industrial radial impellers are designed Narrow radialimpellers (smaller 120593 and smaller eye diameter) have non-twisted blades Wider impellers (larger 120593 and larger eyediameter) by contrast have twisted blades for better adaptionto local flow conditions
In very low flow coefficients stage design the majorchallenges aremechanical configuration anddiffuser stabilityand most significantly the aerodynamic and parasitic lossesare substantial as seen in Figure 1
Lowflow coefficient compressors are used formany appli-cations in industry and generally found as the last stages ofmultistage compressors where the volume rate is lower Two-dimensional radial impeller is usually applied Compared tothe centrifugal compressors with considerably higher flowcoefficient the range of very low flow coefficient centrifugalcompressors is between 0007 and 002 It means that alow volume flow rate passes through the impeller relativeto the outlet diameter and peripheral speed This causesspecial problems in obtaining an acceptable efficiency whichis mainly affected by three sources of efficiency losses skinfriction disc friction and leakage These compressors havegenerally a very narrow impeller channel that leads to highfriction losses The power required to overcome disc frictionand leakage is in the same order as a conventional higherflow stage Therefore efficient design of low flow coefficientcentrifugal compressors still needs more great effort from thedesignersMoreover in themost recent years the demand for
2 International Journal of Rotating Machinery
Axial flow compressor
Common applicationarea of the
radial impeller
Mixed flow impelleror
radial impellerhigh flow coefficient
2015
100806
04
02
01
001
002
004
006
008 0
1
02
04
06
08
10
120593
120595
(a)
120593
0 005 01 015
Aerodynamic losses
Leakage lossesDisc friction losses
Design point efficiency
0
02
04
06
08
120578
(b)
Figure 1 Application areas of high flow coefficient radial impellers and typical industrial compressors [1]
such high pressure ratio compressor operating at lowflow ratehas risen Nevertheless little information is available con-cerning low flow coefficient centrifugal compressor designin the open literature The following descriptions reviewsome research work regarding design of low flow coefficientcentrifugal compressors
Rusak [3] briefly presented three types of impeller designfor low flow application low flow conventional stages with2D impellers low flow high pressure coefficient stages withradial impellers and very low flow stages with wedge-typeimpellers Casey et al [4] designed and tested several low flowcoefficient centrifugal compressors with high head and lowoutlet meridional velocity component Koizumi [5] designedthree different compressors with straight blades S-shapedblades and almost radial blades In the mean time theinfluence of the viscous effect on the slip factor was studiedand the stall-onset condition for rotating stall in the vanelessdiffuser following the impeller was investigated as wellParoubek et al [6] tested six conventional low flow coefficientimpellers The effects of inducer hub to exit shroud diameterratio and channel width parameter on the stage perfor-manceswere investigatedDi Liberti [7] designed several low-flow-coefficient impellers and analyzed them numerically toinvestigate the effect of the design flow coefficient of theoutlet width-outlet blade angle combination and of the bladeleading edge position on the stage performance Biba et al [8]used commercial CFD codes together with in-house programdesign and analyzed two different impellers with low volumeflows and high pressure applications
Based on the above research results this study aims todesign an efficient lowflow coefficient centrifugal compressorwith wide operating range MATLAB is used as a tool todevelop 1D design and analysis codesThe three-dimensionalgeometry model of impeller is built by ldquoBLADEGENrdquo OnceCFD indicates that the performance of centrifugal compres-sor is satisfactory and has an acceptable discrepancy with 1Dprediction the final geometry of impeller will be fixed anddesign process is terminated
2 1D Design and Analysis Methods
1D code developed in this paper is divided into two partsdesign and analysis parts Design part provides basic geomet-ric data of impeller at design point Based on the geometryanalysis part can do the performance analysis using empiricalloss models at design and off-design points [9] and export thewhole performance curve of the centrifugal compressor It isnecessary to keep adjusting geometry until the comparisonof CFD and 1D codes shows that discrepancy is acceptableand design goals have been reached The 1D design andanalysis scheme is illustrated in Figure 2 Clearance loss andrecirculation loss are excluded in this shrouded impeller Infact hub-to-shroud loss and choke loss are not activated aswell which will be discussed in the following section of thispaper
In the case of this paper mass flow rate (119898) inlettotal pressure of impeller (119875
01) inlet total temperature of
impeller (11987901) rotational speed of impeller (119873) impeller
outlet diameter (1198632) and hub diameter (119863
ℎ) are given The
working medium is natural gas and typical compositionis used while setting the fluid properties in CFD In thedesign part the values of 119881
11989821198802 1205732119887
[10] and 1198811199062
1198811199062119887
are assumed within empirical ranges With these parametersimpeller outlet calculation can be completed Then in orderto calculate impeller inlet aerodynamic parameters the ratiosof 11986311198632and119882
21198821must be chosen to relate outlet to inlet
Since the inlet flow coefficient is 0022 impeller inlet shouldbe located in the radial direction which means that inlet hubdiameter is equal to inlet shroud diameter [2] It is because thereturn channel upstream of low coefficient compressor in thereal application guides the flow to be more uniform Inducercan be neglected which reduces flow path in the impellerand produces less skin friction lossMeanwhile impeller axiallength (119871
119911) can be determined as well Number of the blades
(119885) comes from original slip factor formula of Wiesner [11]Analysis part only includes one input variable which is
mass flow rate In the following analysis procedure fluiddensity at impeller inlet is initially approximated and requires
International Journal of Rotating Machinery 3
Given paremeters
Outlet analysis
Inlet analysisOutlet design
Inlet design
Des
ign
part
Export impellerGeometry data
Mass flow rate(variable)
Ana
lysis
par
t
Impeller performance
(design and off-design points)
Internal lossesIncidence lossSkin friction lossWake mixing loss
Clearance lossEntrance diffusion lossHub-to-shroud loading
Choking loss
Blade loading loss
loss
Parasitic lossesDisc friction lossLeakage lossRecirculalion loss
Figure 2 Flow chart of 1D code
an iterative solution procedurewith the constraint of iterationerror being less than 01 The same iterative method isapplied until convergence is reached on the fluid densitycalculation at impeller outlet in which internal losses areinvolved and used for computing impeller efficiency totalpressure static pressure and density The equations used inthe analysis part will be introduced and the related statefunctions and loss models are included
Specific heat at constant pressure is given as a constantprovided by industry in this design case No preswirl exists atthe impeller inlet which makes 119881
1199061= 0 and 119881
1= 1198811198981 Inlet
gas density is initialized by the following equation
1205881asymp 12058801
=11987501
(11987711987901) (1)
According to the fixed geometry data and given designparameters the values of 119881
1198981 1198801 1198821 and 119882th can be
easily calculated Equation (2) below provide the rest ofthermodynamic parameters
1198791= 11987901
minus1198812
1
(2119862119901)
1198751= 11987501(
1198791
11987901
)
119896(119896minus1)
12058811015840 =
1198751
(1198771198791)
(2)
The inlet calculationwill be done once the iteration showsthat the difference between two density values is within theerror range shown in Figure 3 Before moving on to theimpeller outlet calculation fraction area blockage at impeller
exit (1198612) has to be initially approximated first and updated
later Then 1198811199062
can be given after slip factor calculation iscompleted
1205882= 1205881(
1198802
2
(11986211990111987901)+ 1)
1(119896minus1)
1198811198982
=119898
(120587120588211986321198872(1 minus 119861
2))
120590 = 1 minus
radicsin (1205732119887) sin (120572
2119888)
11988507
119890lim =(120590 minus sin (19 + 2120573
2119887))
(1 minus sin (19 + 21205732119887))
119890 =1198631
1198632
If 119890 gt 119890lim 120590 = 120590(1 minus ((119890 minus 119890lim)
(1 minus 119890lim))
radic120573211988710
)
1198811199062
= 120590(1198802minus
1198811198982
tan (1205732119887))
119879and
01= 1198791+
1198821
2
(2119862119901)
119879and
02= 119879and
01+
(1198802
2minus 1198802
1)
(2119862119901)
(3)
4 International Journal of Rotating Machinery
Start
Choose 1205881
Choose 1205882
Input variables m[mmin mmax]
No
No
No
No
Inlet calculationVm1 V1 W1 P1 T1
Yes
Yes
Yes
Yes
1205881998400
Internal losses
Calculate 1205882998400
Stop
|1205881 minus 1205881998400|1205881 lt 01
|1205882 minus 1205882998400|1205882 lt 01
No parasitic losses120578totimp
Calculate P02 P2
Outlet calculationVm2 Vu2Wu2W2 T2
V2 T02 1205732 1205722
Check if Mth = 1
Calculate Mth
Parasitic losses
Include parasitic losses
No parasitic losses
Calculate 120578totstg
Calculate 120578totstg
Calculate Δhvld
Calculate P4 1205884 Vm4998400
Choose Vm4
Choose n
Calculate Vu4 V4 T4
|Vm4 minus Vm4998400|Vm4 lt 01
17ndash20
Figure 3 Detailed flow chart of 1D analysis part
So 1198821199062 1198822 1198812 and flow angles can be easily obtained
based on basic impeller outlet velocity triangleThen (4) willprovide 119879
2and 119879
02
1198792= 119879and
02minus
1198822
2
(2119862119901)
11987902
= 11987901
+11988021198811199062
119862119901
(4)
Then all the internal losses and parasitic losses calcula-tion can be finishedDetailed equations regarding lossmodelscan be found in [2] 119861
2can be updated by (5)
11986121015840 =
(ℎsf + ℎhs)
11988222
+ (03 +1198872
2
1198712119861
)119860119877211988721205882
(1205881119871119861) (5)
120578I =119862119901(11987902
minus 11987901) minus (Δℎinc + Δℎbl + Δℎsf + Δℎmix + Δℎdif)
119862119901(11987902
minus 11987901)
(6)
International Journal of Rotating Machinery 5
If parasitic losses are included a revised formula (7)should be applied
120578II=119862119901(11987902
minus 11987901) minus (Δℎinc + Δℎbl + Δℎsf + Δℎmix + Δℎdif)
119862119901(11987902
minus 11987901) + Δℎdf + Δℎ
119897
(7)
Finally density at impeller outlet is updated and com-pared with the initial one
11987902is = 119879
01+ 120578I (11987902 minus 119879
01)
11987502
= 11987501(11987902is11987901
)
119896(119896minus1)
1198752= 11987502(11987902
1198792
)
119896(119896minus1)
12058821015840 =
1198752
(1198771198792)
(8)
The code will continue running until density at impelleroutlet converges If vaneless diffuser is involved in the analysispart the corresponding loss model shown in Figure 3 has tobe added
Internal losses mainly include incidence loss blade load-ing loss skin friction loss wake mixing loss hub-to-shroudloading loss entrance diffusion loss and clearance loss [2 12]Generally parasitic losses are not involved in CFD In orderto make an efficiency comparison with or without parasiticlosses disc friction recirculation and leakage are also takeninto consideration In this case clearance loss and leakage lossare not considered due to shrouded impeller
Besides the above descriptions how to predict stall andchoke point in the analysis part must be mentioned herebecause these two points determine the operating range ofcentrifugal compressor directly In Figure 3 mass flow rateas the only input variable has a range coming from designpart directly The initial value of mass flow rate at chokepoint is predicted in design part by (9) developed by Dixon[13] Actually (9) always overpredicts mass flow rate whichis because aerodynamic blockage at impeller throat is notconsidered Therefore it is appropriate to apply (9) to obtainlarger mass flow rate for choke point first The initializationof mass flow rate for stall point calculated in design part isto use critical absolute flow angle at diffuser inlet which iscomputed by (10) Pinch between impeller outlet and diffuserinlet is also considered if applied [14]
119898choke = 119860 th1205880111988601[2 + (119896 minus 1)119880
2
11198862
01
119896 + 1]
(k+1)2(119896minus1)
(9)
120572lowast
3119888= 1205723119888
+ (1702 minus1484119887
2
1198892
)(1 minus1198873
1198872
) (10)
In the analysis part for stall point prediction two meth-ods are adopted The main one used by majority designersis to check if 119882
1119904119882th ge 175 which seemed as an inducer
stall criterion The second option is to estimate equivalent
10
12
14
16
18
20
22
02 03 04 05 06 07 08 09 10 11mmchoke
Deq
Figure 4 Equivalent diffusion factor
diffusion factor (119863eq) Lieblein [15] found that blade stalloccurs in the axial compressor when 119863eq is bigger than 2Later on 119863eq is generalized to radial and mixed flow bladesto evaluate the blade loading This criterion is also foundto be an appropriate blade stall limit for impellers [2] Therelated calculation equations are shown below119863eq is checkedat every iteration step in analysis part to see if it reachesthe criteria or not If neither 119882
1119904119882th nor 119863eq indicates the
compressor stalls the initial mass flow rate value from (10)will be considered to be the minimum value
119863eq =119882max1198822
119882max =(1198821+ 1198822+ Δ119882)
2
Δ119882 =212058711986321198802119868119861
(119885119871119861)
(11)
Finally in this case 1D code points out to 119863eq which isdetected beyond the critical value first The distribution of119863eq over mass flow rate is shown in Figure 4 Based on thecase in this paper it is still hard to determine which methodis suitable to stall point prediction so far According to CFDsimulation and test data further evaluation of the 1D codeneeds to be done through huge number of impellers whichwill be focused on in the future research work
As for choke point calculation iterativemethod is applieduntil relative Mach number at the impeller throat reaches 1Generally choke mass flow rate from analysis part is smallerthan initialization based on (9) In this case 1D code predictschokemass flow rate at 80 kgs andCFD shows it at 8155 kgsThe difference is less than 2 However the initial value is8954 kgs larger than analysis code prediction as expected
Since mass flow rate in analysis part is increased byspecific growth increment the real operating range of thecentrifugal compressor will be fixed after choke point cal-culation is done The code will plot the entire performance
6 International Journal of Rotating Machinery
3
4
5
6
7
8
05 06 07 08 09 1 11
Test
120587to
t
mmchoke
1D code
(a) Adiabatic efficiency
076
078
08
082
084
086
088
09
05 06 07 08 09 1 11
Test
mmchoke
1D code
120578
(b) Total pressure ratio
Figure 5 Performance curves between 1-D and test
of the centrifugal compressor automatically including designand off-design points
1D analysis code was calibrated by the test data of one ofthree Krainrsquos impellers [16 17] In Figure 5 it is obvious thattotal pressure ratio and adiabatic efficiency show similar dis-tribution trend and the discrepancies between performancecurves are acceptable Compared to the test wider surgemargin is obtained by 1D code Overall based on this case1D analysis code is functional and satisfying Also a detailedflow parameter comparison of 1D code and test data of a highflow coefficient centrifugal compressor have been carried outwhich also indicates good predictive effect of 1D analysiscode The related results are not shown here
3 1D Design and Analysis Results
Main impeller geometric parameters from 1D code are listedin Table 1 Design parameters like mass flow rate rotationalspeed impeller outlet diameter and shaft diameter areprovided by industry according to practical demand
Since leading edge and trailing edge of the impeller havethe same streamline slope angle in this case hub-to-shroudloss model is not activated The criterion in the chokingloss model is not satisfied and the choking loss is also notconsidered as well Recirculation loss is neglected due to theshrouded impeller designed in this study
Therefore internal losses actually used include wakemixing loss skin friction loss incidence loss blade load-ing loss and inducer diffusion loss Figure 6 shows losscoefficient distribution of impeller It is observed that skin
Table 1 Impeller parameters
119898 48 kgs119873 12800 rpm120593 0022119873119904
0071198631
02172m1198632
0381m1198871
00123m1198872
00082m1205731119887
289∘
1205732119887
40∘
119871119911
00193m11988721198632
00216119885 13
friction is the main loss source in the impeller as expecteddue to narrow flow path of low flow coefficient centrifugalcompressor and increases gradually from surge side to chokeside Wake loss appears near surge point and presents thesmallest loss coefficient Minimum incidence loss occurs atdesign point The distribution of incidence loss is prettytypical Either increasing mass flow rate from design pointto choke side or reducing it from design point to surge sidewill causemore incidence loss Higher pressure ratio is alwaysaccompanied by accordingly higher blade loading loss whichcan explain why blade loading loss distributes like the trendshown in Figure 6 An inducer diffusion loss appears onlyfor applications of less than 63 mass flow rate which is
International Journal of Rotating Machinery 7
0
01
02
03
04
05
06
036 040 044 051 057 063 073 078 086 093 097 100
Loss
coeffi
cien
t
Inducer diffusionBlade loadingIncidence
Skin frictionWake mixing
mmchoke
Figure 6 Loss coefficient distribution of impeller
0
002
004
006
008
01
012
014
036 040 044 051 057 063 073 078 086 093 097 100
Wor
k co
effici
ent
LeakageDisc friction
mmchoke
Figure 7 Distribution of work coefficient due to parasitic losses
the design point For parasitic losses or external losses onlydisc friction loss and leakage loss are involved They presentsimilar distribution trend seen in Figure 7 Overall 1D codeprovides asmuch information as it canMore importantly the1D analysis results look reasonable and acceptable
Note Please refer to reference [2] to look up the equationsused for calculating loss coefficient and work coefficient inFigures 6 and 7 which are based on the results that theanalysis code provides
05
06
07
08
09
10
11
12
13
14
000
015
030
045
060
075
090
105
120
135
004 005 006 007 008 009
Test CFDTest CFD
120578120595
120593
Figure 8 Performance comparison between test and CFD
4 3D CFD Validation
Many impellers coming from either open literature or indus-try have been used to evaluate the accuracy of the CFDanalysis before It is confirmed that our CFD simulation isreasonable and reliable An impeller similar to the case inthis paper is chosen to present our CFD analysis accuracycompared to test data from a cooperative company Thisimpeller also applies two-dimensional blades and is usedin the last stage centrifugal compressor of the multistagecompressors It can be observed in Figure 8 that CFD has agood agreement with test data
Note Vaneless diffuser and return channel are also involvedin the test and CFD
For the case in this paper before running CFD impellermodeling is built in the commercial software ldquoBLADEGENrdquoaccording to the fixed geometry from 1D design codeFigure 9 shows the geometry and meridional view of theimpeller It can be observed that leading edge of impeller is inthe radial direction and flow channel is so narrow which arethe typical characteristics of low flow coefficient centrifugalcompressors Inlet and outlet computational domains haveto be added to avoid reserved flow and improve accuracy ofcomputation in CFD Extended outlet computational domainacts like practical vaneless diffuser and makes impeller runclose to the real environment
Three-dimensional viscous RANS solver and Spalart-Allamaras turbulent model are applied in the steady simu-lation with inlet boundary conditions of 119875
01= 13602 kPa
11987901
= 424K and axial flow Static pressure is set on the outletboundary condition and increased gradually Near lower flowregion using mass flow rate condition captures stall pointinstead of static pressure condition The working medium is
8 International Journal of Rotating Machinery
(a) Impeller geometry
80
100
120
140
160
180
200
220
240
260
280
300
0 20minus40 minus20
Z (mm)
R(m
m)
(b) Meridional view
Figure 9 Impeller design
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 1 11
Grid 1Grid 2Grid 3
120587to
t
mmchoke
(a) Total pressure ratio
010
020
030
040
050
060
070
080
090
100
02 03 04 05 06 07 08 09 1 11
Grid 1Grid 2Grid 3
mmchoke
120578
(b) Adiabatic efficiency
Figure 10 Simulation results with three grid plans
defined as typical natural gas All solidwalls are assumed to besmoothwith roughness of 10minus6m In order to reduce the effectof skin friction coefficient affected by surface roughness samesurface property has to be employed in 1D code whenmakinga comparison between 1D prediction and CFD simulation
In order to understand the analytical accuracy of theCFD on the impeller of this case three grid plans shown inTable 2 were tried to check grid sensitivity Figure 10(a) showsthat total pressure ratio distribution curves from three gridplans match very well Adiabatic efficiency curves seen in
International Journal of Rotating Machinery 9
Table 2 Three grid plans
Circumferential Streamwise Spanwise Grid numberGrid 1 27 87 39 185367Grid 2 35 107 49 295421Grid 3 43 127 57 435309
Figure 10(b) also present a good match However it seemsthat larger stall margin is obtained by applying less gridnumber In consideration of running safety in the test thegrid plan 3 with smaller stall margin will be selected as areference for design because designers can not just pick theoption with the best evaluation
For adiabatic efficiency of impeller 1D code can presentthe results with and without parasitic losses However CFDdoes not usually include parasitic losses unless the exact prac-tical structure of centrifugal compressor is built That is thereason why Figure 11(a) shows three distribution curves forefficiency In addition to evaluate 1D code through comparingwith CFD without parasitic losses the efficiency includingparasitic losses close to real environment is needed to bepresented as well 1D code shows wider operating rangeand further stall point which means that comparing withCFD 1D code predicts that the centrifugal compressor canrun at lower mass flow rate Itrsquos shown that steady CFDsimulation cannot get an accurate stall point Transientsimulation should be done after steady calculation which isnot completed in this paper According to the comparisonof efficiency CFD has a little bit discrepancy in adiabaticefficiency on the right side of blue line However differencein efficiency becomes bigger and distribution trends showdifferent as mass flow rate continues to be reduced
In Figure 11(b) total pressure ratio from CFD is overpre-dicted but has same distribution trend with 1D predictionSince empirical loss models are used in the code and CFDcannot show the exact results with real values we think1D code works well and has the function to finish the per-formance evaluation within acceptable discrepancy Furthervalidation with more impellers needs to be carried out in thefuture to see if a constant coefficient for total pressure ratioexists between 1D code and CFD And if this is the case theprediction accuracy of 1D code can be further improved
Note Equation (6) presents the efficiency without parasiticlosses However parasitic losses are taken into account in(7) As mentioned before these two equations are used to becompared with CFD and test data respectively
Relative Mach number distributions at 10 50 and90 spans are shown in Figure 12 It is very clear that alow velocity region exists near pressure surface and becomessmaller gradually as blade span increases Because high staticpressure near pressure surface accompanies low velocity thelow magnitude area can be expected near pressure surfaceMoreover narrow passage introduces large viscous effectsand the typical velocity distribution of the bend comes upjust before the leading edge of the impeller which makes itobvious why Figure 12 presents relative Mach number like
that Fortunately no flow separation is found in the flow fieldof the impeller
Figure 13 shows 119881119898distribution on the meridional view
No low flow region and separation bubble exist whichindicates that this design is rational It is seen in Figure 13that velocity is gradually increasing from hub to shroud inthe extended inlet region which is a typical flow distributionin the bend High velocity means low static pressure andvice versa High pressure static pressure near hub regioncreates centripetal force to balance centrifugal force In orderto reduce the effect of this kind of flow distribution onthe incidence angles along the span of impeller inlet lowercurvature of shroud in the extended inlet region which cancause higher flow area and reduce hub-to-shroud velocitygradient should be applied for performance optimization inthe future Figure 14 presents the idea that static pressuredistribution is smooth through the impeller as expected
Due to the even absolute flow angle distribution atimpeller exit shown in Figure 15 vaneless or vaned diffuserhas perfect inlet condition and can be easily designed ifneeded Blade loading at 10 50 and 90 spans distributesreasonably which can be checked out in detail in Figure 16The blank area between pressure and suction surface staticcurves represents the load that blade withstands which doesnot vary too much through the blade at different spans Thatis what designers expect
The main performance parameters comparison at designpoint is listed in Table 3 The power calculated by CFD isapproximately in the middle of these two values computed by1D code Compared to CFD the efficiency is overpredictedby 152 in the 1D code which is really satisfying The totalpressure ratio in CFD is 305 higher than 1D code Inaddition parasitic losses drop efficiency a lot based on 1Dprediction
5 Conclusions
1D code is developed in this paper and divided into two partswhich are used to design and analyze Based on the code alowflow coefficient centrifugal compressor is designed and itsperformance is predicted In comparisonwith 1D code steadyCFD simulation has been carried out and provides flow fielddetails in the impeller
Comparing to 1D code CFD overpredicts total pressureratio of impeller but shows the same distribution trend whichis encouraging Further validations through more impellershave to be done in the future to confirm if a constantcoefficient for total pressure ratio exists between CFD and1D code For adiabatic efficiency 1D code without includingparasitic losses matches very well CFD in the operating rangeof near design point and choke point However 1D code isoverpredicted between near design point and stall point Thedifference of mass flow rate at choke point between CFDand 1D code is less than 2 Compared to steady CFD 1Dcode presents stall point at lower mass flow rate No flowseparation is found in the flow field of impeller and even theabsolute flow angle distribution at impeller exit is shownThe
10 International Journal of Rotating Machinery
02 03 04 05 06 07 08 09 10 1100
02
04
06
08
10
CFD1D (with parasitic losses)1D (without parasitic losses)
120578
mmchoke
(a) Adiabatic efficiency
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 10 11
CFD
120587to
t
1D code
mmchoke
(b) Total pressure ratio
Figure 11 Impeller performance curves
0 01 02 03 04 05 06
(a) 10 span (b) 50 span (c) 90 span
Figure 12 Relative Mach number map
120
100
80
60
40
20
0
Vm
Figure 13 Meridional velocity and streamline distribution
15E + 07
145E + 07
14E + 07
135E + 07
155E + 07
13E + 07St
atic
pre
ssur
e
Figure 14 Static pressure distribution
0
5
10
15
20
25
30
0Axial length (mm)
minus9 minus8 minus7 minus6 minus5 minus4 minus3 minus2 minus1
1205722
(∘)
Figure 15 Absolute flow angle distribution at impeller exit
International Journal of Rotating Machinery 11
0Axial length (mm)
10 span50 span90 span
10E + 07
11E + 07
12E + 07
13E + 07
14E + 07
15E + 07
16E + 07
Pst
(Pa)
minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2
Figure 16 Blade loading distribution at different spans
Table 3 Performance comparison between CFD and 1D code atdesign point
CFD 1D(no parasitic losses)
1D(parasitic losses)
Power 1778400W 1656740W 1857339W120587tot 121 11731 11731120578 902 9172 8257
blade loading at three different spans distributes smoothly asexpected
Since the low flow coefficient centrifugal compressordesigned in this paper is not the usual type and empiricalequations used are based on medium flow coefficient com-pressors further research on the improvement and validationof 1D code needs to be done by experiment and CFD toincrease prediction accuracy
Nomenclature
119860 Area (m2)AR Area ratio (119860
2sin(1205732119887)1198601sin(120573th))
119886 Sonic velocity (ms)119861 Fraction area blockage119887 Blade height (m)119862119901 Specific heat at constant pressure(Jkg K)
119890 Impeller mean line radius ratio119863 Diameter (m)119863eq Equivalent diffusion factor119896 Ratio of specific heatsΔℎ Enthalpy increase (Jkg)119868119861 Blade work input coefficient
120590(1 minus 119898cot(1205732119887)((120588211986021198802)(1 minus 119861
2))) minus
119880111986211990611198802
2
119871119885 Impeller axial length (m)
119871119861 Length of blade mean camberline (m)
119872 Relative Mach number119898 Mass flow rate (kgs)119873 Rotation speed (rpm)119873119904 Specific speed
119875 Pressure (pa)119877 Gas constant (J(kgsdotK))119879 Temperature (K)119880 Blade speed (ms)119881 Absolute velocity (ms)119882 Relative velocity (ms)Δ119882 Average blade velocity difference (ms)119885 Number of the blades
Greeks
120572 Absolute flow angle from tangential (∘)120573 Relative flow angle from tangential (∘)120578 Adiabatic efficiency120582 Workenthalpy coefficient Δℎ119880
2
2
120587 Pressure ratio120588 Gas density (kgm
3)
120590 Slip factor120593 Inlet flow coefficient119898(120588
111988021205871198632
24)
Ψ Inlet head coefficient(8544119863
2)21198621199011198791((11987521198751)((119896minus1)119896)
minus 1)
Δ120596 Total pressure loss coefficientΔ1199010(1199010minus 119901)
Subscripts
0 Total condition1 Impeller inlet2 Impeller outlet3 Diffuser inlet4 Diffuser outlet
119887 Bladebl Blade loading119888 Criterionchoke Choke pointdf Disc frictiondif Inducer diffusionℎ Impeller inlet hubhs Hub-to-shroudinc Incidenceis Isentropic119897 Leakagelim Limit119898 Meridional componentmax Maximummin Minimummix Wake mixing119904 Shroudst Staticth Impeller throat
12 International Journal of Rotating Machinery
sf Skin frictiontot Total-to-total119906 Tangential componentvld Vaneless diffuser
Superscripts
lowast Correct value1015840 New valueand Value relative to rotating frame of reference
Conflict of Interests
The authors declare that they have no financial and personalrelationships with other people or organizations that caninappropriately influence their work there is no professionalor other personal interest of any nature or kind in anyproduct service andor company that could be construed asinfluencing the position presented in or the review of thepaper
Acknowledgment
This work is supported by the National Natural ScienceFoundation of China under Grant no 51010007 and theChina Scholarship Council (CSC) The authors would like tothank Dr Marco Vagani and Christopher D Bolin for theirdiscussion and advice
References
[1] T Sato J M Oh and A Engeda ldquoExperimental and numericalinvestigation of the flow in a vaneless diffuser of a centrifugalcompressor stage Part 1 experimental investigationrdquo Proceed-ings of the Institution of Mechanical Engineers C vol 219 no 10pp 1053ndash1059 2005
[2] R H Aungier Centrifugal Compressor A Strategy for Aerody-namic Design and Analysis ASME Press New York NY USA2000
[3] V Rusak ldquoDevelopment and performance of the wedge-typelow specific speed compressor wheelrdquo Tech Rep 82-GT-214ASME 2009
[4] M V Casey P Dalbert and E Schurter ldquoRadial compressorstages for low flow coefficientsrdquo in Proceedings of the IMechEInternational Conference on Machinery for the Oil and GasIndustries 1990
[5] T Koizumi ldquoExperimental studies on performance of centrifu-gal compressors with very small flow coefficientrdquoMitsui ZosenTechnical Review vol 117 pp 28ndash39 1983
[6] J Paroubek J Kyncl and V Cyrus ldquoExperimental investigationand performance analysis of six low flow coefficient centrifugalcompressor stagesrdquo Transactions of the ASME Journal of Turbo-machinery vol 117 no 4 pp 585ndash592 1995
[7] J-L Di Liberti Design and development of low-flow coefficientcentrifugal compressors for industrial application [PhD thesis]Michigan State University 1998
[8] Y I Biba D A Nye and L I U Zheji ldquoPerformance evaluationand fluid flow analysis in low flow stages of industrial centrifu-gal compressorrdquo International Journal of Rotating Machineryvol 8 no 5 pp 309ndash317 2002
[9] M R Galvas ldquoFortran program for predicting off-designperformance of centrifugal com-pressorsrdquo Tech Rep TN D-7487 NASA 1973
[10] K H Ludtke Process Centrifugal Compressors Basic FunctionOperation Design Application Springer Berlin Germany 2010
[11] F J Wiesner ldquoA review of slip factors for centrifugal compres-sorsrdquo Journal of Engineering for Power Transactions of theASMEvol 89 pp 558ndash572 1967
[12] R H Aungier ldquoMean streamline aerodynamic performanceanalysis of centrifugal compressorsrdquo Transactions of the ASMEJournal of Turbomachinery vol 117 no 3 pp 360ndash366 1995
[13] S L Dixon Fluid Mechanics and Thermodnamics of Turboma-chinery Butterworth-Heinemann 4th edition 1998
[14] Y Senoo and Y Kinoshita ldquoLimits of rotating stall and stall invaneless diffusers of centrifugal compressorsrdquo Tech Rep 78-GT-19 ASME 1978
[15] S Lieblein ldquoLoss and stall analysis of compressor cascadesrdquoASME Transactions Journal of Basic Engineering vol 81 pp387ndash400 1959
[16] H Krain and B Hoffmann ldquoFlow physics in high pressure ratiocentrifugal compressorsrdquo in Proceedings of the ASME FluidsEngineering Division Summer Meeting June 1998
[17] G Eisenlohr and H Krain ldquoInvestigation of the flow througha high pressure ratio centrifugal impellerrdquo in Proceedings of theASME Conference Proceedings 2003
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Shock and Vibration
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Journal of
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DistributedSensor Networks
International Journal of
2 International Journal of Rotating Machinery
Axial flow compressor
Common applicationarea of the
radial impeller
Mixed flow impelleror
radial impellerhigh flow coefficient
2015
100806
04
02
01
001
002
004
006
008 0
1
02
04
06
08
10
120593
120595
(a)
120593
0 005 01 015
Aerodynamic losses
Leakage lossesDisc friction losses
Design point efficiency
0
02
04
06
08
120578
(b)
Figure 1 Application areas of high flow coefficient radial impellers and typical industrial compressors [1]
such high pressure ratio compressor operating at lowflow ratehas risen Nevertheless little information is available con-cerning low flow coefficient centrifugal compressor designin the open literature The following descriptions reviewsome research work regarding design of low flow coefficientcentrifugal compressors
Rusak [3] briefly presented three types of impeller designfor low flow application low flow conventional stages with2D impellers low flow high pressure coefficient stages withradial impellers and very low flow stages with wedge-typeimpellers Casey et al [4] designed and tested several low flowcoefficient centrifugal compressors with high head and lowoutlet meridional velocity component Koizumi [5] designedthree different compressors with straight blades S-shapedblades and almost radial blades In the mean time theinfluence of the viscous effect on the slip factor was studiedand the stall-onset condition for rotating stall in the vanelessdiffuser following the impeller was investigated as wellParoubek et al [6] tested six conventional low flow coefficientimpellers The effects of inducer hub to exit shroud diameterratio and channel width parameter on the stage perfor-manceswere investigatedDi Liberti [7] designed several low-flow-coefficient impellers and analyzed them numerically toinvestigate the effect of the design flow coefficient of theoutlet width-outlet blade angle combination and of the bladeleading edge position on the stage performance Biba et al [8]used commercial CFD codes together with in-house programdesign and analyzed two different impellers with low volumeflows and high pressure applications
Based on the above research results this study aims todesign an efficient lowflow coefficient centrifugal compressorwith wide operating range MATLAB is used as a tool todevelop 1D design and analysis codesThe three-dimensionalgeometry model of impeller is built by ldquoBLADEGENrdquo OnceCFD indicates that the performance of centrifugal compres-sor is satisfactory and has an acceptable discrepancy with 1Dprediction the final geometry of impeller will be fixed anddesign process is terminated
2 1D Design and Analysis Methods
1D code developed in this paper is divided into two partsdesign and analysis parts Design part provides basic geomet-ric data of impeller at design point Based on the geometryanalysis part can do the performance analysis using empiricalloss models at design and off-design points [9] and export thewhole performance curve of the centrifugal compressor It isnecessary to keep adjusting geometry until the comparisonof CFD and 1D codes shows that discrepancy is acceptableand design goals have been reached The 1D design andanalysis scheme is illustrated in Figure 2 Clearance loss andrecirculation loss are excluded in this shrouded impeller Infact hub-to-shroud loss and choke loss are not activated aswell which will be discussed in the following section of thispaper
In the case of this paper mass flow rate (119898) inlettotal pressure of impeller (119875
01) inlet total temperature of
impeller (11987901) rotational speed of impeller (119873) impeller
outlet diameter (1198632) and hub diameter (119863
ℎ) are given The
working medium is natural gas and typical compositionis used while setting the fluid properties in CFD In thedesign part the values of 119881
11989821198802 1205732119887
[10] and 1198811199062
1198811199062119887
are assumed within empirical ranges With these parametersimpeller outlet calculation can be completed Then in orderto calculate impeller inlet aerodynamic parameters the ratiosof 11986311198632and119882
21198821must be chosen to relate outlet to inlet
Since the inlet flow coefficient is 0022 impeller inlet shouldbe located in the radial direction which means that inlet hubdiameter is equal to inlet shroud diameter [2] It is because thereturn channel upstream of low coefficient compressor in thereal application guides the flow to be more uniform Inducercan be neglected which reduces flow path in the impellerand produces less skin friction lossMeanwhile impeller axiallength (119871
119911) can be determined as well Number of the blades
(119885) comes from original slip factor formula of Wiesner [11]Analysis part only includes one input variable which is
mass flow rate In the following analysis procedure fluiddensity at impeller inlet is initially approximated and requires
International Journal of Rotating Machinery 3
Given paremeters
Outlet analysis
Inlet analysisOutlet design
Inlet design
Des
ign
part
Export impellerGeometry data
Mass flow rate(variable)
Ana
lysis
par
t
Impeller performance
(design and off-design points)
Internal lossesIncidence lossSkin friction lossWake mixing loss
Clearance lossEntrance diffusion lossHub-to-shroud loading
Choking loss
Blade loading loss
loss
Parasitic lossesDisc friction lossLeakage lossRecirculalion loss
Figure 2 Flow chart of 1D code
an iterative solution procedurewith the constraint of iterationerror being less than 01 The same iterative method isapplied until convergence is reached on the fluid densitycalculation at impeller outlet in which internal losses areinvolved and used for computing impeller efficiency totalpressure static pressure and density The equations used inthe analysis part will be introduced and the related statefunctions and loss models are included
Specific heat at constant pressure is given as a constantprovided by industry in this design case No preswirl exists atthe impeller inlet which makes 119881
1199061= 0 and 119881
1= 1198811198981 Inlet
gas density is initialized by the following equation
1205881asymp 12058801
=11987501
(11987711987901) (1)
According to the fixed geometry data and given designparameters the values of 119881
1198981 1198801 1198821 and 119882th can be
easily calculated Equation (2) below provide the rest ofthermodynamic parameters
1198791= 11987901
minus1198812
1
(2119862119901)
1198751= 11987501(
1198791
11987901
)
119896(119896minus1)
12058811015840 =
1198751
(1198771198791)
(2)
The inlet calculationwill be done once the iteration showsthat the difference between two density values is within theerror range shown in Figure 3 Before moving on to theimpeller outlet calculation fraction area blockage at impeller
exit (1198612) has to be initially approximated first and updated
later Then 1198811199062
can be given after slip factor calculation iscompleted
1205882= 1205881(
1198802
2
(11986211990111987901)+ 1)
1(119896minus1)
1198811198982
=119898
(120587120588211986321198872(1 minus 119861
2))
120590 = 1 minus
radicsin (1205732119887) sin (120572
2119888)
11988507
119890lim =(120590 minus sin (19 + 2120573
2119887))
(1 minus sin (19 + 21205732119887))
119890 =1198631
1198632
If 119890 gt 119890lim 120590 = 120590(1 minus ((119890 minus 119890lim)
(1 minus 119890lim))
radic120573211988710
)
1198811199062
= 120590(1198802minus
1198811198982
tan (1205732119887))
119879and
01= 1198791+
1198821
2
(2119862119901)
119879and
02= 119879and
01+
(1198802
2minus 1198802
1)
(2119862119901)
(3)
4 International Journal of Rotating Machinery
Start
Choose 1205881
Choose 1205882
Input variables m[mmin mmax]
No
No
No
No
Inlet calculationVm1 V1 W1 P1 T1
Yes
Yes
Yes
Yes
1205881998400
Internal losses
Calculate 1205882998400
Stop
|1205881 minus 1205881998400|1205881 lt 01
|1205882 minus 1205882998400|1205882 lt 01
No parasitic losses120578totimp
Calculate P02 P2
Outlet calculationVm2 Vu2Wu2W2 T2
V2 T02 1205732 1205722
Check if Mth = 1
Calculate Mth
Parasitic losses
Include parasitic losses
No parasitic losses
Calculate 120578totstg
Calculate 120578totstg
Calculate Δhvld
Calculate P4 1205884 Vm4998400
Choose Vm4
Choose n
Calculate Vu4 V4 T4
|Vm4 minus Vm4998400|Vm4 lt 01
17ndash20
Figure 3 Detailed flow chart of 1D analysis part
So 1198821199062 1198822 1198812 and flow angles can be easily obtained
based on basic impeller outlet velocity triangleThen (4) willprovide 119879
2and 119879
02
1198792= 119879and
02minus
1198822
2
(2119862119901)
11987902
= 11987901
+11988021198811199062
119862119901
(4)
Then all the internal losses and parasitic losses calcula-tion can be finishedDetailed equations regarding lossmodelscan be found in [2] 119861
2can be updated by (5)
11986121015840 =
(ℎsf + ℎhs)
11988222
+ (03 +1198872
2
1198712119861
)119860119877211988721205882
(1205881119871119861) (5)
120578I =119862119901(11987902
minus 11987901) minus (Δℎinc + Δℎbl + Δℎsf + Δℎmix + Δℎdif)
119862119901(11987902
minus 11987901)
(6)
International Journal of Rotating Machinery 5
If parasitic losses are included a revised formula (7)should be applied
120578II=119862119901(11987902
minus 11987901) minus (Δℎinc + Δℎbl + Δℎsf + Δℎmix + Δℎdif)
119862119901(11987902
minus 11987901) + Δℎdf + Δℎ
119897
(7)
Finally density at impeller outlet is updated and com-pared with the initial one
11987902is = 119879
01+ 120578I (11987902 minus 119879
01)
11987502
= 11987501(11987902is11987901
)
119896(119896minus1)
1198752= 11987502(11987902
1198792
)
119896(119896minus1)
12058821015840 =
1198752
(1198771198792)
(8)
The code will continue running until density at impelleroutlet converges If vaneless diffuser is involved in the analysispart the corresponding loss model shown in Figure 3 has tobe added
Internal losses mainly include incidence loss blade load-ing loss skin friction loss wake mixing loss hub-to-shroudloading loss entrance diffusion loss and clearance loss [2 12]Generally parasitic losses are not involved in CFD In orderto make an efficiency comparison with or without parasiticlosses disc friction recirculation and leakage are also takeninto consideration In this case clearance loss and leakage lossare not considered due to shrouded impeller
Besides the above descriptions how to predict stall andchoke point in the analysis part must be mentioned herebecause these two points determine the operating range ofcentrifugal compressor directly In Figure 3 mass flow rateas the only input variable has a range coming from designpart directly The initial value of mass flow rate at chokepoint is predicted in design part by (9) developed by Dixon[13] Actually (9) always overpredicts mass flow rate whichis because aerodynamic blockage at impeller throat is notconsidered Therefore it is appropriate to apply (9) to obtainlarger mass flow rate for choke point first The initializationof mass flow rate for stall point calculated in design part isto use critical absolute flow angle at diffuser inlet which iscomputed by (10) Pinch between impeller outlet and diffuserinlet is also considered if applied [14]
119898choke = 119860 th1205880111988601[2 + (119896 minus 1)119880
2
11198862
01
119896 + 1]
(k+1)2(119896minus1)
(9)
120572lowast
3119888= 1205723119888
+ (1702 minus1484119887
2
1198892
)(1 minus1198873
1198872
) (10)
In the analysis part for stall point prediction two meth-ods are adopted The main one used by majority designersis to check if 119882
1119904119882th ge 175 which seemed as an inducer
stall criterion The second option is to estimate equivalent
10
12
14
16
18
20
22
02 03 04 05 06 07 08 09 10 11mmchoke
Deq
Figure 4 Equivalent diffusion factor
diffusion factor (119863eq) Lieblein [15] found that blade stalloccurs in the axial compressor when 119863eq is bigger than 2Later on 119863eq is generalized to radial and mixed flow bladesto evaluate the blade loading This criterion is also foundto be an appropriate blade stall limit for impellers [2] Therelated calculation equations are shown below119863eq is checkedat every iteration step in analysis part to see if it reachesthe criteria or not If neither 119882
1119904119882th nor 119863eq indicates the
compressor stalls the initial mass flow rate value from (10)will be considered to be the minimum value
119863eq =119882max1198822
119882max =(1198821+ 1198822+ Δ119882)
2
Δ119882 =212058711986321198802119868119861
(119885119871119861)
(11)
Finally in this case 1D code points out to 119863eq which isdetected beyond the critical value first The distribution of119863eq over mass flow rate is shown in Figure 4 Based on thecase in this paper it is still hard to determine which methodis suitable to stall point prediction so far According to CFDsimulation and test data further evaluation of the 1D codeneeds to be done through huge number of impellers whichwill be focused on in the future research work
As for choke point calculation iterativemethod is applieduntil relative Mach number at the impeller throat reaches 1Generally choke mass flow rate from analysis part is smallerthan initialization based on (9) In this case 1D code predictschokemass flow rate at 80 kgs andCFD shows it at 8155 kgsThe difference is less than 2 However the initial value is8954 kgs larger than analysis code prediction as expected
Since mass flow rate in analysis part is increased byspecific growth increment the real operating range of thecentrifugal compressor will be fixed after choke point cal-culation is done The code will plot the entire performance
6 International Journal of Rotating Machinery
3
4
5
6
7
8
05 06 07 08 09 1 11
Test
120587to
t
mmchoke
1D code
(a) Adiabatic efficiency
076
078
08
082
084
086
088
09
05 06 07 08 09 1 11
Test
mmchoke
1D code
120578
(b) Total pressure ratio
Figure 5 Performance curves between 1-D and test
of the centrifugal compressor automatically including designand off-design points
1D analysis code was calibrated by the test data of one ofthree Krainrsquos impellers [16 17] In Figure 5 it is obvious thattotal pressure ratio and adiabatic efficiency show similar dis-tribution trend and the discrepancies between performancecurves are acceptable Compared to the test wider surgemargin is obtained by 1D code Overall based on this case1D analysis code is functional and satisfying Also a detailedflow parameter comparison of 1D code and test data of a highflow coefficient centrifugal compressor have been carried outwhich also indicates good predictive effect of 1D analysiscode The related results are not shown here
3 1D Design and Analysis Results
Main impeller geometric parameters from 1D code are listedin Table 1 Design parameters like mass flow rate rotationalspeed impeller outlet diameter and shaft diameter areprovided by industry according to practical demand
Since leading edge and trailing edge of the impeller havethe same streamline slope angle in this case hub-to-shroudloss model is not activated The criterion in the chokingloss model is not satisfied and the choking loss is also notconsidered as well Recirculation loss is neglected due to theshrouded impeller designed in this study
Therefore internal losses actually used include wakemixing loss skin friction loss incidence loss blade load-ing loss and inducer diffusion loss Figure 6 shows losscoefficient distribution of impeller It is observed that skin
Table 1 Impeller parameters
119898 48 kgs119873 12800 rpm120593 0022119873119904
0071198631
02172m1198632
0381m1198871
00123m1198872
00082m1205731119887
289∘
1205732119887
40∘
119871119911
00193m11988721198632
00216119885 13
friction is the main loss source in the impeller as expecteddue to narrow flow path of low flow coefficient centrifugalcompressor and increases gradually from surge side to chokeside Wake loss appears near surge point and presents thesmallest loss coefficient Minimum incidence loss occurs atdesign point The distribution of incidence loss is prettytypical Either increasing mass flow rate from design pointto choke side or reducing it from design point to surge sidewill causemore incidence loss Higher pressure ratio is alwaysaccompanied by accordingly higher blade loading loss whichcan explain why blade loading loss distributes like the trendshown in Figure 6 An inducer diffusion loss appears onlyfor applications of less than 63 mass flow rate which is
International Journal of Rotating Machinery 7
0
01
02
03
04
05
06
036 040 044 051 057 063 073 078 086 093 097 100
Loss
coeffi
cien
t
Inducer diffusionBlade loadingIncidence
Skin frictionWake mixing
mmchoke
Figure 6 Loss coefficient distribution of impeller
0
002
004
006
008
01
012
014
036 040 044 051 057 063 073 078 086 093 097 100
Wor
k co
effici
ent
LeakageDisc friction
mmchoke
Figure 7 Distribution of work coefficient due to parasitic losses
the design point For parasitic losses or external losses onlydisc friction loss and leakage loss are involved They presentsimilar distribution trend seen in Figure 7 Overall 1D codeprovides asmuch information as it canMore importantly the1D analysis results look reasonable and acceptable
Note Please refer to reference [2] to look up the equationsused for calculating loss coefficient and work coefficient inFigures 6 and 7 which are based on the results that theanalysis code provides
05
06
07
08
09
10
11
12
13
14
000
015
030
045
060
075
090
105
120
135
004 005 006 007 008 009
Test CFDTest CFD
120578120595
120593
Figure 8 Performance comparison between test and CFD
4 3D CFD Validation
Many impellers coming from either open literature or indus-try have been used to evaluate the accuracy of the CFDanalysis before It is confirmed that our CFD simulation isreasonable and reliable An impeller similar to the case inthis paper is chosen to present our CFD analysis accuracycompared to test data from a cooperative company Thisimpeller also applies two-dimensional blades and is usedin the last stage centrifugal compressor of the multistagecompressors It can be observed in Figure 8 that CFD has agood agreement with test data
Note Vaneless diffuser and return channel are also involvedin the test and CFD
For the case in this paper before running CFD impellermodeling is built in the commercial software ldquoBLADEGENrdquoaccording to the fixed geometry from 1D design codeFigure 9 shows the geometry and meridional view of theimpeller It can be observed that leading edge of impeller is inthe radial direction and flow channel is so narrow which arethe typical characteristics of low flow coefficient centrifugalcompressors Inlet and outlet computational domains haveto be added to avoid reserved flow and improve accuracy ofcomputation in CFD Extended outlet computational domainacts like practical vaneless diffuser and makes impeller runclose to the real environment
Three-dimensional viscous RANS solver and Spalart-Allamaras turbulent model are applied in the steady simu-lation with inlet boundary conditions of 119875
01= 13602 kPa
11987901
= 424K and axial flow Static pressure is set on the outletboundary condition and increased gradually Near lower flowregion using mass flow rate condition captures stall pointinstead of static pressure condition The working medium is
8 International Journal of Rotating Machinery
(a) Impeller geometry
80
100
120
140
160
180
200
220
240
260
280
300
0 20minus40 minus20
Z (mm)
R(m
m)
(b) Meridional view
Figure 9 Impeller design
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 1 11
Grid 1Grid 2Grid 3
120587to
t
mmchoke
(a) Total pressure ratio
010
020
030
040
050
060
070
080
090
100
02 03 04 05 06 07 08 09 1 11
Grid 1Grid 2Grid 3
mmchoke
120578
(b) Adiabatic efficiency
Figure 10 Simulation results with three grid plans
defined as typical natural gas All solidwalls are assumed to besmoothwith roughness of 10minus6m In order to reduce the effectof skin friction coefficient affected by surface roughness samesurface property has to be employed in 1D code whenmakinga comparison between 1D prediction and CFD simulation
In order to understand the analytical accuracy of theCFD on the impeller of this case three grid plans shown inTable 2 were tried to check grid sensitivity Figure 10(a) showsthat total pressure ratio distribution curves from three gridplans match very well Adiabatic efficiency curves seen in
International Journal of Rotating Machinery 9
Table 2 Three grid plans
Circumferential Streamwise Spanwise Grid numberGrid 1 27 87 39 185367Grid 2 35 107 49 295421Grid 3 43 127 57 435309
Figure 10(b) also present a good match However it seemsthat larger stall margin is obtained by applying less gridnumber In consideration of running safety in the test thegrid plan 3 with smaller stall margin will be selected as areference for design because designers can not just pick theoption with the best evaluation
For adiabatic efficiency of impeller 1D code can presentthe results with and without parasitic losses However CFDdoes not usually include parasitic losses unless the exact prac-tical structure of centrifugal compressor is built That is thereason why Figure 11(a) shows three distribution curves forefficiency In addition to evaluate 1D code through comparingwith CFD without parasitic losses the efficiency includingparasitic losses close to real environment is needed to bepresented as well 1D code shows wider operating rangeand further stall point which means that comparing withCFD 1D code predicts that the centrifugal compressor canrun at lower mass flow rate Itrsquos shown that steady CFDsimulation cannot get an accurate stall point Transientsimulation should be done after steady calculation which isnot completed in this paper According to the comparisonof efficiency CFD has a little bit discrepancy in adiabaticefficiency on the right side of blue line However differencein efficiency becomes bigger and distribution trends showdifferent as mass flow rate continues to be reduced
In Figure 11(b) total pressure ratio from CFD is overpre-dicted but has same distribution trend with 1D predictionSince empirical loss models are used in the code and CFDcannot show the exact results with real values we think1D code works well and has the function to finish the per-formance evaluation within acceptable discrepancy Furthervalidation with more impellers needs to be carried out in thefuture to see if a constant coefficient for total pressure ratioexists between 1D code and CFD And if this is the case theprediction accuracy of 1D code can be further improved
Note Equation (6) presents the efficiency without parasiticlosses However parasitic losses are taken into account in(7) As mentioned before these two equations are used to becompared with CFD and test data respectively
Relative Mach number distributions at 10 50 and90 spans are shown in Figure 12 It is very clear that alow velocity region exists near pressure surface and becomessmaller gradually as blade span increases Because high staticpressure near pressure surface accompanies low velocity thelow magnitude area can be expected near pressure surfaceMoreover narrow passage introduces large viscous effectsand the typical velocity distribution of the bend comes upjust before the leading edge of the impeller which makes itobvious why Figure 12 presents relative Mach number like
that Fortunately no flow separation is found in the flow fieldof the impeller
Figure 13 shows 119881119898distribution on the meridional view
No low flow region and separation bubble exist whichindicates that this design is rational It is seen in Figure 13that velocity is gradually increasing from hub to shroud inthe extended inlet region which is a typical flow distributionin the bend High velocity means low static pressure andvice versa High pressure static pressure near hub regioncreates centripetal force to balance centrifugal force In orderto reduce the effect of this kind of flow distribution onthe incidence angles along the span of impeller inlet lowercurvature of shroud in the extended inlet region which cancause higher flow area and reduce hub-to-shroud velocitygradient should be applied for performance optimization inthe future Figure 14 presents the idea that static pressuredistribution is smooth through the impeller as expected
Due to the even absolute flow angle distribution atimpeller exit shown in Figure 15 vaneless or vaned diffuserhas perfect inlet condition and can be easily designed ifneeded Blade loading at 10 50 and 90 spans distributesreasonably which can be checked out in detail in Figure 16The blank area between pressure and suction surface staticcurves represents the load that blade withstands which doesnot vary too much through the blade at different spans Thatis what designers expect
The main performance parameters comparison at designpoint is listed in Table 3 The power calculated by CFD isapproximately in the middle of these two values computed by1D code Compared to CFD the efficiency is overpredictedby 152 in the 1D code which is really satisfying The totalpressure ratio in CFD is 305 higher than 1D code Inaddition parasitic losses drop efficiency a lot based on 1Dprediction
5 Conclusions
1D code is developed in this paper and divided into two partswhich are used to design and analyze Based on the code alowflow coefficient centrifugal compressor is designed and itsperformance is predicted In comparisonwith 1D code steadyCFD simulation has been carried out and provides flow fielddetails in the impeller
Comparing to 1D code CFD overpredicts total pressureratio of impeller but shows the same distribution trend whichis encouraging Further validations through more impellershave to be done in the future to confirm if a constantcoefficient for total pressure ratio exists between CFD and1D code For adiabatic efficiency 1D code without includingparasitic losses matches very well CFD in the operating rangeof near design point and choke point However 1D code isoverpredicted between near design point and stall point Thedifference of mass flow rate at choke point between CFDand 1D code is less than 2 Compared to steady CFD 1Dcode presents stall point at lower mass flow rate No flowseparation is found in the flow field of impeller and even theabsolute flow angle distribution at impeller exit is shownThe
10 International Journal of Rotating Machinery
02 03 04 05 06 07 08 09 10 1100
02
04
06
08
10
CFD1D (with parasitic losses)1D (without parasitic losses)
120578
mmchoke
(a) Adiabatic efficiency
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 10 11
CFD
120587to
t
1D code
mmchoke
(b) Total pressure ratio
Figure 11 Impeller performance curves
0 01 02 03 04 05 06
(a) 10 span (b) 50 span (c) 90 span
Figure 12 Relative Mach number map
120
100
80
60
40
20
0
Vm
Figure 13 Meridional velocity and streamline distribution
15E + 07
145E + 07
14E + 07
135E + 07
155E + 07
13E + 07St
atic
pre
ssur
e
Figure 14 Static pressure distribution
0
5
10
15
20
25
30
0Axial length (mm)
minus9 minus8 minus7 minus6 minus5 minus4 minus3 minus2 minus1
1205722
(∘)
Figure 15 Absolute flow angle distribution at impeller exit
International Journal of Rotating Machinery 11
0Axial length (mm)
10 span50 span90 span
10E + 07
11E + 07
12E + 07
13E + 07
14E + 07
15E + 07
16E + 07
Pst
(Pa)
minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2
Figure 16 Blade loading distribution at different spans
Table 3 Performance comparison between CFD and 1D code atdesign point
CFD 1D(no parasitic losses)
1D(parasitic losses)
Power 1778400W 1656740W 1857339W120587tot 121 11731 11731120578 902 9172 8257
blade loading at three different spans distributes smoothly asexpected
Since the low flow coefficient centrifugal compressordesigned in this paper is not the usual type and empiricalequations used are based on medium flow coefficient com-pressors further research on the improvement and validationof 1D code needs to be done by experiment and CFD toincrease prediction accuracy
Nomenclature
119860 Area (m2)AR Area ratio (119860
2sin(1205732119887)1198601sin(120573th))
119886 Sonic velocity (ms)119861 Fraction area blockage119887 Blade height (m)119862119901 Specific heat at constant pressure(Jkg K)
119890 Impeller mean line radius ratio119863 Diameter (m)119863eq Equivalent diffusion factor119896 Ratio of specific heatsΔℎ Enthalpy increase (Jkg)119868119861 Blade work input coefficient
120590(1 minus 119898cot(1205732119887)((120588211986021198802)(1 minus 119861
2))) minus
119880111986211990611198802
2
119871119885 Impeller axial length (m)
119871119861 Length of blade mean camberline (m)
119872 Relative Mach number119898 Mass flow rate (kgs)119873 Rotation speed (rpm)119873119904 Specific speed
119875 Pressure (pa)119877 Gas constant (J(kgsdotK))119879 Temperature (K)119880 Blade speed (ms)119881 Absolute velocity (ms)119882 Relative velocity (ms)Δ119882 Average blade velocity difference (ms)119885 Number of the blades
Greeks
120572 Absolute flow angle from tangential (∘)120573 Relative flow angle from tangential (∘)120578 Adiabatic efficiency120582 Workenthalpy coefficient Δℎ119880
2
2
120587 Pressure ratio120588 Gas density (kgm
3)
120590 Slip factor120593 Inlet flow coefficient119898(120588
111988021205871198632
24)
Ψ Inlet head coefficient(8544119863
2)21198621199011198791((11987521198751)((119896minus1)119896)
minus 1)
Δ120596 Total pressure loss coefficientΔ1199010(1199010minus 119901)
Subscripts
0 Total condition1 Impeller inlet2 Impeller outlet3 Diffuser inlet4 Diffuser outlet
119887 Bladebl Blade loading119888 Criterionchoke Choke pointdf Disc frictiondif Inducer diffusionℎ Impeller inlet hubhs Hub-to-shroudinc Incidenceis Isentropic119897 Leakagelim Limit119898 Meridional componentmax Maximummin Minimummix Wake mixing119904 Shroudst Staticth Impeller throat
12 International Journal of Rotating Machinery
sf Skin frictiontot Total-to-total119906 Tangential componentvld Vaneless diffuser
Superscripts
lowast Correct value1015840 New valueand Value relative to rotating frame of reference
Conflict of Interests
The authors declare that they have no financial and personalrelationships with other people or organizations that caninappropriately influence their work there is no professionalor other personal interest of any nature or kind in anyproduct service andor company that could be construed asinfluencing the position presented in or the review of thepaper
Acknowledgment
This work is supported by the National Natural ScienceFoundation of China under Grant no 51010007 and theChina Scholarship Council (CSC) The authors would like tothank Dr Marco Vagani and Christopher D Bolin for theirdiscussion and advice
References
[1] T Sato J M Oh and A Engeda ldquoExperimental and numericalinvestigation of the flow in a vaneless diffuser of a centrifugalcompressor stage Part 1 experimental investigationrdquo Proceed-ings of the Institution of Mechanical Engineers C vol 219 no 10pp 1053ndash1059 2005
[2] R H Aungier Centrifugal Compressor A Strategy for Aerody-namic Design and Analysis ASME Press New York NY USA2000
[3] V Rusak ldquoDevelopment and performance of the wedge-typelow specific speed compressor wheelrdquo Tech Rep 82-GT-214ASME 2009
[4] M V Casey P Dalbert and E Schurter ldquoRadial compressorstages for low flow coefficientsrdquo in Proceedings of the IMechEInternational Conference on Machinery for the Oil and GasIndustries 1990
[5] T Koizumi ldquoExperimental studies on performance of centrifu-gal compressors with very small flow coefficientrdquoMitsui ZosenTechnical Review vol 117 pp 28ndash39 1983
[6] J Paroubek J Kyncl and V Cyrus ldquoExperimental investigationand performance analysis of six low flow coefficient centrifugalcompressor stagesrdquo Transactions of the ASME Journal of Turbo-machinery vol 117 no 4 pp 585ndash592 1995
[7] J-L Di Liberti Design and development of low-flow coefficientcentrifugal compressors for industrial application [PhD thesis]Michigan State University 1998
[8] Y I Biba D A Nye and L I U Zheji ldquoPerformance evaluationand fluid flow analysis in low flow stages of industrial centrifu-gal compressorrdquo International Journal of Rotating Machineryvol 8 no 5 pp 309ndash317 2002
[9] M R Galvas ldquoFortran program for predicting off-designperformance of centrifugal com-pressorsrdquo Tech Rep TN D-7487 NASA 1973
[10] K H Ludtke Process Centrifugal Compressors Basic FunctionOperation Design Application Springer Berlin Germany 2010
[11] F J Wiesner ldquoA review of slip factors for centrifugal compres-sorsrdquo Journal of Engineering for Power Transactions of theASMEvol 89 pp 558ndash572 1967
[12] R H Aungier ldquoMean streamline aerodynamic performanceanalysis of centrifugal compressorsrdquo Transactions of the ASMEJournal of Turbomachinery vol 117 no 3 pp 360ndash366 1995
[13] S L Dixon Fluid Mechanics and Thermodnamics of Turboma-chinery Butterworth-Heinemann 4th edition 1998
[14] Y Senoo and Y Kinoshita ldquoLimits of rotating stall and stall invaneless diffusers of centrifugal compressorsrdquo Tech Rep 78-GT-19 ASME 1978
[15] S Lieblein ldquoLoss and stall analysis of compressor cascadesrdquoASME Transactions Journal of Basic Engineering vol 81 pp387ndash400 1959
[16] H Krain and B Hoffmann ldquoFlow physics in high pressure ratiocentrifugal compressorsrdquo in Proceedings of the ASME FluidsEngineering Division Summer Meeting June 1998
[17] G Eisenlohr and H Krain ldquoInvestigation of the flow througha high pressure ratio centrifugal impellerrdquo in Proceedings of theASME Conference Proceedings 2003
International Journal of
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International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
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Shock and Vibration
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Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
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Volume 2014
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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DistributedSensor Networks
International Journal of
International Journal of Rotating Machinery 3
Given paremeters
Outlet analysis
Inlet analysisOutlet design
Inlet design
Des
ign
part
Export impellerGeometry data
Mass flow rate(variable)
Ana
lysis
par
t
Impeller performance
(design and off-design points)
Internal lossesIncidence lossSkin friction lossWake mixing loss
Clearance lossEntrance diffusion lossHub-to-shroud loading
Choking loss
Blade loading loss
loss
Parasitic lossesDisc friction lossLeakage lossRecirculalion loss
Figure 2 Flow chart of 1D code
an iterative solution procedurewith the constraint of iterationerror being less than 01 The same iterative method isapplied until convergence is reached on the fluid densitycalculation at impeller outlet in which internal losses areinvolved and used for computing impeller efficiency totalpressure static pressure and density The equations used inthe analysis part will be introduced and the related statefunctions and loss models are included
Specific heat at constant pressure is given as a constantprovided by industry in this design case No preswirl exists atthe impeller inlet which makes 119881
1199061= 0 and 119881
1= 1198811198981 Inlet
gas density is initialized by the following equation
1205881asymp 12058801
=11987501
(11987711987901) (1)
According to the fixed geometry data and given designparameters the values of 119881
1198981 1198801 1198821 and 119882th can be
easily calculated Equation (2) below provide the rest ofthermodynamic parameters
1198791= 11987901
minus1198812
1
(2119862119901)
1198751= 11987501(
1198791
11987901
)
119896(119896minus1)
12058811015840 =
1198751
(1198771198791)
(2)
The inlet calculationwill be done once the iteration showsthat the difference between two density values is within theerror range shown in Figure 3 Before moving on to theimpeller outlet calculation fraction area blockage at impeller
exit (1198612) has to be initially approximated first and updated
later Then 1198811199062
can be given after slip factor calculation iscompleted
1205882= 1205881(
1198802
2
(11986211990111987901)+ 1)
1(119896minus1)
1198811198982
=119898
(120587120588211986321198872(1 minus 119861
2))
120590 = 1 minus
radicsin (1205732119887) sin (120572
2119888)
11988507
119890lim =(120590 minus sin (19 + 2120573
2119887))
(1 minus sin (19 + 21205732119887))
119890 =1198631
1198632
If 119890 gt 119890lim 120590 = 120590(1 minus ((119890 minus 119890lim)
(1 minus 119890lim))
radic120573211988710
)
1198811199062
= 120590(1198802minus
1198811198982
tan (1205732119887))
119879and
01= 1198791+
1198821
2
(2119862119901)
119879and
02= 119879and
01+
(1198802
2minus 1198802
1)
(2119862119901)
(3)
4 International Journal of Rotating Machinery
Start
Choose 1205881
Choose 1205882
Input variables m[mmin mmax]
No
No
No
No
Inlet calculationVm1 V1 W1 P1 T1
Yes
Yes
Yes
Yes
1205881998400
Internal losses
Calculate 1205882998400
Stop
|1205881 minus 1205881998400|1205881 lt 01
|1205882 minus 1205882998400|1205882 lt 01
No parasitic losses120578totimp
Calculate P02 P2
Outlet calculationVm2 Vu2Wu2W2 T2
V2 T02 1205732 1205722
Check if Mth = 1
Calculate Mth
Parasitic losses
Include parasitic losses
No parasitic losses
Calculate 120578totstg
Calculate 120578totstg
Calculate Δhvld
Calculate P4 1205884 Vm4998400
Choose Vm4
Choose n
Calculate Vu4 V4 T4
|Vm4 minus Vm4998400|Vm4 lt 01
17ndash20
Figure 3 Detailed flow chart of 1D analysis part
So 1198821199062 1198822 1198812 and flow angles can be easily obtained
based on basic impeller outlet velocity triangleThen (4) willprovide 119879
2and 119879
02
1198792= 119879and
02minus
1198822
2
(2119862119901)
11987902
= 11987901
+11988021198811199062
119862119901
(4)
Then all the internal losses and parasitic losses calcula-tion can be finishedDetailed equations regarding lossmodelscan be found in [2] 119861
2can be updated by (5)
11986121015840 =
(ℎsf + ℎhs)
11988222
+ (03 +1198872
2
1198712119861
)119860119877211988721205882
(1205881119871119861) (5)
120578I =119862119901(11987902
minus 11987901) minus (Δℎinc + Δℎbl + Δℎsf + Δℎmix + Δℎdif)
119862119901(11987902
minus 11987901)
(6)
International Journal of Rotating Machinery 5
If parasitic losses are included a revised formula (7)should be applied
120578II=119862119901(11987902
minus 11987901) minus (Δℎinc + Δℎbl + Δℎsf + Δℎmix + Δℎdif)
119862119901(11987902
minus 11987901) + Δℎdf + Δℎ
119897
(7)
Finally density at impeller outlet is updated and com-pared with the initial one
11987902is = 119879
01+ 120578I (11987902 minus 119879
01)
11987502
= 11987501(11987902is11987901
)
119896(119896minus1)
1198752= 11987502(11987902
1198792
)
119896(119896minus1)
12058821015840 =
1198752
(1198771198792)
(8)
The code will continue running until density at impelleroutlet converges If vaneless diffuser is involved in the analysispart the corresponding loss model shown in Figure 3 has tobe added
Internal losses mainly include incidence loss blade load-ing loss skin friction loss wake mixing loss hub-to-shroudloading loss entrance diffusion loss and clearance loss [2 12]Generally parasitic losses are not involved in CFD In orderto make an efficiency comparison with or without parasiticlosses disc friction recirculation and leakage are also takeninto consideration In this case clearance loss and leakage lossare not considered due to shrouded impeller
Besides the above descriptions how to predict stall andchoke point in the analysis part must be mentioned herebecause these two points determine the operating range ofcentrifugal compressor directly In Figure 3 mass flow rateas the only input variable has a range coming from designpart directly The initial value of mass flow rate at chokepoint is predicted in design part by (9) developed by Dixon[13] Actually (9) always overpredicts mass flow rate whichis because aerodynamic blockage at impeller throat is notconsidered Therefore it is appropriate to apply (9) to obtainlarger mass flow rate for choke point first The initializationof mass flow rate for stall point calculated in design part isto use critical absolute flow angle at diffuser inlet which iscomputed by (10) Pinch between impeller outlet and diffuserinlet is also considered if applied [14]
119898choke = 119860 th1205880111988601[2 + (119896 minus 1)119880
2
11198862
01
119896 + 1]
(k+1)2(119896minus1)
(9)
120572lowast
3119888= 1205723119888
+ (1702 minus1484119887
2
1198892
)(1 minus1198873
1198872
) (10)
In the analysis part for stall point prediction two meth-ods are adopted The main one used by majority designersis to check if 119882
1119904119882th ge 175 which seemed as an inducer
stall criterion The second option is to estimate equivalent
10
12
14
16
18
20
22
02 03 04 05 06 07 08 09 10 11mmchoke
Deq
Figure 4 Equivalent diffusion factor
diffusion factor (119863eq) Lieblein [15] found that blade stalloccurs in the axial compressor when 119863eq is bigger than 2Later on 119863eq is generalized to radial and mixed flow bladesto evaluate the blade loading This criterion is also foundto be an appropriate blade stall limit for impellers [2] Therelated calculation equations are shown below119863eq is checkedat every iteration step in analysis part to see if it reachesthe criteria or not If neither 119882
1119904119882th nor 119863eq indicates the
compressor stalls the initial mass flow rate value from (10)will be considered to be the minimum value
119863eq =119882max1198822
119882max =(1198821+ 1198822+ Δ119882)
2
Δ119882 =212058711986321198802119868119861
(119885119871119861)
(11)
Finally in this case 1D code points out to 119863eq which isdetected beyond the critical value first The distribution of119863eq over mass flow rate is shown in Figure 4 Based on thecase in this paper it is still hard to determine which methodis suitable to stall point prediction so far According to CFDsimulation and test data further evaluation of the 1D codeneeds to be done through huge number of impellers whichwill be focused on in the future research work
As for choke point calculation iterativemethod is applieduntil relative Mach number at the impeller throat reaches 1Generally choke mass flow rate from analysis part is smallerthan initialization based on (9) In this case 1D code predictschokemass flow rate at 80 kgs andCFD shows it at 8155 kgsThe difference is less than 2 However the initial value is8954 kgs larger than analysis code prediction as expected
Since mass flow rate in analysis part is increased byspecific growth increment the real operating range of thecentrifugal compressor will be fixed after choke point cal-culation is done The code will plot the entire performance
6 International Journal of Rotating Machinery
3
4
5
6
7
8
05 06 07 08 09 1 11
Test
120587to
t
mmchoke
1D code
(a) Adiabatic efficiency
076
078
08
082
084
086
088
09
05 06 07 08 09 1 11
Test
mmchoke
1D code
120578
(b) Total pressure ratio
Figure 5 Performance curves between 1-D and test
of the centrifugal compressor automatically including designand off-design points
1D analysis code was calibrated by the test data of one ofthree Krainrsquos impellers [16 17] In Figure 5 it is obvious thattotal pressure ratio and adiabatic efficiency show similar dis-tribution trend and the discrepancies between performancecurves are acceptable Compared to the test wider surgemargin is obtained by 1D code Overall based on this case1D analysis code is functional and satisfying Also a detailedflow parameter comparison of 1D code and test data of a highflow coefficient centrifugal compressor have been carried outwhich also indicates good predictive effect of 1D analysiscode The related results are not shown here
3 1D Design and Analysis Results
Main impeller geometric parameters from 1D code are listedin Table 1 Design parameters like mass flow rate rotationalspeed impeller outlet diameter and shaft diameter areprovided by industry according to practical demand
Since leading edge and trailing edge of the impeller havethe same streamline slope angle in this case hub-to-shroudloss model is not activated The criterion in the chokingloss model is not satisfied and the choking loss is also notconsidered as well Recirculation loss is neglected due to theshrouded impeller designed in this study
Therefore internal losses actually used include wakemixing loss skin friction loss incidence loss blade load-ing loss and inducer diffusion loss Figure 6 shows losscoefficient distribution of impeller It is observed that skin
Table 1 Impeller parameters
119898 48 kgs119873 12800 rpm120593 0022119873119904
0071198631
02172m1198632
0381m1198871
00123m1198872
00082m1205731119887
289∘
1205732119887
40∘
119871119911
00193m11988721198632
00216119885 13
friction is the main loss source in the impeller as expecteddue to narrow flow path of low flow coefficient centrifugalcompressor and increases gradually from surge side to chokeside Wake loss appears near surge point and presents thesmallest loss coefficient Minimum incidence loss occurs atdesign point The distribution of incidence loss is prettytypical Either increasing mass flow rate from design pointto choke side or reducing it from design point to surge sidewill causemore incidence loss Higher pressure ratio is alwaysaccompanied by accordingly higher blade loading loss whichcan explain why blade loading loss distributes like the trendshown in Figure 6 An inducer diffusion loss appears onlyfor applications of less than 63 mass flow rate which is
International Journal of Rotating Machinery 7
0
01
02
03
04
05
06
036 040 044 051 057 063 073 078 086 093 097 100
Loss
coeffi
cien
t
Inducer diffusionBlade loadingIncidence
Skin frictionWake mixing
mmchoke
Figure 6 Loss coefficient distribution of impeller
0
002
004
006
008
01
012
014
036 040 044 051 057 063 073 078 086 093 097 100
Wor
k co
effici
ent
LeakageDisc friction
mmchoke
Figure 7 Distribution of work coefficient due to parasitic losses
the design point For parasitic losses or external losses onlydisc friction loss and leakage loss are involved They presentsimilar distribution trend seen in Figure 7 Overall 1D codeprovides asmuch information as it canMore importantly the1D analysis results look reasonable and acceptable
Note Please refer to reference [2] to look up the equationsused for calculating loss coefficient and work coefficient inFigures 6 and 7 which are based on the results that theanalysis code provides
05
06
07
08
09
10
11
12
13
14
000
015
030
045
060
075
090
105
120
135
004 005 006 007 008 009
Test CFDTest CFD
120578120595
120593
Figure 8 Performance comparison between test and CFD
4 3D CFD Validation
Many impellers coming from either open literature or indus-try have been used to evaluate the accuracy of the CFDanalysis before It is confirmed that our CFD simulation isreasonable and reliable An impeller similar to the case inthis paper is chosen to present our CFD analysis accuracycompared to test data from a cooperative company Thisimpeller also applies two-dimensional blades and is usedin the last stage centrifugal compressor of the multistagecompressors It can be observed in Figure 8 that CFD has agood agreement with test data
Note Vaneless diffuser and return channel are also involvedin the test and CFD
For the case in this paper before running CFD impellermodeling is built in the commercial software ldquoBLADEGENrdquoaccording to the fixed geometry from 1D design codeFigure 9 shows the geometry and meridional view of theimpeller It can be observed that leading edge of impeller is inthe radial direction and flow channel is so narrow which arethe typical characteristics of low flow coefficient centrifugalcompressors Inlet and outlet computational domains haveto be added to avoid reserved flow and improve accuracy ofcomputation in CFD Extended outlet computational domainacts like practical vaneless diffuser and makes impeller runclose to the real environment
Three-dimensional viscous RANS solver and Spalart-Allamaras turbulent model are applied in the steady simu-lation with inlet boundary conditions of 119875
01= 13602 kPa
11987901
= 424K and axial flow Static pressure is set on the outletboundary condition and increased gradually Near lower flowregion using mass flow rate condition captures stall pointinstead of static pressure condition The working medium is
8 International Journal of Rotating Machinery
(a) Impeller geometry
80
100
120
140
160
180
200
220
240
260
280
300
0 20minus40 minus20
Z (mm)
R(m
m)
(b) Meridional view
Figure 9 Impeller design
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 1 11
Grid 1Grid 2Grid 3
120587to
t
mmchoke
(a) Total pressure ratio
010
020
030
040
050
060
070
080
090
100
02 03 04 05 06 07 08 09 1 11
Grid 1Grid 2Grid 3
mmchoke
120578
(b) Adiabatic efficiency
Figure 10 Simulation results with three grid plans
defined as typical natural gas All solidwalls are assumed to besmoothwith roughness of 10minus6m In order to reduce the effectof skin friction coefficient affected by surface roughness samesurface property has to be employed in 1D code whenmakinga comparison between 1D prediction and CFD simulation
In order to understand the analytical accuracy of theCFD on the impeller of this case three grid plans shown inTable 2 were tried to check grid sensitivity Figure 10(a) showsthat total pressure ratio distribution curves from three gridplans match very well Adiabatic efficiency curves seen in
International Journal of Rotating Machinery 9
Table 2 Three grid plans
Circumferential Streamwise Spanwise Grid numberGrid 1 27 87 39 185367Grid 2 35 107 49 295421Grid 3 43 127 57 435309
Figure 10(b) also present a good match However it seemsthat larger stall margin is obtained by applying less gridnumber In consideration of running safety in the test thegrid plan 3 with smaller stall margin will be selected as areference for design because designers can not just pick theoption with the best evaluation
For adiabatic efficiency of impeller 1D code can presentthe results with and without parasitic losses However CFDdoes not usually include parasitic losses unless the exact prac-tical structure of centrifugal compressor is built That is thereason why Figure 11(a) shows three distribution curves forefficiency In addition to evaluate 1D code through comparingwith CFD without parasitic losses the efficiency includingparasitic losses close to real environment is needed to bepresented as well 1D code shows wider operating rangeand further stall point which means that comparing withCFD 1D code predicts that the centrifugal compressor canrun at lower mass flow rate Itrsquos shown that steady CFDsimulation cannot get an accurate stall point Transientsimulation should be done after steady calculation which isnot completed in this paper According to the comparisonof efficiency CFD has a little bit discrepancy in adiabaticefficiency on the right side of blue line However differencein efficiency becomes bigger and distribution trends showdifferent as mass flow rate continues to be reduced
In Figure 11(b) total pressure ratio from CFD is overpre-dicted but has same distribution trend with 1D predictionSince empirical loss models are used in the code and CFDcannot show the exact results with real values we think1D code works well and has the function to finish the per-formance evaluation within acceptable discrepancy Furthervalidation with more impellers needs to be carried out in thefuture to see if a constant coefficient for total pressure ratioexists between 1D code and CFD And if this is the case theprediction accuracy of 1D code can be further improved
Note Equation (6) presents the efficiency without parasiticlosses However parasitic losses are taken into account in(7) As mentioned before these two equations are used to becompared with CFD and test data respectively
Relative Mach number distributions at 10 50 and90 spans are shown in Figure 12 It is very clear that alow velocity region exists near pressure surface and becomessmaller gradually as blade span increases Because high staticpressure near pressure surface accompanies low velocity thelow magnitude area can be expected near pressure surfaceMoreover narrow passage introduces large viscous effectsand the typical velocity distribution of the bend comes upjust before the leading edge of the impeller which makes itobvious why Figure 12 presents relative Mach number like
that Fortunately no flow separation is found in the flow fieldof the impeller
Figure 13 shows 119881119898distribution on the meridional view
No low flow region and separation bubble exist whichindicates that this design is rational It is seen in Figure 13that velocity is gradually increasing from hub to shroud inthe extended inlet region which is a typical flow distributionin the bend High velocity means low static pressure andvice versa High pressure static pressure near hub regioncreates centripetal force to balance centrifugal force In orderto reduce the effect of this kind of flow distribution onthe incidence angles along the span of impeller inlet lowercurvature of shroud in the extended inlet region which cancause higher flow area and reduce hub-to-shroud velocitygradient should be applied for performance optimization inthe future Figure 14 presents the idea that static pressuredistribution is smooth through the impeller as expected
Due to the even absolute flow angle distribution atimpeller exit shown in Figure 15 vaneless or vaned diffuserhas perfect inlet condition and can be easily designed ifneeded Blade loading at 10 50 and 90 spans distributesreasonably which can be checked out in detail in Figure 16The blank area between pressure and suction surface staticcurves represents the load that blade withstands which doesnot vary too much through the blade at different spans Thatis what designers expect
The main performance parameters comparison at designpoint is listed in Table 3 The power calculated by CFD isapproximately in the middle of these two values computed by1D code Compared to CFD the efficiency is overpredictedby 152 in the 1D code which is really satisfying The totalpressure ratio in CFD is 305 higher than 1D code Inaddition parasitic losses drop efficiency a lot based on 1Dprediction
5 Conclusions
1D code is developed in this paper and divided into two partswhich are used to design and analyze Based on the code alowflow coefficient centrifugal compressor is designed and itsperformance is predicted In comparisonwith 1D code steadyCFD simulation has been carried out and provides flow fielddetails in the impeller
Comparing to 1D code CFD overpredicts total pressureratio of impeller but shows the same distribution trend whichis encouraging Further validations through more impellershave to be done in the future to confirm if a constantcoefficient for total pressure ratio exists between CFD and1D code For adiabatic efficiency 1D code without includingparasitic losses matches very well CFD in the operating rangeof near design point and choke point However 1D code isoverpredicted between near design point and stall point Thedifference of mass flow rate at choke point between CFDand 1D code is less than 2 Compared to steady CFD 1Dcode presents stall point at lower mass flow rate No flowseparation is found in the flow field of impeller and even theabsolute flow angle distribution at impeller exit is shownThe
10 International Journal of Rotating Machinery
02 03 04 05 06 07 08 09 10 1100
02
04
06
08
10
CFD1D (with parasitic losses)1D (without parasitic losses)
120578
mmchoke
(a) Adiabatic efficiency
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 10 11
CFD
120587to
t
1D code
mmchoke
(b) Total pressure ratio
Figure 11 Impeller performance curves
0 01 02 03 04 05 06
(a) 10 span (b) 50 span (c) 90 span
Figure 12 Relative Mach number map
120
100
80
60
40
20
0
Vm
Figure 13 Meridional velocity and streamline distribution
15E + 07
145E + 07
14E + 07
135E + 07
155E + 07
13E + 07St
atic
pre
ssur
e
Figure 14 Static pressure distribution
0
5
10
15
20
25
30
0Axial length (mm)
minus9 minus8 minus7 minus6 minus5 minus4 minus3 minus2 minus1
1205722
(∘)
Figure 15 Absolute flow angle distribution at impeller exit
International Journal of Rotating Machinery 11
0Axial length (mm)
10 span50 span90 span
10E + 07
11E + 07
12E + 07
13E + 07
14E + 07
15E + 07
16E + 07
Pst
(Pa)
minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2
Figure 16 Blade loading distribution at different spans
Table 3 Performance comparison between CFD and 1D code atdesign point
CFD 1D(no parasitic losses)
1D(parasitic losses)
Power 1778400W 1656740W 1857339W120587tot 121 11731 11731120578 902 9172 8257
blade loading at three different spans distributes smoothly asexpected
Since the low flow coefficient centrifugal compressordesigned in this paper is not the usual type and empiricalequations used are based on medium flow coefficient com-pressors further research on the improvement and validationof 1D code needs to be done by experiment and CFD toincrease prediction accuracy
Nomenclature
119860 Area (m2)AR Area ratio (119860
2sin(1205732119887)1198601sin(120573th))
119886 Sonic velocity (ms)119861 Fraction area blockage119887 Blade height (m)119862119901 Specific heat at constant pressure(Jkg K)
119890 Impeller mean line radius ratio119863 Diameter (m)119863eq Equivalent diffusion factor119896 Ratio of specific heatsΔℎ Enthalpy increase (Jkg)119868119861 Blade work input coefficient
120590(1 minus 119898cot(1205732119887)((120588211986021198802)(1 minus 119861
2))) minus
119880111986211990611198802
2
119871119885 Impeller axial length (m)
119871119861 Length of blade mean camberline (m)
119872 Relative Mach number119898 Mass flow rate (kgs)119873 Rotation speed (rpm)119873119904 Specific speed
119875 Pressure (pa)119877 Gas constant (J(kgsdotK))119879 Temperature (K)119880 Blade speed (ms)119881 Absolute velocity (ms)119882 Relative velocity (ms)Δ119882 Average blade velocity difference (ms)119885 Number of the blades
Greeks
120572 Absolute flow angle from tangential (∘)120573 Relative flow angle from tangential (∘)120578 Adiabatic efficiency120582 Workenthalpy coefficient Δℎ119880
2
2
120587 Pressure ratio120588 Gas density (kgm
3)
120590 Slip factor120593 Inlet flow coefficient119898(120588
111988021205871198632
24)
Ψ Inlet head coefficient(8544119863
2)21198621199011198791((11987521198751)((119896minus1)119896)
minus 1)
Δ120596 Total pressure loss coefficientΔ1199010(1199010minus 119901)
Subscripts
0 Total condition1 Impeller inlet2 Impeller outlet3 Diffuser inlet4 Diffuser outlet
119887 Bladebl Blade loading119888 Criterionchoke Choke pointdf Disc frictiondif Inducer diffusionℎ Impeller inlet hubhs Hub-to-shroudinc Incidenceis Isentropic119897 Leakagelim Limit119898 Meridional componentmax Maximummin Minimummix Wake mixing119904 Shroudst Staticth Impeller throat
12 International Journal of Rotating Machinery
sf Skin frictiontot Total-to-total119906 Tangential componentvld Vaneless diffuser
Superscripts
lowast Correct value1015840 New valueand Value relative to rotating frame of reference
Conflict of Interests
The authors declare that they have no financial and personalrelationships with other people or organizations that caninappropriately influence their work there is no professionalor other personal interest of any nature or kind in anyproduct service andor company that could be construed asinfluencing the position presented in or the review of thepaper
Acknowledgment
This work is supported by the National Natural ScienceFoundation of China under Grant no 51010007 and theChina Scholarship Council (CSC) The authors would like tothank Dr Marco Vagani and Christopher D Bolin for theirdiscussion and advice
References
[1] T Sato J M Oh and A Engeda ldquoExperimental and numericalinvestigation of the flow in a vaneless diffuser of a centrifugalcompressor stage Part 1 experimental investigationrdquo Proceed-ings of the Institution of Mechanical Engineers C vol 219 no 10pp 1053ndash1059 2005
[2] R H Aungier Centrifugal Compressor A Strategy for Aerody-namic Design and Analysis ASME Press New York NY USA2000
[3] V Rusak ldquoDevelopment and performance of the wedge-typelow specific speed compressor wheelrdquo Tech Rep 82-GT-214ASME 2009
[4] M V Casey P Dalbert and E Schurter ldquoRadial compressorstages for low flow coefficientsrdquo in Proceedings of the IMechEInternational Conference on Machinery for the Oil and GasIndustries 1990
[5] T Koizumi ldquoExperimental studies on performance of centrifu-gal compressors with very small flow coefficientrdquoMitsui ZosenTechnical Review vol 117 pp 28ndash39 1983
[6] J Paroubek J Kyncl and V Cyrus ldquoExperimental investigationand performance analysis of six low flow coefficient centrifugalcompressor stagesrdquo Transactions of the ASME Journal of Turbo-machinery vol 117 no 4 pp 585ndash592 1995
[7] J-L Di Liberti Design and development of low-flow coefficientcentrifugal compressors for industrial application [PhD thesis]Michigan State University 1998
[8] Y I Biba D A Nye and L I U Zheji ldquoPerformance evaluationand fluid flow analysis in low flow stages of industrial centrifu-gal compressorrdquo International Journal of Rotating Machineryvol 8 no 5 pp 309ndash317 2002
[9] M R Galvas ldquoFortran program for predicting off-designperformance of centrifugal com-pressorsrdquo Tech Rep TN D-7487 NASA 1973
[10] K H Ludtke Process Centrifugal Compressors Basic FunctionOperation Design Application Springer Berlin Germany 2010
[11] F J Wiesner ldquoA review of slip factors for centrifugal compres-sorsrdquo Journal of Engineering for Power Transactions of theASMEvol 89 pp 558ndash572 1967
[12] R H Aungier ldquoMean streamline aerodynamic performanceanalysis of centrifugal compressorsrdquo Transactions of the ASMEJournal of Turbomachinery vol 117 no 3 pp 360ndash366 1995
[13] S L Dixon Fluid Mechanics and Thermodnamics of Turboma-chinery Butterworth-Heinemann 4th edition 1998
[14] Y Senoo and Y Kinoshita ldquoLimits of rotating stall and stall invaneless diffusers of centrifugal compressorsrdquo Tech Rep 78-GT-19 ASME 1978
[15] S Lieblein ldquoLoss and stall analysis of compressor cascadesrdquoASME Transactions Journal of Basic Engineering vol 81 pp387ndash400 1959
[16] H Krain and B Hoffmann ldquoFlow physics in high pressure ratiocentrifugal compressorsrdquo in Proceedings of the ASME FluidsEngineering Division Summer Meeting June 1998
[17] G Eisenlohr and H Krain ldquoInvestigation of the flow througha high pressure ratio centrifugal impellerrdquo in Proceedings of theASME Conference Proceedings 2003
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International Journal of
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Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
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VLSI Design
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Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
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Electrical and Computer Engineering
Journal of
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DistributedSensor Networks
International Journal of
4 International Journal of Rotating Machinery
Start
Choose 1205881
Choose 1205882
Input variables m[mmin mmax]
No
No
No
No
Inlet calculationVm1 V1 W1 P1 T1
Yes
Yes
Yes
Yes
1205881998400
Internal losses
Calculate 1205882998400
Stop
|1205881 minus 1205881998400|1205881 lt 01
|1205882 minus 1205882998400|1205882 lt 01
No parasitic losses120578totimp
Calculate P02 P2
Outlet calculationVm2 Vu2Wu2W2 T2
V2 T02 1205732 1205722
Check if Mth = 1
Calculate Mth
Parasitic losses
Include parasitic losses
No parasitic losses
Calculate 120578totstg
Calculate 120578totstg
Calculate Δhvld
Calculate P4 1205884 Vm4998400
Choose Vm4
Choose n
Calculate Vu4 V4 T4
|Vm4 minus Vm4998400|Vm4 lt 01
17ndash20
Figure 3 Detailed flow chart of 1D analysis part
So 1198821199062 1198822 1198812 and flow angles can be easily obtained
based on basic impeller outlet velocity triangleThen (4) willprovide 119879
2and 119879
02
1198792= 119879and
02minus
1198822
2
(2119862119901)
11987902
= 11987901
+11988021198811199062
119862119901
(4)
Then all the internal losses and parasitic losses calcula-tion can be finishedDetailed equations regarding lossmodelscan be found in [2] 119861
2can be updated by (5)
11986121015840 =
(ℎsf + ℎhs)
11988222
+ (03 +1198872
2
1198712119861
)119860119877211988721205882
(1205881119871119861) (5)
120578I =119862119901(11987902
minus 11987901) minus (Δℎinc + Δℎbl + Δℎsf + Δℎmix + Δℎdif)
119862119901(11987902
minus 11987901)
(6)
International Journal of Rotating Machinery 5
If parasitic losses are included a revised formula (7)should be applied
120578II=119862119901(11987902
minus 11987901) minus (Δℎinc + Δℎbl + Δℎsf + Δℎmix + Δℎdif)
119862119901(11987902
minus 11987901) + Δℎdf + Δℎ
119897
(7)
Finally density at impeller outlet is updated and com-pared with the initial one
11987902is = 119879
01+ 120578I (11987902 minus 119879
01)
11987502
= 11987501(11987902is11987901
)
119896(119896minus1)
1198752= 11987502(11987902
1198792
)
119896(119896minus1)
12058821015840 =
1198752
(1198771198792)
(8)
The code will continue running until density at impelleroutlet converges If vaneless diffuser is involved in the analysispart the corresponding loss model shown in Figure 3 has tobe added
Internal losses mainly include incidence loss blade load-ing loss skin friction loss wake mixing loss hub-to-shroudloading loss entrance diffusion loss and clearance loss [2 12]Generally parasitic losses are not involved in CFD In orderto make an efficiency comparison with or without parasiticlosses disc friction recirculation and leakage are also takeninto consideration In this case clearance loss and leakage lossare not considered due to shrouded impeller
Besides the above descriptions how to predict stall andchoke point in the analysis part must be mentioned herebecause these two points determine the operating range ofcentrifugal compressor directly In Figure 3 mass flow rateas the only input variable has a range coming from designpart directly The initial value of mass flow rate at chokepoint is predicted in design part by (9) developed by Dixon[13] Actually (9) always overpredicts mass flow rate whichis because aerodynamic blockage at impeller throat is notconsidered Therefore it is appropriate to apply (9) to obtainlarger mass flow rate for choke point first The initializationof mass flow rate for stall point calculated in design part isto use critical absolute flow angle at diffuser inlet which iscomputed by (10) Pinch between impeller outlet and diffuserinlet is also considered if applied [14]
119898choke = 119860 th1205880111988601[2 + (119896 minus 1)119880
2
11198862
01
119896 + 1]
(k+1)2(119896minus1)
(9)
120572lowast
3119888= 1205723119888
+ (1702 minus1484119887
2
1198892
)(1 minus1198873
1198872
) (10)
In the analysis part for stall point prediction two meth-ods are adopted The main one used by majority designersis to check if 119882
1119904119882th ge 175 which seemed as an inducer
stall criterion The second option is to estimate equivalent
10
12
14
16
18
20
22
02 03 04 05 06 07 08 09 10 11mmchoke
Deq
Figure 4 Equivalent diffusion factor
diffusion factor (119863eq) Lieblein [15] found that blade stalloccurs in the axial compressor when 119863eq is bigger than 2Later on 119863eq is generalized to radial and mixed flow bladesto evaluate the blade loading This criterion is also foundto be an appropriate blade stall limit for impellers [2] Therelated calculation equations are shown below119863eq is checkedat every iteration step in analysis part to see if it reachesthe criteria or not If neither 119882
1119904119882th nor 119863eq indicates the
compressor stalls the initial mass flow rate value from (10)will be considered to be the minimum value
119863eq =119882max1198822
119882max =(1198821+ 1198822+ Δ119882)
2
Δ119882 =212058711986321198802119868119861
(119885119871119861)
(11)
Finally in this case 1D code points out to 119863eq which isdetected beyond the critical value first The distribution of119863eq over mass flow rate is shown in Figure 4 Based on thecase in this paper it is still hard to determine which methodis suitable to stall point prediction so far According to CFDsimulation and test data further evaluation of the 1D codeneeds to be done through huge number of impellers whichwill be focused on in the future research work
As for choke point calculation iterativemethod is applieduntil relative Mach number at the impeller throat reaches 1Generally choke mass flow rate from analysis part is smallerthan initialization based on (9) In this case 1D code predictschokemass flow rate at 80 kgs andCFD shows it at 8155 kgsThe difference is less than 2 However the initial value is8954 kgs larger than analysis code prediction as expected
Since mass flow rate in analysis part is increased byspecific growth increment the real operating range of thecentrifugal compressor will be fixed after choke point cal-culation is done The code will plot the entire performance
6 International Journal of Rotating Machinery
3
4
5
6
7
8
05 06 07 08 09 1 11
Test
120587to
t
mmchoke
1D code
(a) Adiabatic efficiency
076
078
08
082
084
086
088
09
05 06 07 08 09 1 11
Test
mmchoke
1D code
120578
(b) Total pressure ratio
Figure 5 Performance curves between 1-D and test
of the centrifugal compressor automatically including designand off-design points
1D analysis code was calibrated by the test data of one ofthree Krainrsquos impellers [16 17] In Figure 5 it is obvious thattotal pressure ratio and adiabatic efficiency show similar dis-tribution trend and the discrepancies between performancecurves are acceptable Compared to the test wider surgemargin is obtained by 1D code Overall based on this case1D analysis code is functional and satisfying Also a detailedflow parameter comparison of 1D code and test data of a highflow coefficient centrifugal compressor have been carried outwhich also indicates good predictive effect of 1D analysiscode The related results are not shown here
3 1D Design and Analysis Results
Main impeller geometric parameters from 1D code are listedin Table 1 Design parameters like mass flow rate rotationalspeed impeller outlet diameter and shaft diameter areprovided by industry according to practical demand
Since leading edge and trailing edge of the impeller havethe same streamline slope angle in this case hub-to-shroudloss model is not activated The criterion in the chokingloss model is not satisfied and the choking loss is also notconsidered as well Recirculation loss is neglected due to theshrouded impeller designed in this study
Therefore internal losses actually used include wakemixing loss skin friction loss incidence loss blade load-ing loss and inducer diffusion loss Figure 6 shows losscoefficient distribution of impeller It is observed that skin
Table 1 Impeller parameters
119898 48 kgs119873 12800 rpm120593 0022119873119904
0071198631
02172m1198632
0381m1198871
00123m1198872
00082m1205731119887
289∘
1205732119887
40∘
119871119911
00193m11988721198632
00216119885 13
friction is the main loss source in the impeller as expecteddue to narrow flow path of low flow coefficient centrifugalcompressor and increases gradually from surge side to chokeside Wake loss appears near surge point and presents thesmallest loss coefficient Minimum incidence loss occurs atdesign point The distribution of incidence loss is prettytypical Either increasing mass flow rate from design pointto choke side or reducing it from design point to surge sidewill causemore incidence loss Higher pressure ratio is alwaysaccompanied by accordingly higher blade loading loss whichcan explain why blade loading loss distributes like the trendshown in Figure 6 An inducer diffusion loss appears onlyfor applications of less than 63 mass flow rate which is
International Journal of Rotating Machinery 7
0
01
02
03
04
05
06
036 040 044 051 057 063 073 078 086 093 097 100
Loss
coeffi
cien
t
Inducer diffusionBlade loadingIncidence
Skin frictionWake mixing
mmchoke
Figure 6 Loss coefficient distribution of impeller
0
002
004
006
008
01
012
014
036 040 044 051 057 063 073 078 086 093 097 100
Wor
k co
effici
ent
LeakageDisc friction
mmchoke
Figure 7 Distribution of work coefficient due to parasitic losses
the design point For parasitic losses or external losses onlydisc friction loss and leakage loss are involved They presentsimilar distribution trend seen in Figure 7 Overall 1D codeprovides asmuch information as it canMore importantly the1D analysis results look reasonable and acceptable
Note Please refer to reference [2] to look up the equationsused for calculating loss coefficient and work coefficient inFigures 6 and 7 which are based on the results that theanalysis code provides
05
06
07
08
09
10
11
12
13
14
000
015
030
045
060
075
090
105
120
135
004 005 006 007 008 009
Test CFDTest CFD
120578120595
120593
Figure 8 Performance comparison between test and CFD
4 3D CFD Validation
Many impellers coming from either open literature or indus-try have been used to evaluate the accuracy of the CFDanalysis before It is confirmed that our CFD simulation isreasonable and reliable An impeller similar to the case inthis paper is chosen to present our CFD analysis accuracycompared to test data from a cooperative company Thisimpeller also applies two-dimensional blades and is usedin the last stage centrifugal compressor of the multistagecompressors It can be observed in Figure 8 that CFD has agood agreement with test data
Note Vaneless diffuser and return channel are also involvedin the test and CFD
For the case in this paper before running CFD impellermodeling is built in the commercial software ldquoBLADEGENrdquoaccording to the fixed geometry from 1D design codeFigure 9 shows the geometry and meridional view of theimpeller It can be observed that leading edge of impeller is inthe radial direction and flow channel is so narrow which arethe typical characteristics of low flow coefficient centrifugalcompressors Inlet and outlet computational domains haveto be added to avoid reserved flow and improve accuracy ofcomputation in CFD Extended outlet computational domainacts like practical vaneless diffuser and makes impeller runclose to the real environment
Three-dimensional viscous RANS solver and Spalart-Allamaras turbulent model are applied in the steady simu-lation with inlet boundary conditions of 119875
01= 13602 kPa
11987901
= 424K and axial flow Static pressure is set on the outletboundary condition and increased gradually Near lower flowregion using mass flow rate condition captures stall pointinstead of static pressure condition The working medium is
8 International Journal of Rotating Machinery
(a) Impeller geometry
80
100
120
140
160
180
200
220
240
260
280
300
0 20minus40 minus20
Z (mm)
R(m
m)
(b) Meridional view
Figure 9 Impeller design
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 1 11
Grid 1Grid 2Grid 3
120587to
t
mmchoke
(a) Total pressure ratio
010
020
030
040
050
060
070
080
090
100
02 03 04 05 06 07 08 09 1 11
Grid 1Grid 2Grid 3
mmchoke
120578
(b) Adiabatic efficiency
Figure 10 Simulation results with three grid plans
defined as typical natural gas All solidwalls are assumed to besmoothwith roughness of 10minus6m In order to reduce the effectof skin friction coefficient affected by surface roughness samesurface property has to be employed in 1D code whenmakinga comparison between 1D prediction and CFD simulation
In order to understand the analytical accuracy of theCFD on the impeller of this case three grid plans shown inTable 2 were tried to check grid sensitivity Figure 10(a) showsthat total pressure ratio distribution curves from three gridplans match very well Adiabatic efficiency curves seen in
International Journal of Rotating Machinery 9
Table 2 Three grid plans
Circumferential Streamwise Spanwise Grid numberGrid 1 27 87 39 185367Grid 2 35 107 49 295421Grid 3 43 127 57 435309
Figure 10(b) also present a good match However it seemsthat larger stall margin is obtained by applying less gridnumber In consideration of running safety in the test thegrid plan 3 with smaller stall margin will be selected as areference for design because designers can not just pick theoption with the best evaluation
For adiabatic efficiency of impeller 1D code can presentthe results with and without parasitic losses However CFDdoes not usually include parasitic losses unless the exact prac-tical structure of centrifugal compressor is built That is thereason why Figure 11(a) shows three distribution curves forefficiency In addition to evaluate 1D code through comparingwith CFD without parasitic losses the efficiency includingparasitic losses close to real environment is needed to bepresented as well 1D code shows wider operating rangeand further stall point which means that comparing withCFD 1D code predicts that the centrifugal compressor canrun at lower mass flow rate Itrsquos shown that steady CFDsimulation cannot get an accurate stall point Transientsimulation should be done after steady calculation which isnot completed in this paper According to the comparisonof efficiency CFD has a little bit discrepancy in adiabaticefficiency on the right side of blue line However differencein efficiency becomes bigger and distribution trends showdifferent as mass flow rate continues to be reduced
In Figure 11(b) total pressure ratio from CFD is overpre-dicted but has same distribution trend with 1D predictionSince empirical loss models are used in the code and CFDcannot show the exact results with real values we think1D code works well and has the function to finish the per-formance evaluation within acceptable discrepancy Furthervalidation with more impellers needs to be carried out in thefuture to see if a constant coefficient for total pressure ratioexists between 1D code and CFD And if this is the case theprediction accuracy of 1D code can be further improved
Note Equation (6) presents the efficiency without parasiticlosses However parasitic losses are taken into account in(7) As mentioned before these two equations are used to becompared with CFD and test data respectively
Relative Mach number distributions at 10 50 and90 spans are shown in Figure 12 It is very clear that alow velocity region exists near pressure surface and becomessmaller gradually as blade span increases Because high staticpressure near pressure surface accompanies low velocity thelow magnitude area can be expected near pressure surfaceMoreover narrow passage introduces large viscous effectsand the typical velocity distribution of the bend comes upjust before the leading edge of the impeller which makes itobvious why Figure 12 presents relative Mach number like
that Fortunately no flow separation is found in the flow fieldof the impeller
Figure 13 shows 119881119898distribution on the meridional view
No low flow region and separation bubble exist whichindicates that this design is rational It is seen in Figure 13that velocity is gradually increasing from hub to shroud inthe extended inlet region which is a typical flow distributionin the bend High velocity means low static pressure andvice versa High pressure static pressure near hub regioncreates centripetal force to balance centrifugal force In orderto reduce the effect of this kind of flow distribution onthe incidence angles along the span of impeller inlet lowercurvature of shroud in the extended inlet region which cancause higher flow area and reduce hub-to-shroud velocitygradient should be applied for performance optimization inthe future Figure 14 presents the idea that static pressuredistribution is smooth through the impeller as expected
Due to the even absolute flow angle distribution atimpeller exit shown in Figure 15 vaneless or vaned diffuserhas perfect inlet condition and can be easily designed ifneeded Blade loading at 10 50 and 90 spans distributesreasonably which can be checked out in detail in Figure 16The blank area between pressure and suction surface staticcurves represents the load that blade withstands which doesnot vary too much through the blade at different spans Thatis what designers expect
The main performance parameters comparison at designpoint is listed in Table 3 The power calculated by CFD isapproximately in the middle of these two values computed by1D code Compared to CFD the efficiency is overpredictedby 152 in the 1D code which is really satisfying The totalpressure ratio in CFD is 305 higher than 1D code Inaddition parasitic losses drop efficiency a lot based on 1Dprediction
5 Conclusions
1D code is developed in this paper and divided into two partswhich are used to design and analyze Based on the code alowflow coefficient centrifugal compressor is designed and itsperformance is predicted In comparisonwith 1D code steadyCFD simulation has been carried out and provides flow fielddetails in the impeller
Comparing to 1D code CFD overpredicts total pressureratio of impeller but shows the same distribution trend whichis encouraging Further validations through more impellershave to be done in the future to confirm if a constantcoefficient for total pressure ratio exists between CFD and1D code For adiabatic efficiency 1D code without includingparasitic losses matches very well CFD in the operating rangeof near design point and choke point However 1D code isoverpredicted between near design point and stall point Thedifference of mass flow rate at choke point between CFDand 1D code is less than 2 Compared to steady CFD 1Dcode presents stall point at lower mass flow rate No flowseparation is found in the flow field of impeller and even theabsolute flow angle distribution at impeller exit is shownThe
10 International Journal of Rotating Machinery
02 03 04 05 06 07 08 09 10 1100
02
04
06
08
10
CFD1D (with parasitic losses)1D (without parasitic losses)
120578
mmchoke
(a) Adiabatic efficiency
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 10 11
CFD
120587to
t
1D code
mmchoke
(b) Total pressure ratio
Figure 11 Impeller performance curves
0 01 02 03 04 05 06
(a) 10 span (b) 50 span (c) 90 span
Figure 12 Relative Mach number map
120
100
80
60
40
20
0
Vm
Figure 13 Meridional velocity and streamline distribution
15E + 07
145E + 07
14E + 07
135E + 07
155E + 07
13E + 07St
atic
pre
ssur
e
Figure 14 Static pressure distribution
0
5
10
15
20
25
30
0Axial length (mm)
minus9 minus8 minus7 minus6 minus5 minus4 minus3 minus2 minus1
1205722
(∘)
Figure 15 Absolute flow angle distribution at impeller exit
International Journal of Rotating Machinery 11
0Axial length (mm)
10 span50 span90 span
10E + 07
11E + 07
12E + 07
13E + 07
14E + 07
15E + 07
16E + 07
Pst
(Pa)
minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2
Figure 16 Blade loading distribution at different spans
Table 3 Performance comparison between CFD and 1D code atdesign point
CFD 1D(no parasitic losses)
1D(parasitic losses)
Power 1778400W 1656740W 1857339W120587tot 121 11731 11731120578 902 9172 8257
blade loading at three different spans distributes smoothly asexpected
Since the low flow coefficient centrifugal compressordesigned in this paper is not the usual type and empiricalequations used are based on medium flow coefficient com-pressors further research on the improvement and validationof 1D code needs to be done by experiment and CFD toincrease prediction accuracy
Nomenclature
119860 Area (m2)AR Area ratio (119860
2sin(1205732119887)1198601sin(120573th))
119886 Sonic velocity (ms)119861 Fraction area blockage119887 Blade height (m)119862119901 Specific heat at constant pressure(Jkg K)
119890 Impeller mean line radius ratio119863 Diameter (m)119863eq Equivalent diffusion factor119896 Ratio of specific heatsΔℎ Enthalpy increase (Jkg)119868119861 Blade work input coefficient
120590(1 minus 119898cot(1205732119887)((120588211986021198802)(1 minus 119861
2))) minus
119880111986211990611198802
2
119871119885 Impeller axial length (m)
119871119861 Length of blade mean camberline (m)
119872 Relative Mach number119898 Mass flow rate (kgs)119873 Rotation speed (rpm)119873119904 Specific speed
119875 Pressure (pa)119877 Gas constant (J(kgsdotK))119879 Temperature (K)119880 Blade speed (ms)119881 Absolute velocity (ms)119882 Relative velocity (ms)Δ119882 Average blade velocity difference (ms)119885 Number of the blades
Greeks
120572 Absolute flow angle from tangential (∘)120573 Relative flow angle from tangential (∘)120578 Adiabatic efficiency120582 Workenthalpy coefficient Δℎ119880
2
2
120587 Pressure ratio120588 Gas density (kgm
3)
120590 Slip factor120593 Inlet flow coefficient119898(120588
111988021205871198632
24)
Ψ Inlet head coefficient(8544119863
2)21198621199011198791((11987521198751)((119896minus1)119896)
minus 1)
Δ120596 Total pressure loss coefficientΔ1199010(1199010minus 119901)
Subscripts
0 Total condition1 Impeller inlet2 Impeller outlet3 Diffuser inlet4 Diffuser outlet
119887 Bladebl Blade loading119888 Criterionchoke Choke pointdf Disc frictiondif Inducer diffusionℎ Impeller inlet hubhs Hub-to-shroudinc Incidenceis Isentropic119897 Leakagelim Limit119898 Meridional componentmax Maximummin Minimummix Wake mixing119904 Shroudst Staticth Impeller throat
12 International Journal of Rotating Machinery
sf Skin frictiontot Total-to-total119906 Tangential componentvld Vaneless diffuser
Superscripts
lowast Correct value1015840 New valueand Value relative to rotating frame of reference
Conflict of Interests
The authors declare that they have no financial and personalrelationships with other people or organizations that caninappropriately influence their work there is no professionalor other personal interest of any nature or kind in anyproduct service andor company that could be construed asinfluencing the position presented in or the review of thepaper
Acknowledgment
This work is supported by the National Natural ScienceFoundation of China under Grant no 51010007 and theChina Scholarship Council (CSC) The authors would like tothank Dr Marco Vagani and Christopher D Bolin for theirdiscussion and advice
References
[1] T Sato J M Oh and A Engeda ldquoExperimental and numericalinvestigation of the flow in a vaneless diffuser of a centrifugalcompressor stage Part 1 experimental investigationrdquo Proceed-ings of the Institution of Mechanical Engineers C vol 219 no 10pp 1053ndash1059 2005
[2] R H Aungier Centrifugal Compressor A Strategy for Aerody-namic Design and Analysis ASME Press New York NY USA2000
[3] V Rusak ldquoDevelopment and performance of the wedge-typelow specific speed compressor wheelrdquo Tech Rep 82-GT-214ASME 2009
[4] M V Casey P Dalbert and E Schurter ldquoRadial compressorstages for low flow coefficientsrdquo in Proceedings of the IMechEInternational Conference on Machinery for the Oil and GasIndustries 1990
[5] T Koizumi ldquoExperimental studies on performance of centrifu-gal compressors with very small flow coefficientrdquoMitsui ZosenTechnical Review vol 117 pp 28ndash39 1983
[6] J Paroubek J Kyncl and V Cyrus ldquoExperimental investigationand performance analysis of six low flow coefficient centrifugalcompressor stagesrdquo Transactions of the ASME Journal of Turbo-machinery vol 117 no 4 pp 585ndash592 1995
[7] J-L Di Liberti Design and development of low-flow coefficientcentrifugal compressors for industrial application [PhD thesis]Michigan State University 1998
[8] Y I Biba D A Nye and L I U Zheji ldquoPerformance evaluationand fluid flow analysis in low flow stages of industrial centrifu-gal compressorrdquo International Journal of Rotating Machineryvol 8 no 5 pp 309ndash317 2002
[9] M R Galvas ldquoFortran program for predicting off-designperformance of centrifugal com-pressorsrdquo Tech Rep TN D-7487 NASA 1973
[10] K H Ludtke Process Centrifugal Compressors Basic FunctionOperation Design Application Springer Berlin Germany 2010
[11] F J Wiesner ldquoA review of slip factors for centrifugal compres-sorsrdquo Journal of Engineering for Power Transactions of theASMEvol 89 pp 558ndash572 1967
[12] R H Aungier ldquoMean streamline aerodynamic performanceanalysis of centrifugal compressorsrdquo Transactions of the ASMEJournal of Turbomachinery vol 117 no 3 pp 360ndash366 1995
[13] S L Dixon Fluid Mechanics and Thermodnamics of Turboma-chinery Butterworth-Heinemann 4th edition 1998
[14] Y Senoo and Y Kinoshita ldquoLimits of rotating stall and stall invaneless diffusers of centrifugal compressorsrdquo Tech Rep 78-GT-19 ASME 1978
[15] S Lieblein ldquoLoss and stall analysis of compressor cascadesrdquoASME Transactions Journal of Basic Engineering vol 81 pp387ndash400 1959
[16] H Krain and B Hoffmann ldquoFlow physics in high pressure ratiocentrifugal compressorsrdquo in Proceedings of the ASME FluidsEngineering Division Summer Meeting June 1998
[17] G Eisenlohr and H Krain ldquoInvestigation of the flow througha high pressure ratio centrifugal impellerrdquo in Proceedings of theASME Conference Proceedings 2003
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International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
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Shock and Vibration
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DistributedSensor Networks
International Journal of
International Journal of Rotating Machinery 5
If parasitic losses are included a revised formula (7)should be applied
120578II=119862119901(11987902
minus 11987901) minus (Δℎinc + Δℎbl + Δℎsf + Δℎmix + Δℎdif)
119862119901(11987902
minus 11987901) + Δℎdf + Δℎ
119897
(7)
Finally density at impeller outlet is updated and com-pared with the initial one
11987902is = 119879
01+ 120578I (11987902 minus 119879
01)
11987502
= 11987501(11987902is11987901
)
119896(119896minus1)
1198752= 11987502(11987902
1198792
)
119896(119896minus1)
12058821015840 =
1198752
(1198771198792)
(8)
The code will continue running until density at impelleroutlet converges If vaneless diffuser is involved in the analysispart the corresponding loss model shown in Figure 3 has tobe added
Internal losses mainly include incidence loss blade load-ing loss skin friction loss wake mixing loss hub-to-shroudloading loss entrance diffusion loss and clearance loss [2 12]Generally parasitic losses are not involved in CFD In orderto make an efficiency comparison with or without parasiticlosses disc friction recirculation and leakage are also takeninto consideration In this case clearance loss and leakage lossare not considered due to shrouded impeller
Besides the above descriptions how to predict stall andchoke point in the analysis part must be mentioned herebecause these two points determine the operating range ofcentrifugal compressor directly In Figure 3 mass flow rateas the only input variable has a range coming from designpart directly The initial value of mass flow rate at chokepoint is predicted in design part by (9) developed by Dixon[13] Actually (9) always overpredicts mass flow rate whichis because aerodynamic blockage at impeller throat is notconsidered Therefore it is appropriate to apply (9) to obtainlarger mass flow rate for choke point first The initializationof mass flow rate for stall point calculated in design part isto use critical absolute flow angle at diffuser inlet which iscomputed by (10) Pinch between impeller outlet and diffuserinlet is also considered if applied [14]
119898choke = 119860 th1205880111988601[2 + (119896 minus 1)119880
2
11198862
01
119896 + 1]
(k+1)2(119896minus1)
(9)
120572lowast
3119888= 1205723119888
+ (1702 minus1484119887
2
1198892
)(1 minus1198873
1198872
) (10)
In the analysis part for stall point prediction two meth-ods are adopted The main one used by majority designersis to check if 119882
1119904119882th ge 175 which seemed as an inducer
stall criterion The second option is to estimate equivalent
10
12
14
16
18
20
22
02 03 04 05 06 07 08 09 10 11mmchoke
Deq
Figure 4 Equivalent diffusion factor
diffusion factor (119863eq) Lieblein [15] found that blade stalloccurs in the axial compressor when 119863eq is bigger than 2Later on 119863eq is generalized to radial and mixed flow bladesto evaluate the blade loading This criterion is also foundto be an appropriate blade stall limit for impellers [2] Therelated calculation equations are shown below119863eq is checkedat every iteration step in analysis part to see if it reachesthe criteria or not If neither 119882
1119904119882th nor 119863eq indicates the
compressor stalls the initial mass flow rate value from (10)will be considered to be the minimum value
119863eq =119882max1198822
119882max =(1198821+ 1198822+ Δ119882)
2
Δ119882 =212058711986321198802119868119861
(119885119871119861)
(11)
Finally in this case 1D code points out to 119863eq which isdetected beyond the critical value first The distribution of119863eq over mass flow rate is shown in Figure 4 Based on thecase in this paper it is still hard to determine which methodis suitable to stall point prediction so far According to CFDsimulation and test data further evaluation of the 1D codeneeds to be done through huge number of impellers whichwill be focused on in the future research work
As for choke point calculation iterativemethod is applieduntil relative Mach number at the impeller throat reaches 1Generally choke mass flow rate from analysis part is smallerthan initialization based on (9) In this case 1D code predictschokemass flow rate at 80 kgs andCFD shows it at 8155 kgsThe difference is less than 2 However the initial value is8954 kgs larger than analysis code prediction as expected
Since mass flow rate in analysis part is increased byspecific growth increment the real operating range of thecentrifugal compressor will be fixed after choke point cal-culation is done The code will plot the entire performance
6 International Journal of Rotating Machinery
3
4
5
6
7
8
05 06 07 08 09 1 11
Test
120587to
t
mmchoke
1D code
(a) Adiabatic efficiency
076
078
08
082
084
086
088
09
05 06 07 08 09 1 11
Test
mmchoke
1D code
120578
(b) Total pressure ratio
Figure 5 Performance curves between 1-D and test
of the centrifugal compressor automatically including designand off-design points
1D analysis code was calibrated by the test data of one ofthree Krainrsquos impellers [16 17] In Figure 5 it is obvious thattotal pressure ratio and adiabatic efficiency show similar dis-tribution trend and the discrepancies between performancecurves are acceptable Compared to the test wider surgemargin is obtained by 1D code Overall based on this case1D analysis code is functional and satisfying Also a detailedflow parameter comparison of 1D code and test data of a highflow coefficient centrifugal compressor have been carried outwhich also indicates good predictive effect of 1D analysiscode The related results are not shown here
3 1D Design and Analysis Results
Main impeller geometric parameters from 1D code are listedin Table 1 Design parameters like mass flow rate rotationalspeed impeller outlet diameter and shaft diameter areprovided by industry according to practical demand
Since leading edge and trailing edge of the impeller havethe same streamline slope angle in this case hub-to-shroudloss model is not activated The criterion in the chokingloss model is not satisfied and the choking loss is also notconsidered as well Recirculation loss is neglected due to theshrouded impeller designed in this study
Therefore internal losses actually used include wakemixing loss skin friction loss incidence loss blade load-ing loss and inducer diffusion loss Figure 6 shows losscoefficient distribution of impeller It is observed that skin
Table 1 Impeller parameters
119898 48 kgs119873 12800 rpm120593 0022119873119904
0071198631
02172m1198632
0381m1198871
00123m1198872
00082m1205731119887
289∘
1205732119887
40∘
119871119911
00193m11988721198632
00216119885 13
friction is the main loss source in the impeller as expecteddue to narrow flow path of low flow coefficient centrifugalcompressor and increases gradually from surge side to chokeside Wake loss appears near surge point and presents thesmallest loss coefficient Minimum incidence loss occurs atdesign point The distribution of incidence loss is prettytypical Either increasing mass flow rate from design pointto choke side or reducing it from design point to surge sidewill causemore incidence loss Higher pressure ratio is alwaysaccompanied by accordingly higher blade loading loss whichcan explain why blade loading loss distributes like the trendshown in Figure 6 An inducer diffusion loss appears onlyfor applications of less than 63 mass flow rate which is
International Journal of Rotating Machinery 7
0
01
02
03
04
05
06
036 040 044 051 057 063 073 078 086 093 097 100
Loss
coeffi
cien
t
Inducer diffusionBlade loadingIncidence
Skin frictionWake mixing
mmchoke
Figure 6 Loss coefficient distribution of impeller
0
002
004
006
008
01
012
014
036 040 044 051 057 063 073 078 086 093 097 100
Wor
k co
effici
ent
LeakageDisc friction
mmchoke
Figure 7 Distribution of work coefficient due to parasitic losses
the design point For parasitic losses or external losses onlydisc friction loss and leakage loss are involved They presentsimilar distribution trend seen in Figure 7 Overall 1D codeprovides asmuch information as it canMore importantly the1D analysis results look reasonable and acceptable
Note Please refer to reference [2] to look up the equationsused for calculating loss coefficient and work coefficient inFigures 6 and 7 which are based on the results that theanalysis code provides
05
06
07
08
09
10
11
12
13
14
000
015
030
045
060
075
090
105
120
135
004 005 006 007 008 009
Test CFDTest CFD
120578120595
120593
Figure 8 Performance comparison between test and CFD
4 3D CFD Validation
Many impellers coming from either open literature or indus-try have been used to evaluate the accuracy of the CFDanalysis before It is confirmed that our CFD simulation isreasonable and reliable An impeller similar to the case inthis paper is chosen to present our CFD analysis accuracycompared to test data from a cooperative company Thisimpeller also applies two-dimensional blades and is usedin the last stage centrifugal compressor of the multistagecompressors It can be observed in Figure 8 that CFD has agood agreement with test data
Note Vaneless diffuser and return channel are also involvedin the test and CFD
For the case in this paper before running CFD impellermodeling is built in the commercial software ldquoBLADEGENrdquoaccording to the fixed geometry from 1D design codeFigure 9 shows the geometry and meridional view of theimpeller It can be observed that leading edge of impeller is inthe radial direction and flow channel is so narrow which arethe typical characteristics of low flow coefficient centrifugalcompressors Inlet and outlet computational domains haveto be added to avoid reserved flow and improve accuracy ofcomputation in CFD Extended outlet computational domainacts like practical vaneless diffuser and makes impeller runclose to the real environment
Three-dimensional viscous RANS solver and Spalart-Allamaras turbulent model are applied in the steady simu-lation with inlet boundary conditions of 119875
01= 13602 kPa
11987901
= 424K and axial flow Static pressure is set on the outletboundary condition and increased gradually Near lower flowregion using mass flow rate condition captures stall pointinstead of static pressure condition The working medium is
8 International Journal of Rotating Machinery
(a) Impeller geometry
80
100
120
140
160
180
200
220
240
260
280
300
0 20minus40 minus20
Z (mm)
R(m
m)
(b) Meridional view
Figure 9 Impeller design
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 1 11
Grid 1Grid 2Grid 3
120587to
t
mmchoke
(a) Total pressure ratio
010
020
030
040
050
060
070
080
090
100
02 03 04 05 06 07 08 09 1 11
Grid 1Grid 2Grid 3
mmchoke
120578
(b) Adiabatic efficiency
Figure 10 Simulation results with three grid plans
defined as typical natural gas All solidwalls are assumed to besmoothwith roughness of 10minus6m In order to reduce the effectof skin friction coefficient affected by surface roughness samesurface property has to be employed in 1D code whenmakinga comparison between 1D prediction and CFD simulation
In order to understand the analytical accuracy of theCFD on the impeller of this case three grid plans shown inTable 2 were tried to check grid sensitivity Figure 10(a) showsthat total pressure ratio distribution curves from three gridplans match very well Adiabatic efficiency curves seen in
International Journal of Rotating Machinery 9
Table 2 Three grid plans
Circumferential Streamwise Spanwise Grid numberGrid 1 27 87 39 185367Grid 2 35 107 49 295421Grid 3 43 127 57 435309
Figure 10(b) also present a good match However it seemsthat larger stall margin is obtained by applying less gridnumber In consideration of running safety in the test thegrid plan 3 with smaller stall margin will be selected as areference for design because designers can not just pick theoption with the best evaluation
For adiabatic efficiency of impeller 1D code can presentthe results with and without parasitic losses However CFDdoes not usually include parasitic losses unless the exact prac-tical structure of centrifugal compressor is built That is thereason why Figure 11(a) shows three distribution curves forefficiency In addition to evaluate 1D code through comparingwith CFD without parasitic losses the efficiency includingparasitic losses close to real environment is needed to bepresented as well 1D code shows wider operating rangeand further stall point which means that comparing withCFD 1D code predicts that the centrifugal compressor canrun at lower mass flow rate Itrsquos shown that steady CFDsimulation cannot get an accurate stall point Transientsimulation should be done after steady calculation which isnot completed in this paper According to the comparisonof efficiency CFD has a little bit discrepancy in adiabaticefficiency on the right side of blue line However differencein efficiency becomes bigger and distribution trends showdifferent as mass flow rate continues to be reduced
In Figure 11(b) total pressure ratio from CFD is overpre-dicted but has same distribution trend with 1D predictionSince empirical loss models are used in the code and CFDcannot show the exact results with real values we think1D code works well and has the function to finish the per-formance evaluation within acceptable discrepancy Furthervalidation with more impellers needs to be carried out in thefuture to see if a constant coefficient for total pressure ratioexists between 1D code and CFD And if this is the case theprediction accuracy of 1D code can be further improved
Note Equation (6) presents the efficiency without parasiticlosses However parasitic losses are taken into account in(7) As mentioned before these two equations are used to becompared with CFD and test data respectively
Relative Mach number distributions at 10 50 and90 spans are shown in Figure 12 It is very clear that alow velocity region exists near pressure surface and becomessmaller gradually as blade span increases Because high staticpressure near pressure surface accompanies low velocity thelow magnitude area can be expected near pressure surfaceMoreover narrow passage introduces large viscous effectsand the typical velocity distribution of the bend comes upjust before the leading edge of the impeller which makes itobvious why Figure 12 presents relative Mach number like
that Fortunately no flow separation is found in the flow fieldof the impeller
Figure 13 shows 119881119898distribution on the meridional view
No low flow region and separation bubble exist whichindicates that this design is rational It is seen in Figure 13that velocity is gradually increasing from hub to shroud inthe extended inlet region which is a typical flow distributionin the bend High velocity means low static pressure andvice versa High pressure static pressure near hub regioncreates centripetal force to balance centrifugal force In orderto reduce the effect of this kind of flow distribution onthe incidence angles along the span of impeller inlet lowercurvature of shroud in the extended inlet region which cancause higher flow area and reduce hub-to-shroud velocitygradient should be applied for performance optimization inthe future Figure 14 presents the idea that static pressuredistribution is smooth through the impeller as expected
Due to the even absolute flow angle distribution atimpeller exit shown in Figure 15 vaneless or vaned diffuserhas perfect inlet condition and can be easily designed ifneeded Blade loading at 10 50 and 90 spans distributesreasonably which can be checked out in detail in Figure 16The blank area between pressure and suction surface staticcurves represents the load that blade withstands which doesnot vary too much through the blade at different spans Thatis what designers expect
The main performance parameters comparison at designpoint is listed in Table 3 The power calculated by CFD isapproximately in the middle of these two values computed by1D code Compared to CFD the efficiency is overpredictedby 152 in the 1D code which is really satisfying The totalpressure ratio in CFD is 305 higher than 1D code Inaddition parasitic losses drop efficiency a lot based on 1Dprediction
5 Conclusions
1D code is developed in this paper and divided into two partswhich are used to design and analyze Based on the code alowflow coefficient centrifugal compressor is designed and itsperformance is predicted In comparisonwith 1D code steadyCFD simulation has been carried out and provides flow fielddetails in the impeller
Comparing to 1D code CFD overpredicts total pressureratio of impeller but shows the same distribution trend whichis encouraging Further validations through more impellershave to be done in the future to confirm if a constantcoefficient for total pressure ratio exists between CFD and1D code For adiabatic efficiency 1D code without includingparasitic losses matches very well CFD in the operating rangeof near design point and choke point However 1D code isoverpredicted between near design point and stall point Thedifference of mass flow rate at choke point between CFDand 1D code is less than 2 Compared to steady CFD 1Dcode presents stall point at lower mass flow rate No flowseparation is found in the flow field of impeller and even theabsolute flow angle distribution at impeller exit is shownThe
10 International Journal of Rotating Machinery
02 03 04 05 06 07 08 09 10 1100
02
04
06
08
10
CFD1D (with parasitic losses)1D (without parasitic losses)
120578
mmchoke
(a) Adiabatic efficiency
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 10 11
CFD
120587to
t
1D code
mmchoke
(b) Total pressure ratio
Figure 11 Impeller performance curves
0 01 02 03 04 05 06
(a) 10 span (b) 50 span (c) 90 span
Figure 12 Relative Mach number map
120
100
80
60
40
20
0
Vm
Figure 13 Meridional velocity and streamline distribution
15E + 07
145E + 07
14E + 07
135E + 07
155E + 07
13E + 07St
atic
pre
ssur
e
Figure 14 Static pressure distribution
0
5
10
15
20
25
30
0Axial length (mm)
minus9 minus8 minus7 minus6 minus5 minus4 minus3 minus2 minus1
1205722
(∘)
Figure 15 Absolute flow angle distribution at impeller exit
International Journal of Rotating Machinery 11
0Axial length (mm)
10 span50 span90 span
10E + 07
11E + 07
12E + 07
13E + 07
14E + 07
15E + 07
16E + 07
Pst
(Pa)
minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2
Figure 16 Blade loading distribution at different spans
Table 3 Performance comparison between CFD and 1D code atdesign point
CFD 1D(no parasitic losses)
1D(parasitic losses)
Power 1778400W 1656740W 1857339W120587tot 121 11731 11731120578 902 9172 8257
blade loading at three different spans distributes smoothly asexpected
Since the low flow coefficient centrifugal compressordesigned in this paper is not the usual type and empiricalequations used are based on medium flow coefficient com-pressors further research on the improvement and validationof 1D code needs to be done by experiment and CFD toincrease prediction accuracy
Nomenclature
119860 Area (m2)AR Area ratio (119860
2sin(1205732119887)1198601sin(120573th))
119886 Sonic velocity (ms)119861 Fraction area blockage119887 Blade height (m)119862119901 Specific heat at constant pressure(Jkg K)
119890 Impeller mean line radius ratio119863 Diameter (m)119863eq Equivalent diffusion factor119896 Ratio of specific heatsΔℎ Enthalpy increase (Jkg)119868119861 Blade work input coefficient
120590(1 minus 119898cot(1205732119887)((120588211986021198802)(1 minus 119861
2))) minus
119880111986211990611198802
2
119871119885 Impeller axial length (m)
119871119861 Length of blade mean camberline (m)
119872 Relative Mach number119898 Mass flow rate (kgs)119873 Rotation speed (rpm)119873119904 Specific speed
119875 Pressure (pa)119877 Gas constant (J(kgsdotK))119879 Temperature (K)119880 Blade speed (ms)119881 Absolute velocity (ms)119882 Relative velocity (ms)Δ119882 Average blade velocity difference (ms)119885 Number of the blades
Greeks
120572 Absolute flow angle from tangential (∘)120573 Relative flow angle from tangential (∘)120578 Adiabatic efficiency120582 Workenthalpy coefficient Δℎ119880
2
2
120587 Pressure ratio120588 Gas density (kgm
3)
120590 Slip factor120593 Inlet flow coefficient119898(120588
111988021205871198632
24)
Ψ Inlet head coefficient(8544119863
2)21198621199011198791((11987521198751)((119896minus1)119896)
minus 1)
Δ120596 Total pressure loss coefficientΔ1199010(1199010minus 119901)
Subscripts
0 Total condition1 Impeller inlet2 Impeller outlet3 Diffuser inlet4 Diffuser outlet
119887 Bladebl Blade loading119888 Criterionchoke Choke pointdf Disc frictiondif Inducer diffusionℎ Impeller inlet hubhs Hub-to-shroudinc Incidenceis Isentropic119897 Leakagelim Limit119898 Meridional componentmax Maximummin Minimummix Wake mixing119904 Shroudst Staticth Impeller throat
12 International Journal of Rotating Machinery
sf Skin frictiontot Total-to-total119906 Tangential componentvld Vaneless diffuser
Superscripts
lowast Correct value1015840 New valueand Value relative to rotating frame of reference
Conflict of Interests
The authors declare that they have no financial and personalrelationships with other people or organizations that caninappropriately influence their work there is no professionalor other personal interest of any nature or kind in anyproduct service andor company that could be construed asinfluencing the position presented in or the review of thepaper
Acknowledgment
This work is supported by the National Natural ScienceFoundation of China under Grant no 51010007 and theChina Scholarship Council (CSC) The authors would like tothank Dr Marco Vagani and Christopher D Bolin for theirdiscussion and advice
References
[1] T Sato J M Oh and A Engeda ldquoExperimental and numericalinvestigation of the flow in a vaneless diffuser of a centrifugalcompressor stage Part 1 experimental investigationrdquo Proceed-ings of the Institution of Mechanical Engineers C vol 219 no 10pp 1053ndash1059 2005
[2] R H Aungier Centrifugal Compressor A Strategy for Aerody-namic Design and Analysis ASME Press New York NY USA2000
[3] V Rusak ldquoDevelopment and performance of the wedge-typelow specific speed compressor wheelrdquo Tech Rep 82-GT-214ASME 2009
[4] M V Casey P Dalbert and E Schurter ldquoRadial compressorstages for low flow coefficientsrdquo in Proceedings of the IMechEInternational Conference on Machinery for the Oil and GasIndustries 1990
[5] T Koizumi ldquoExperimental studies on performance of centrifu-gal compressors with very small flow coefficientrdquoMitsui ZosenTechnical Review vol 117 pp 28ndash39 1983
[6] J Paroubek J Kyncl and V Cyrus ldquoExperimental investigationand performance analysis of six low flow coefficient centrifugalcompressor stagesrdquo Transactions of the ASME Journal of Turbo-machinery vol 117 no 4 pp 585ndash592 1995
[7] J-L Di Liberti Design and development of low-flow coefficientcentrifugal compressors for industrial application [PhD thesis]Michigan State University 1998
[8] Y I Biba D A Nye and L I U Zheji ldquoPerformance evaluationand fluid flow analysis in low flow stages of industrial centrifu-gal compressorrdquo International Journal of Rotating Machineryvol 8 no 5 pp 309ndash317 2002
[9] M R Galvas ldquoFortran program for predicting off-designperformance of centrifugal com-pressorsrdquo Tech Rep TN D-7487 NASA 1973
[10] K H Ludtke Process Centrifugal Compressors Basic FunctionOperation Design Application Springer Berlin Germany 2010
[11] F J Wiesner ldquoA review of slip factors for centrifugal compres-sorsrdquo Journal of Engineering for Power Transactions of theASMEvol 89 pp 558ndash572 1967
[12] R H Aungier ldquoMean streamline aerodynamic performanceanalysis of centrifugal compressorsrdquo Transactions of the ASMEJournal of Turbomachinery vol 117 no 3 pp 360ndash366 1995
[13] S L Dixon Fluid Mechanics and Thermodnamics of Turboma-chinery Butterworth-Heinemann 4th edition 1998
[14] Y Senoo and Y Kinoshita ldquoLimits of rotating stall and stall invaneless diffusers of centrifugal compressorsrdquo Tech Rep 78-GT-19 ASME 1978
[15] S Lieblein ldquoLoss and stall analysis of compressor cascadesrdquoASME Transactions Journal of Basic Engineering vol 81 pp387ndash400 1959
[16] H Krain and B Hoffmann ldquoFlow physics in high pressure ratiocentrifugal compressorsrdquo in Proceedings of the ASME FluidsEngineering Division Summer Meeting June 1998
[17] G Eisenlohr and H Krain ldquoInvestigation of the flow througha high pressure ratio centrifugal impellerrdquo in Proceedings of theASME Conference Proceedings 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
6 International Journal of Rotating Machinery
3
4
5
6
7
8
05 06 07 08 09 1 11
Test
120587to
t
mmchoke
1D code
(a) Adiabatic efficiency
076
078
08
082
084
086
088
09
05 06 07 08 09 1 11
Test
mmchoke
1D code
120578
(b) Total pressure ratio
Figure 5 Performance curves between 1-D and test
of the centrifugal compressor automatically including designand off-design points
1D analysis code was calibrated by the test data of one ofthree Krainrsquos impellers [16 17] In Figure 5 it is obvious thattotal pressure ratio and adiabatic efficiency show similar dis-tribution trend and the discrepancies between performancecurves are acceptable Compared to the test wider surgemargin is obtained by 1D code Overall based on this case1D analysis code is functional and satisfying Also a detailedflow parameter comparison of 1D code and test data of a highflow coefficient centrifugal compressor have been carried outwhich also indicates good predictive effect of 1D analysiscode The related results are not shown here
3 1D Design and Analysis Results
Main impeller geometric parameters from 1D code are listedin Table 1 Design parameters like mass flow rate rotationalspeed impeller outlet diameter and shaft diameter areprovided by industry according to practical demand
Since leading edge and trailing edge of the impeller havethe same streamline slope angle in this case hub-to-shroudloss model is not activated The criterion in the chokingloss model is not satisfied and the choking loss is also notconsidered as well Recirculation loss is neglected due to theshrouded impeller designed in this study
Therefore internal losses actually used include wakemixing loss skin friction loss incidence loss blade load-ing loss and inducer diffusion loss Figure 6 shows losscoefficient distribution of impeller It is observed that skin
Table 1 Impeller parameters
119898 48 kgs119873 12800 rpm120593 0022119873119904
0071198631
02172m1198632
0381m1198871
00123m1198872
00082m1205731119887
289∘
1205732119887
40∘
119871119911
00193m11988721198632
00216119885 13
friction is the main loss source in the impeller as expecteddue to narrow flow path of low flow coefficient centrifugalcompressor and increases gradually from surge side to chokeside Wake loss appears near surge point and presents thesmallest loss coefficient Minimum incidence loss occurs atdesign point The distribution of incidence loss is prettytypical Either increasing mass flow rate from design pointto choke side or reducing it from design point to surge sidewill causemore incidence loss Higher pressure ratio is alwaysaccompanied by accordingly higher blade loading loss whichcan explain why blade loading loss distributes like the trendshown in Figure 6 An inducer diffusion loss appears onlyfor applications of less than 63 mass flow rate which is
International Journal of Rotating Machinery 7
0
01
02
03
04
05
06
036 040 044 051 057 063 073 078 086 093 097 100
Loss
coeffi
cien
t
Inducer diffusionBlade loadingIncidence
Skin frictionWake mixing
mmchoke
Figure 6 Loss coefficient distribution of impeller
0
002
004
006
008
01
012
014
036 040 044 051 057 063 073 078 086 093 097 100
Wor
k co
effici
ent
LeakageDisc friction
mmchoke
Figure 7 Distribution of work coefficient due to parasitic losses
the design point For parasitic losses or external losses onlydisc friction loss and leakage loss are involved They presentsimilar distribution trend seen in Figure 7 Overall 1D codeprovides asmuch information as it canMore importantly the1D analysis results look reasonable and acceptable
Note Please refer to reference [2] to look up the equationsused for calculating loss coefficient and work coefficient inFigures 6 and 7 which are based on the results that theanalysis code provides
05
06
07
08
09
10
11
12
13
14
000
015
030
045
060
075
090
105
120
135
004 005 006 007 008 009
Test CFDTest CFD
120578120595
120593
Figure 8 Performance comparison between test and CFD
4 3D CFD Validation
Many impellers coming from either open literature or indus-try have been used to evaluate the accuracy of the CFDanalysis before It is confirmed that our CFD simulation isreasonable and reliable An impeller similar to the case inthis paper is chosen to present our CFD analysis accuracycompared to test data from a cooperative company Thisimpeller also applies two-dimensional blades and is usedin the last stage centrifugal compressor of the multistagecompressors It can be observed in Figure 8 that CFD has agood agreement with test data
Note Vaneless diffuser and return channel are also involvedin the test and CFD
For the case in this paper before running CFD impellermodeling is built in the commercial software ldquoBLADEGENrdquoaccording to the fixed geometry from 1D design codeFigure 9 shows the geometry and meridional view of theimpeller It can be observed that leading edge of impeller is inthe radial direction and flow channel is so narrow which arethe typical characteristics of low flow coefficient centrifugalcompressors Inlet and outlet computational domains haveto be added to avoid reserved flow and improve accuracy ofcomputation in CFD Extended outlet computational domainacts like practical vaneless diffuser and makes impeller runclose to the real environment
Three-dimensional viscous RANS solver and Spalart-Allamaras turbulent model are applied in the steady simu-lation with inlet boundary conditions of 119875
01= 13602 kPa
11987901
= 424K and axial flow Static pressure is set on the outletboundary condition and increased gradually Near lower flowregion using mass flow rate condition captures stall pointinstead of static pressure condition The working medium is
8 International Journal of Rotating Machinery
(a) Impeller geometry
80
100
120
140
160
180
200
220
240
260
280
300
0 20minus40 minus20
Z (mm)
R(m
m)
(b) Meridional view
Figure 9 Impeller design
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 1 11
Grid 1Grid 2Grid 3
120587to
t
mmchoke
(a) Total pressure ratio
010
020
030
040
050
060
070
080
090
100
02 03 04 05 06 07 08 09 1 11
Grid 1Grid 2Grid 3
mmchoke
120578
(b) Adiabatic efficiency
Figure 10 Simulation results with three grid plans
defined as typical natural gas All solidwalls are assumed to besmoothwith roughness of 10minus6m In order to reduce the effectof skin friction coefficient affected by surface roughness samesurface property has to be employed in 1D code whenmakinga comparison between 1D prediction and CFD simulation
In order to understand the analytical accuracy of theCFD on the impeller of this case three grid plans shown inTable 2 were tried to check grid sensitivity Figure 10(a) showsthat total pressure ratio distribution curves from three gridplans match very well Adiabatic efficiency curves seen in
International Journal of Rotating Machinery 9
Table 2 Three grid plans
Circumferential Streamwise Spanwise Grid numberGrid 1 27 87 39 185367Grid 2 35 107 49 295421Grid 3 43 127 57 435309
Figure 10(b) also present a good match However it seemsthat larger stall margin is obtained by applying less gridnumber In consideration of running safety in the test thegrid plan 3 with smaller stall margin will be selected as areference for design because designers can not just pick theoption with the best evaluation
For adiabatic efficiency of impeller 1D code can presentthe results with and without parasitic losses However CFDdoes not usually include parasitic losses unless the exact prac-tical structure of centrifugal compressor is built That is thereason why Figure 11(a) shows three distribution curves forefficiency In addition to evaluate 1D code through comparingwith CFD without parasitic losses the efficiency includingparasitic losses close to real environment is needed to bepresented as well 1D code shows wider operating rangeand further stall point which means that comparing withCFD 1D code predicts that the centrifugal compressor canrun at lower mass flow rate Itrsquos shown that steady CFDsimulation cannot get an accurate stall point Transientsimulation should be done after steady calculation which isnot completed in this paper According to the comparisonof efficiency CFD has a little bit discrepancy in adiabaticefficiency on the right side of blue line However differencein efficiency becomes bigger and distribution trends showdifferent as mass flow rate continues to be reduced
In Figure 11(b) total pressure ratio from CFD is overpre-dicted but has same distribution trend with 1D predictionSince empirical loss models are used in the code and CFDcannot show the exact results with real values we think1D code works well and has the function to finish the per-formance evaluation within acceptable discrepancy Furthervalidation with more impellers needs to be carried out in thefuture to see if a constant coefficient for total pressure ratioexists between 1D code and CFD And if this is the case theprediction accuracy of 1D code can be further improved
Note Equation (6) presents the efficiency without parasiticlosses However parasitic losses are taken into account in(7) As mentioned before these two equations are used to becompared with CFD and test data respectively
Relative Mach number distributions at 10 50 and90 spans are shown in Figure 12 It is very clear that alow velocity region exists near pressure surface and becomessmaller gradually as blade span increases Because high staticpressure near pressure surface accompanies low velocity thelow magnitude area can be expected near pressure surfaceMoreover narrow passage introduces large viscous effectsand the typical velocity distribution of the bend comes upjust before the leading edge of the impeller which makes itobvious why Figure 12 presents relative Mach number like
that Fortunately no flow separation is found in the flow fieldof the impeller
Figure 13 shows 119881119898distribution on the meridional view
No low flow region and separation bubble exist whichindicates that this design is rational It is seen in Figure 13that velocity is gradually increasing from hub to shroud inthe extended inlet region which is a typical flow distributionin the bend High velocity means low static pressure andvice versa High pressure static pressure near hub regioncreates centripetal force to balance centrifugal force In orderto reduce the effect of this kind of flow distribution onthe incidence angles along the span of impeller inlet lowercurvature of shroud in the extended inlet region which cancause higher flow area and reduce hub-to-shroud velocitygradient should be applied for performance optimization inthe future Figure 14 presents the idea that static pressuredistribution is smooth through the impeller as expected
Due to the even absolute flow angle distribution atimpeller exit shown in Figure 15 vaneless or vaned diffuserhas perfect inlet condition and can be easily designed ifneeded Blade loading at 10 50 and 90 spans distributesreasonably which can be checked out in detail in Figure 16The blank area between pressure and suction surface staticcurves represents the load that blade withstands which doesnot vary too much through the blade at different spans Thatis what designers expect
The main performance parameters comparison at designpoint is listed in Table 3 The power calculated by CFD isapproximately in the middle of these two values computed by1D code Compared to CFD the efficiency is overpredictedby 152 in the 1D code which is really satisfying The totalpressure ratio in CFD is 305 higher than 1D code Inaddition parasitic losses drop efficiency a lot based on 1Dprediction
5 Conclusions
1D code is developed in this paper and divided into two partswhich are used to design and analyze Based on the code alowflow coefficient centrifugal compressor is designed and itsperformance is predicted In comparisonwith 1D code steadyCFD simulation has been carried out and provides flow fielddetails in the impeller
Comparing to 1D code CFD overpredicts total pressureratio of impeller but shows the same distribution trend whichis encouraging Further validations through more impellershave to be done in the future to confirm if a constantcoefficient for total pressure ratio exists between CFD and1D code For adiabatic efficiency 1D code without includingparasitic losses matches very well CFD in the operating rangeof near design point and choke point However 1D code isoverpredicted between near design point and stall point Thedifference of mass flow rate at choke point between CFDand 1D code is less than 2 Compared to steady CFD 1Dcode presents stall point at lower mass flow rate No flowseparation is found in the flow field of impeller and even theabsolute flow angle distribution at impeller exit is shownThe
10 International Journal of Rotating Machinery
02 03 04 05 06 07 08 09 10 1100
02
04
06
08
10
CFD1D (with parasitic losses)1D (without parasitic losses)
120578
mmchoke
(a) Adiabatic efficiency
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 10 11
CFD
120587to
t
1D code
mmchoke
(b) Total pressure ratio
Figure 11 Impeller performance curves
0 01 02 03 04 05 06
(a) 10 span (b) 50 span (c) 90 span
Figure 12 Relative Mach number map
120
100
80
60
40
20
0
Vm
Figure 13 Meridional velocity and streamline distribution
15E + 07
145E + 07
14E + 07
135E + 07
155E + 07
13E + 07St
atic
pre
ssur
e
Figure 14 Static pressure distribution
0
5
10
15
20
25
30
0Axial length (mm)
minus9 minus8 minus7 minus6 minus5 minus4 minus3 minus2 minus1
1205722
(∘)
Figure 15 Absolute flow angle distribution at impeller exit
International Journal of Rotating Machinery 11
0Axial length (mm)
10 span50 span90 span
10E + 07
11E + 07
12E + 07
13E + 07
14E + 07
15E + 07
16E + 07
Pst
(Pa)
minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2
Figure 16 Blade loading distribution at different spans
Table 3 Performance comparison between CFD and 1D code atdesign point
CFD 1D(no parasitic losses)
1D(parasitic losses)
Power 1778400W 1656740W 1857339W120587tot 121 11731 11731120578 902 9172 8257
blade loading at three different spans distributes smoothly asexpected
Since the low flow coefficient centrifugal compressordesigned in this paper is not the usual type and empiricalequations used are based on medium flow coefficient com-pressors further research on the improvement and validationof 1D code needs to be done by experiment and CFD toincrease prediction accuracy
Nomenclature
119860 Area (m2)AR Area ratio (119860
2sin(1205732119887)1198601sin(120573th))
119886 Sonic velocity (ms)119861 Fraction area blockage119887 Blade height (m)119862119901 Specific heat at constant pressure(Jkg K)
119890 Impeller mean line radius ratio119863 Diameter (m)119863eq Equivalent diffusion factor119896 Ratio of specific heatsΔℎ Enthalpy increase (Jkg)119868119861 Blade work input coefficient
120590(1 minus 119898cot(1205732119887)((120588211986021198802)(1 minus 119861
2))) minus
119880111986211990611198802
2
119871119885 Impeller axial length (m)
119871119861 Length of blade mean camberline (m)
119872 Relative Mach number119898 Mass flow rate (kgs)119873 Rotation speed (rpm)119873119904 Specific speed
119875 Pressure (pa)119877 Gas constant (J(kgsdotK))119879 Temperature (K)119880 Blade speed (ms)119881 Absolute velocity (ms)119882 Relative velocity (ms)Δ119882 Average blade velocity difference (ms)119885 Number of the blades
Greeks
120572 Absolute flow angle from tangential (∘)120573 Relative flow angle from tangential (∘)120578 Adiabatic efficiency120582 Workenthalpy coefficient Δℎ119880
2
2
120587 Pressure ratio120588 Gas density (kgm
3)
120590 Slip factor120593 Inlet flow coefficient119898(120588
111988021205871198632
24)
Ψ Inlet head coefficient(8544119863
2)21198621199011198791((11987521198751)((119896minus1)119896)
minus 1)
Δ120596 Total pressure loss coefficientΔ1199010(1199010minus 119901)
Subscripts
0 Total condition1 Impeller inlet2 Impeller outlet3 Diffuser inlet4 Diffuser outlet
119887 Bladebl Blade loading119888 Criterionchoke Choke pointdf Disc frictiondif Inducer diffusionℎ Impeller inlet hubhs Hub-to-shroudinc Incidenceis Isentropic119897 Leakagelim Limit119898 Meridional componentmax Maximummin Minimummix Wake mixing119904 Shroudst Staticth Impeller throat
12 International Journal of Rotating Machinery
sf Skin frictiontot Total-to-total119906 Tangential componentvld Vaneless diffuser
Superscripts
lowast Correct value1015840 New valueand Value relative to rotating frame of reference
Conflict of Interests
The authors declare that they have no financial and personalrelationships with other people or organizations that caninappropriately influence their work there is no professionalor other personal interest of any nature or kind in anyproduct service andor company that could be construed asinfluencing the position presented in or the review of thepaper
Acknowledgment
This work is supported by the National Natural ScienceFoundation of China under Grant no 51010007 and theChina Scholarship Council (CSC) The authors would like tothank Dr Marco Vagani and Christopher D Bolin for theirdiscussion and advice
References
[1] T Sato J M Oh and A Engeda ldquoExperimental and numericalinvestigation of the flow in a vaneless diffuser of a centrifugalcompressor stage Part 1 experimental investigationrdquo Proceed-ings of the Institution of Mechanical Engineers C vol 219 no 10pp 1053ndash1059 2005
[2] R H Aungier Centrifugal Compressor A Strategy for Aerody-namic Design and Analysis ASME Press New York NY USA2000
[3] V Rusak ldquoDevelopment and performance of the wedge-typelow specific speed compressor wheelrdquo Tech Rep 82-GT-214ASME 2009
[4] M V Casey P Dalbert and E Schurter ldquoRadial compressorstages for low flow coefficientsrdquo in Proceedings of the IMechEInternational Conference on Machinery for the Oil and GasIndustries 1990
[5] T Koizumi ldquoExperimental studies on performance of centrifu-gal compressors with very small flow coefficientrdquoMitsui ZosenTechnical Review vol 117 pp 28ndash39 1983
[6] J Paroubek J Kyncl and V Cyrus ldquoExperimental investigationand performance analysis of six low flow coefficient centrifugalcompressor stagesrdquo Transactions of the ASME Journal of Turbo-machinery vol 117 no 4 pp 585ndash592 1995
[7] J-L Di Liberti Design and development of low-flow coefficientcentrifugal compressors for industrial application [PhD thesis]Michigan State University 1998
[8] Y I Biba D A Nye and L I U Zheji ldquoPerformance evaluationand fluid flow analysis in low flow stages of industrial centrifu-gal compressorrdquo International Journal of Rotating Machineryvol 8 no 5 pp 309ndash317 2002
[9] M R Galvas ldquoFortran program for predicting off-designperformance of centrifugal com-pressorsrdquo Tech Rep TN D-7487 NASA 1973
[10] K H Ludtke Process Centrifugal Compressors Basic FunctionOperation Design Application Springer Berlin Germany 2010
[11] F J Wiesner ldquoA review of slip factors for centrifugal compres-sorsrdquo Journal of Engineering for Power Transactions of theASMEvol 89 pp 558ndash572 1967
[12] R H Aungier ldquoMean streamline aerodynamic performanceanalysis of centrifugal compressorsrdquo Transactions of the ASMEJournal of Turbomachinery vol 117 no 3 pp 360ndash366 1995
[13] S L Dixon Fluid Mechanics and Thermodnamics of Turboma-chinery Butterworth-Heinemann 4th edition 1998
[14] Y Senoo and Y Kinoshita ldquoLimits of rotating stall and stall invaneless diffusers of centrifugal compressorsrdquo Tech Rep 78-GT-19 ASME 1978
[15] S Lieblein ldquoLoss and stall analysis of compressor cascadesrdquoASME Transactions Journal of Basic Engineering vol 81 pp387ndash400 1959
[16] H Krain and B Hoffmann ldquoFlow physics in high pressure ratiocentrifugal compressorsrdquo in Proceedings of the ASME FluidsEngineering Division Summer Meeting June 1998
[17] G Eisenlohr and H Krain ldquoInvestigation of the flow througha high pressure ratio centrifugal impellerrdquo in Proceedings of theASME Conference Proceedings 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Rotating Machinery 7
0
01
02
03
04
05
06
036 040 044 051 057 063 073 078 086 093 097 100
Loss
coeffi
cien
t
Inducer diffusionBlade loadingIncidence
Skin frictionWake mixing
mmchoke
Figure 6 Loss coefficient distribution of impeller
0
002
004
006
008
01
012
014
036 040 044 051 057 063 073 078 086 093 097 100
Wor
k co
effici
ent
LeakageDisc friction
mmchoke
Figure 7 Distribution of work coefficient due to parasitic losses
the design point For parasitic losses or external losses onlydisc friction loss and leakage loss are involved They presentsimilar distribution trend seen in Figure 7 Overall 1D codeprovides asmuch information as it canMore importantly the1D analysis results look reasonable and acceptable
Note Please refer to reference [2] to look up the equationsused for calculating loss coefficient and work coefficient inFigures 6 and 7 which are based on the results that theanalysis code provides
05
06
07
08
09
10
11
12
13
14
000
015
030
045
060
075
090
105
120
135
004 005 006 007 008 009
Test CFDTest CFD
120578120595
120593
Figure 8 Performance comparison between test and CFD
4 3D CFD Validation
Many impellers coming from either open literature or indus-try have been used to evaluate the accuracy of the CFDanalysis before It is confirmed that our CFD simulation isreasonable and reliable An impeller similar to the case inthis paper is chosen to present our CFD analysis accuracycompared to test data from a cooperative company Thisimpeller also applies two-dimensional blades and is usedin the last stage centrifugal compressor of the multistagecompressors It can be observed in Figure 8 that CFD has agood agreement with test data
Note Vaneless diffuser and return channel are also involvedin the test and CFD
For the case in this paper before running CFD impellermodeling is built in the commercial software ldquoBLADEGENrdquoaccording to the fixed geometry from 1D design codeFigure 9 shows the geometry and meridional view of theimpeller It can be observed that leading edge of impeller is inthe radial direction and flow channel is so narrow which arethe typical characteristics of low flow coefficient centrifugalcompressors Inlet and outlet computational domains haveto be added to avoid reserved flow and improve accuracy ofcomputation in CFD Extended outlet computational domainacts like practical vaneless diffuser and makes impeller runclose to the real environment
Three-dimensional viscous RANS solver and Spalart-Allamaras turbulent model are applied in the steady simu-lation with inlet boundary conditions of 119875
01= 13602 kPa
11987901
= 424K and axial flow Static pressure is set on the outletboundary condition and increased gradually Near lower flowregion using mass flow rate condition captures stall pointinstead of static pressure condition The working medium is
8 International Journal of Rotating Machinery
(a) Impeller geometry
80
100
120
140
160
180
200
220
240
260
280
300
0 20minus40 minus20
Z (mm)
R(m
m)
(b) Meridional view
Figure 9 Impeller design
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 1 11
Grid 1Grid 2Grid 3
120587to
t
mmchoke
(a) Total pressure ratio
010
020
030
040
050
060
070
080
090
100
02 03 04 05 06 07 08 09 1 11
Grid 1Grid 2Grid 3
mmchoke
120578
(b) Adiabatic efficiency
Figure 10 Simulation results with three grid plans
defined as typical natural gas All solidwalls are assumed to besmoothwith roughness of 10minus6m In order to reduce the effectof skin friction coefficient affected by surface roughness samesurface property has to be employed in 1D code whenmakinga comparison between 1D prediction and CFD simulation
In order to understand the analytical accuracy of theCFD on the impeller of this case three grid plans shown inTable 2 were tried to check grid sensitivity Figure 10(a) showsthat total pressure ratio distribution curves from three gridplans match very well Adiabatic efficiency curves seen in
International Journal of Rotating Machinery 9
Table 2 Three grid plans
Circumferential Streamwise Spanwise Grid numberGrid 1 27 87 39 185367Grid 2 35 107 49 295421Grid 3 43 127 57 435309
Figure 10(b) also present a good match However it seemsthat larger stall margin is obtained by applying less gridnumber In consideration of running safety in the test thegrid plan 3 with smaller stall margin will be selected as areference for design because designers can not just pick theoption with the best evaluation
For adiabatic efficiency of impeller 1D code can presentthe results with and without parasitic losses However CFDdoes not usually include parasitic losses unless the exact prac-tical structure of centrifugal compressor is built That is thereason why Figure 11(a) shows three distribution curves forefficiency In addition to evaluate 1D code through comparingwith CFD without parasitic losses the efficiency includingparasitic losses close to real environment is needed to bepresented as well 1D code shows wider operating rangeand further stall point which means that comparing withCFD 1D code predicts that the centrifugal compressor canrun at lower mass flow rate Itrsquos shown that steady CFDsimulation cannot get an accurate stall point Transientsimulation should be done after steady calculation which isnot completed in this paper According to the comparisonof efficiency CFD has a little bit discrepancy in adiabaticefficiency on the right side of blue line However differencein efficiency becomes bigger and distribution trends showdifferent as mass flow rate continues to be reduced
In Figure 11(b) total pressure ratio from CFD is overpre-dicted but has same distribution trend with 1D predictionSince empirical loss models are used in the code and CFDcannot show the exact results with real values we think1D code works well and has the function to finish the per-formance evaluation within acceptable discrepancy Furthervalidation with more impellers needs to be carried out in thefuture to see if a constant coefficient for total pressure ratioexists between 1D code and CFD And if this is the case theprediction accuracy of 1D code can be further improved
Note Equation (6) presents the efficiency without parasiticlosses However parasitic losses are taken into account in(7) As mentioned before these two equations are used to becompared with CFD and test data respectively
Relative Mach number distributions at 10 50 and90 spans are shown in Figure 12 It is very clear that alow velocity region exists near pressure surface and becomessmaller gradually as blade span increases Because high staticpressure near pressure surface accompanies low velocity thelow magnitude area can be expected near pressure surfaceMoreover narrow passage introduces large viscous effectsand the typical velocity distribution of the bend comes upjust before the leading edge of the impeller which makes itobvious why Figure 12 presents relative Mach number like
that Fortunately no flow separation is found in the flow fieldof the impeller
Figure 13 shows 119881119898distribution on the meridional view
No low flow region and separation bubble exist whichindicates that this design is rational It is seen in Figure 13that velocity is gradually increasing from hub to shroud inthe extended inlet region which is a typical flow distributionin the bend High velocity means low static pressure andvice versa High pressure static pressure near hub regioncreates centripetal force to balance centrifugal force In orderto reduce the effect of this kind of flow distribution onthe incidence angles along the span of impeller inlet lowercurvature of shroud in the extended inlet region which cancause higher flow area and reduce hub-to-shroud velocitygradient should be applied for performance optimization inthe future Figure 14 presents the idea that static pressuredistribution is smooth through the impeller as expected
Due to the even absolute flow angle distribution atimpeller exit shown in Figure 15 vaneless or vaned diffuserhas perfect inlet condition and can be easily designed ifneeded Blade loading at 10 50 and 90 spans distributesreasonably which can be checked out in detail in Figure 16The blank area between pressure and suction surface staticcurves represents the load that blade withstands which doesnot vary too much through the blade at different spans Thatis what designers expect
The main performance parameters comparison at designpoint is listed in Table 3 The power calculated by CFD isapproximately in the middle of these two values computed by1D code Compared to CFD the efficiency is overpredictedby 152 in the 1D code which is really satisfying The totalpressure ratio in CFD is 305 higher than 1D code Inaddition parasitic losses drop efficiency a lot based on 1Dprediction
5 Conclusions
1D code is developed in this paper and divided into two partswhich are used to design and analyze Based on the code alowflow coefficient centrifugal compressor is designed and itsperformance is predicted In comparisonwith 1D code steadyCFD simulation has been carried out and provides flow fielddetails in the impeller
Comparing to 1D code CFD overpredicts total pressureratio of impeller but shows the same distribution trend whichis encouraging Further validations through more impellershave to be done in the future to confirm if a constantcoefficient for total pressure ratio exists between CFD and1D code For adiabatic efficiency 1D code without includingparasitic losses matches very well CFD in the operating rangeof near design point and choke point However 1D code isoverpredicted between near design point and stall point Thedifference of mass flow rate at choke point between CFDand 1D code is less than 2 Compared to steady CFD 1Dcode presents stall point at lower mass flow rate No flowseparation is found in the flow field of impeller and even theabsolute flow angle distribution at impeller exit is shownThe
10 International Journal of Rotating Machinery
02 03 04 05 06 07 08 09 10 1100
02
04
06
08
10
CFD1D (with parasitic losses)1D (without parasitic losses)
120578
mmchoke
(a) Adiabatic efficiency
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 10 11
CFD
120587to
t
1D code
mmchoke
(b) Total pressure ratio
Figure 11 Impeller performance curves
0 01 02 03 04 05 06
(a) 10 span (b) 50 span (c) 90 span
Figure 12 Relative Mach number map
120
100
80
60
40
20
0
Vm
Figure 13 Meridional velocity and streamline distribution
15E + 07
145E + 07
14E + 07
135E + 07
155E + 07
13E + 07St
atic
pre
ssur
e
Figure 14 Static pressure distribution
0
5
10
15
20
25
30
0Axial length (mm)
minus9 minus8 minus7 minus6 minus5 minus4 minus3 minus2 minus1
1205722
(∘)
Figure 15 Absolute flow angle distribution at impeller exit
International Journal of Rotating Machinery 11
0Axial length (mm)
10 span50 span90 span
10E + 07
11E + 07
12E + 07
13E + 07
14E + 07
15E + 07
16E + 07
Pst
(Pa)
minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2
Figure 16 Blade loading distribution at different spans
Table 3 Performance comparison between CFD and 1D code atdesign point
CFD 1D(no parasitic losses)
1D(parasitic losses)
Power 1778400W 1656740W 1857339W120587tot 121 11731 11731120578 902 9172 8257
blade loading at three different spans distributes smoothly asexpected
Since the low flow coefficient centrifugal compressordesigned in this paper is not the usual type and empiricalequations used are based on medium flow coefficient com-pressors further research on the improvement and validationof 1D code needs to be done by experiment and CFD toincrease prediction accuracy
Nomenclature
119860 Area (m2)AR Area ratio (119860
2sin(1205732119887)1198601sin(120573th))
119886 Sonic velocity (ms)119861 Fraction area blockage119887 Blade height (m)119862119901 Specific heat at constant pressure(Jkg K)
119890 Impeller mean line radius ratio119863 Diameter (m)119863eq Equivalent diffusion factor119896 Ratio of specific heatsΔℎ Enthalpy increase (Jkg)119868119861 Blade work input coefficient
120590(1 minus 119898cot(1205732119887)((120588211986021198802)(1 minus 119861
2))) minus
119880111986211990611198802
2
119871119885 Impeller axial length (m)
119871119861 Length of blade mean camberline (m)
119872 Relative Mach number119898 Mass flow rate (kgs)119873 Rotation speed (rpm)119873119904 Specific speed
119875 Pressure (pa)119877 Gas constant (J(kgsdotK))119879 Temperature (K)119880 Blade speed (ms)119881 Absolute velocity (ms)119882 Relative velocity (ms)Δ119882 Average blade velocity difference (ms)119885 Number of the blades
Greeks
120572 Absolute flow angle from tangential (∘)120573 Relative flow angle from tangential (∘)120578 Adiabatic efficiency120582 Workenthalpy coefficient Δℎ119880
2
2
120587 Pressure ratio120588 Gas density (kgm
3)
120590 Slip factor120593 Inlet flow coefficient119898(120588
111988021205871198632
24)
Ψ Inlet head coefficient(8544119863
2)21198621199011198791((11987521198751)((119896minus1)119896)
minus 1)
Δ120596 Total pressure loss coefficientΔ1199010(1199010minus 119901)
Subscripts
0 Total condition1 Impeller inlet2 Impeller outlet3 Diffuser inlet4 Diffuser outlet
119887 Bladebl Blade loading119888 Criterionchoke Choke pointdf Disc frictiondif Inducer diffusionℎ Impeller inlet hubhs Hub-to-shroudinc Incidenceis Isentropic119897 Leakagelim Limit119898 Meridional componentmax Maximummin Minimummix Wake mixing119904 Shroudst Staticth Impeller throat
12 International Journal of Rotating Machinery
sf Skin frictiontot Total-to-total119906 Tangential componentvld Vaneless diffuser
Superscripts
lowast Correct value1015840 New valueand Value relative to rotating frame of reference
Conflict of Interests
The authors declare that they have no financial and personalrelationships with other people or organizations that caninappropriately influence their work there is no professionalor other personal interest of any nature or kind in anyproduct service andor company that could be construed asinfluencing the position presented in or the review of thepaper
Acknowledgment
This work is supported by the National Natural ScienceFoundation of China under Grant no 51010007 and theChina Scholarship Council (CSC) The authors would like tothank Dr Marco Vagani and Christopher D Bolin for theirdiscussion and advice
References
[1] T Sato J M Oh and A Engeda ldquoExperimental and numericalinvestigation of the flow in a vaneless diffuser of a centrifugalcompressor stage Part 1 experimental investigationrdquo Proceed-ings of the Institution of Mechanical Engineers C vol 219 no 10pp 1053ndash1059 2005
[2] R H Aungier Centrifugal Compressor A Strategy for Aerody-namic Design and Analysis ASME Press New York NY USA2000
[3] V Rusak ldquoDevelopment and performance of the wedge-typelow specific speed compressor wheelrdquo Tech Rep 82-GT-214ASME 2009
[4] M V Casey P Dalbert and E Schurter ldquoRadial compressorstages for low flow coefficientsrdquo in Proceedings of the IMechEInternational Conference on Machinery for the Oil and GasIndustries 1990
[5] T Koizumi ldquoExperimental studies on performance of centrifu-gal compressors with very small flow coefficientrdquoMitsui ZosenTechnical Review vol 117 pp 28ndash39 1983
[6] J Paroubek J Kyncl and V Cyrus ldquoExperimental investigationand performance analysis of six low flow coefficient centrifugalcompressor stagesrdquo Transactions of the ASME Journal of Turbo-machinery vol 117 no 4 pp 585ndash592 1995
[7] J-L Di Liberti Design and development of low-flow coefficientcentrifugal compressors for industrial application [PhD thesis]Michigan State University 1998
[8] Y I Biba D A Nye and L I U Zheji ldquoPerformance evaluationand fluid flow analysis in low flow stages of industrial centrifu-gal compressorrdquo International Journal of Rotating Machineryvol 8 no 5 pp 309ndash317 2002
[9] M R Galvas ldquoFortran program for predicting off-designperformance of centrifugal com-pressorsrdquo Tech Rep TN D-7487 NASA 1973
[10] K H Ludtke Process Centrifugal Compressors Basic FunctionOperation Design Application Springer Berlin Germany 2010
[11] F J Wiesner ldquoA review of slip factors for centrifugal compres-sorsrdquo Journal of Engineering for Power Transactions of theASMEvol 89 pp 558ndash572 1967
[12] R H Aungier ldquoMean streamline aerodynamic performanceanalysis of centrifugal compressorsrdquo Transactions of the ASMEJournal of Turbomachinery vol 117 no 3 pp 360ndash366 1995
[13] S L Dixon Fluid Mechanics and Thermodnamics of Turboma-chinery Butterworth-Heinemann 4th edition 1998
[14] Y Senoo and Y Kinoshita ldquoLimits of rotating stall and stall invaneless diffusers of centrifugal compressorsrdquo Tech Rep 78-GT-19 ASME 1978
[15] S Lieblein ldquoLoss and stall analysis of compressor cascadesrdquoASME Transactions Journal of Basic Engineering vol 81 pp387ndash400 1959
[16] H Krain and B Hoffmann ldquoFlow physics in high pressure ratiocentrifugal compressorsrdquo in Proceedings of the ASME FluidsEngineering Division Summer Meeting June 1998
[17] G Eisenlohr and H Krain ldquoInvestigation of the flow througha high pressure ratio centrifugal impellerrdquo in Proceedings of theASME Conference Proceedings 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Active and Passive Electronic Components
Control Scienceand Engineering
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International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
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Shock and Vibration
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Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
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Electrical and Computer Engineering
Journal of
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Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
8 International Journal of Rotating Machinery
(a) Impeller geometry
80
100
120
140
160
180
200
220
240
260
280
300
0 20minus40 minus20
Z (mm)
R(m
m)
(b) Meridional view
Figure 9 Impeller design
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 1 11
Grid 1Grid 2Grid 3
120587to
t
mmchoke
(a) Total pressure ratio
010
020
030
040
050
060
070
080
090
100
02 03 04 05 06 07 08 09 1 11
Grid 1Grid 2Grid 3
mmchoke
120578
(b) Adiabatic efficiency
Figure 10 Simulation results with three grid plans
defined as typical natural gas All solidwalls are assumed to besmoothwith roughness of 10minus6m In order to reduce the effectof skin friction coefficient affected by surface roughness samesurface property has to be employed in 1D code whenmakinga comparison between 1D prediction and CFD simulation
In order to understand the analytical accuracy of theCFD on the impeller of this case three grid plans shown inTable 2 were tried to check grid sensitivity Figure 10(a) showsthat total pressure ratio distribution curves from three gridplans match very well Adiabatic efficiency curves seen in
International Journal of Rotating Machinery 9
Table 2 Three grid plans
Circumferential Streamwise Spanwise Grid numberGrid 1 27 87 39 185367Grid 2 35 107 49 295421Grid 3 43 127 57 435309
Figure 10(b) also present a good match However it seemsthat larger stall margin is obtained by applying less gridnumber In consideration of running safety in the test thegrid plan 3 with smaller stall margin will be selected as areference for design because designers can not just pick theoption with the best evaluation
For adiabatic efficiency of impeller 1D code can presentthe results with and without parasitic losses However CFDdoes not usually include parasitic losses unless the exact prac-tical structure of centrifugal compressor is built That is thereason why Figure 11(a) shows three distribution curves forefficiency In addition to evaluate 1D code through comparingwith CFD without parasitic losses the efficiency includingparasitic losses close to real environment is needed to bepresented as well 1D code shows wider operating rangeand further stall point which means that comparing withCFD 1D code predicts that the centrifugal compressor canrun at lower mass flow rate Itrsquos shown that steady CFDsimulation cannot get an accurate stall point Transientsimulation should be done after steady calculation which isnot completed in this paper According to the comparisonof efficiency CFD has a little bit discrepancy in adiabaticefficiency on the right side of blue line However differencein efficiency becomes bigger and distribution trends showdifferent as mass flow rate continues to be reduced
In Figure 11(b) total pressure ratio from CFD is overpre-dicted but has same distribution trend with 1D predictionSince empirical loss models are used in the code and CFDcannot show the exact results with real values we think1D code works well and has the function to finish the per-formance evaluation within acceptable discrepancy Furthervalidation with more impellers needs to be carried out in thefuture to see if a constant coefficient for total pressure ratioexists between 1D code and CFD And if this is the case theprediction accuracy of 1D code can be further improved
Note Equation (6) presents the efficiency without parasiticlosses However parasitic losses are taken into account in(7) As mentioned before these two equations are used to becompared with CFD and test data respectively
Relative Mach number distributions at 10 50 and90 spans are shown in Figure 12 It is very clear that alow velocity region exists near pressure surface and becomessmaller gradually as blade span increases Because high staticpressure near pressure surface accompanies low velocity thelow magnitude area can be expected near pressure surfaceMoreover narrow passage introduces large viscous effectsand the typical velocity distribution of the bend comes upjust before the leading edge of the impeller which makes itobvious why Figure 12 presents relative Mach number like
that Fortunately no flow separation is found in the flow fieldof the impeller
Figure 13 shows 119881119898distribution on the meridional view
No low flow region and separation bubble exist whichindicates that this design is rational It is seen in Figure 13that velocity is gradually increasing from hub to shroud inthe extended inlet region which is a typical flow distributionin the bend High velocity means low static pressure andvice versa High pressure static pressure near hub regioncreates centripetal force to balance centrifugal force In orderto reduce the effect of this kind of flow distribution onthe incidence angles along the span of impeller inlet lowercurvature of shroud in the extended inlet region which cancause higher flow area and reduce hub-to-shroud velocitygradient should be applied for performance optimization inthe future Figure 14 presents the idea that static pressuredistribution is smooth through the impeller as expected
Due to the even absolute flow angle distribution atimpeller exit shown in Figure 15 vaneless or vaned diffuserhas perfect inlet condition and can be easily designed ifneeded Blade loading at 10 50 and 90 spans distributesreasonably which can be checked out in detail in Figure 16The blank area between pressure and suction surface staticcurves represents the load that blade withstands which doesnot vary too much through the blade at different spans Thatis what designers expect
The main performance parameters comparison at designpoint is listed in Table 3 The power calculated by CFD isapproximately in the middle of these two values computed by1D code Compared to CFD the efficiency is overpredictedby 152 in the 1D code which is really satisfying The totalpressure ratio in CFD is 305 higher than 1D code Inaddition parasitic losses drop efficiency a lot based on 1Dprediction
5 Conclusions
1D code is developed in this paper and divided into two partswhich are used to design and analyze Based on the code alowflow coefficient centrifugal compressor is designed and itsperformance is predicted In comparisonwith 1D code steadyCFD simulation has been carried out and provides flow fielddetails in the impeller
Comparing to 1D code CFD overpredicts total pressureratio of impeller but shows the same distribution trend whichis encouraging Further validations through more impellershave to be done in the future to confirm if a constantcoefficient for total pressure ratio exists between CFD and1D code For adiabatic efficiency 1D code without includingparasitic losses matches very well CFD in the operating rangeof near design point and choke point However 1D code isoverpredicted between near design point and stall point Thedifference of mass flow rate at choke point between CFDand 1D code is less than 2 Compared to steady CFD 1Dcode presents stall point at lower mass flow rate No flowseparation is found in the flow field of impeller and even theabsolute flow angle distribution at impeller exit is shownThe
10 International Journal of Rotating Machinery
02 03 04 05 06 07 08 09 10 1100
02
04
06
08
10
CFD1D (with parasitic losses)1D (without parasitic losses)
120578
mmchoke
(a) Adiabatic efficiency
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 10 11
CFD
120587to
t
1D code
mmchoke
(b) Total pressure ratio
Figure 11 Impeller performance curves
0 01 02 03 04 05 06
(a) 10 span (b) 50 span (c) 90 span
Figure 12 Relative Mach number map
120
100
80
60
40
20
0
Vm
Figure 13 Meridional velocity and streamline distribution
15E + 07
145E + 07
14E + 07
135E + 07
155E + 07
13E + 07St
atic
pre
ssur
e
Figure 14 Static pressure distribution
0
5
10
15
20
25
30
0Axial length (mm)
minus9 minus8 minus7 minus6 minus5 minus4 minus3 minus2 minus1
1205722
(∘)
Figure 15 Absolute flow angle distribution at impeller exit
International Journal of Rotating Machinery 11
0Axial length (mm)
10 span50 span90 span
10E + 07
11E + 07
12E + 07
13E + 07
14E + 07
15E + 07
16E + 07
Pst
(Pa)
minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2
Figure 16 Blade loading distribution at different spans
Table 3 Performance comparison between CFD and 1D code atdesign point
CFD 1D(no parasitic losses)
1D(parasitic losses)
Power 1778400W 1656740W 1857339W120587tot 121 11731 11731120578 902 9172 8257
blade loading at three different spans distributes smoothly asexpected
Since the low flow coefficient centrifugal compressordesigned in this paper is not the usual type and empiricalequations used are based on medium flow coefficient com-pressors further research on the improvement and validationof 1D code needs to be done by experiment and CFD toincrease prediction accuracy
Nomenclature
119860 Area (m2)AR Area ratio (119860
2sin(1205732119887)1198601sin(120573th))
119886 Sonic velocity (ms)119861 Fraction area blockage119887 Blade height (m)119862119901 Specific heat at constant pressure(Jkg K)
119890 Impeller mean line radius ratio119863 Diameter (m)119863eq Equivalent diffusion factor119896 Ratio of specific heatsΔℎ Enthalpy increase (Jkg)119868119861 Blade work input coefficient
120590(1 minus 119898cot(1205732119887)((120588211986021198802)(1 minus 119861
2))) minus
119880111986211990611198802
2
119871119885 Impeller axial length (m)
119871119861 Length of blade mean camberline (m)
119872 Relative Mach number119898 Mass flow rate (kgs)119873 Rotation speed (rpm)119873119904 Specific speed
119875 Pressure (pa)119877 Gas constant (J(kgsdotK))119879 Temperature (K)119880 Blade speed (ms)119881 Absolute velocity (ms)119882 Relative velocity (ms)Δ119882 Average blade velocity difference (ms)119885 Number of the blades
Greeks
120572 Absolute flow angle from tangential (∘)120573 Relative flow angle from tangential (∘)120578 Adiabatic efficiency120582 Workenthalpy coefficient Δℎ119880
2
2
120587 Pressure ratio120588 Gas density (kgm
3)
120590 Slip factor120593 Inlet flow coefficient119898(120588
111988021205871198632
24)
Ψ Inlet head coefficient(8544119863
2)21198621199011198791((11987521198751)((119896minus1)119896)
minus 1)
Δ120596 Total pressure loss coefficientΔ1199010(1199010minus 119901)
Subscripts
0 Total condition1 Impeller inlet2 Impeller outlet3 Diffuser inlet4 Diffuser outlet
119887 Bladebl Blade loading119888 Criterionchoke Choke pointdf Disc frictiondif Inducer diffusionℎ Impeller inlet hubhs Hub-to-shroudinc Incidenceis Isentropic119897 Leakagelim Limit119898 Meridional componentmax Maximummin Minimummix Wake mixing119904 Shroudst Staticth Impeller throat
12 International Journal of Rotating Machinery
sf Skin frictiontot Total-to-total119906 Tangential componentvld Vaneless diffuser
Superscripts
lowast Correct value1015840 New valueand Value relative to rotating frame of reference
Conflict of Interests
The authors declare that they have no financial and personalrelationships with other people or organizations that caninappropriately influence their work there is no professionalor other personal interest of any nature or kind in anyproduct service andor company that could be construed asinfluencing the position presented in or the review of thepaper
Acknowledgment
This work is supported by the National Natural ScienceFoundation of China under Grant no 51010007 and theChina Scholarship Council (CSC) The authors would like tothank Dr Marco Vagani and Christopher D Bolin for theirdiscussion and advice
References
[1] T Sato J M Oh and A Engeda ldquoExperimental and numericalinvestigation of the flow in a vaneless diffuser of a centrifugalcompressor stage Part 1 experimental investigationrdquo Proceed-ings of the Institution of Mechanical Engineers C vol 219 no 10pp 1053ndash1059 2005
[2] R H Aungier Centrifugal Compressor A Strategy for Aerody-namic Design and Analysis ASME Press New York NY USA2000
[3] V Rusak ldquoDevelopment and performance of the wedge-typelow specific speed compressor wheelrdquo Tech Rep 82-GT-214ASME 2009
[4] M V Casey P Dalbert and E Schurter ldquoRadial compressorstages for low flow coefficientsrdquo in Proceedings of the IMechEInternational Conference on Machinery for the Oil and GasIndustries 1990
[5] T Koizumi ldquoExperimental studies on performance of centrifu-gal compressors with very small flow coefficientrdquoMitsui ZosenTechnical Review vol 117 pp 28ndash39 1983
[6] J Paroubek J Kyncl and V Cyrus ldquoExperimental investigationand performance analysis of six low flow coefficient centrifugalcompressor stagesrdquo Transactions of the ASME Journal of Turbo-machinery vol 117 no 4 pp 585ndash592 1995
[7] J-L Di Liberti Design and development of low-flow coefficientcentrifugal compressors for industrial application [PhD thesis]Michigan State University 1998
[8] Y I Biba D A Nye and L I U Zheji ldquoPerformance evaluationand fluid flow analysis in low flow stages of industrial centrifu-gal compressorrdquo International Journal of Rotating Machineryvol 8 no 5 pp 309ndash317 2002
[9] M R Galvas ldquoFortran program for predicting off-designperformance of centrifugal com-pressorsrdquo Tech Rep TN D-7487 NASA 1973
[10] K H Ludtke Process Centrifugal Compressors Basic FunctionOperation Design Application Springer Berlin Germany 2010
[11] F J Wiesner ldquoA review of slip factors for centrifugal compres-sorsrdquo Journal of Engineering for Power Transactions of theASMEvol 89 pp 558ndash572 1967
[12] R H Aungier ldquoMean streamline aerodynamic performanceanalysis of centrifugal compressorsrdquo Transactions of the ASMEJournal of Turbomachinery vol 117 no 3 pp 360ndash366 1995
[13] S L Dixon Fluid Mechanics and Thermodnamics of Turboma-chinery Butterworth-Heinemann 4th edition 1998
[14] Y Senoo and Y Kinoshita ldquoLimits of rotating stall and stall invaneless diffusers of centrifugal compressorsrdquo Tech Rep 78-GT-19 ASME 1978
[15] S Lieblein ldquoLoss and stall analysis of compressor cascadesrdquoASME Transactions Journal of Basic Engineering vol 81 pp387ndash400 1959
[16] H Krain and B Hoffmann ldquoFlow physics in high pressure ratiocentrifugal compressorsrdquo in Proceedings of the ASME FluidsEngineering Division Summer Meeting June 1998
[17] G Eisenlohr and H Krain ldquoInvestigation of the flow througha high pressure ratio centrifugal impellerrdquo in Proceedings of theASME Conference Proceedings 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Rotating Machinery 9
Table 2 Three grid plans
Circumferential Streamwise Spanwise Grid numberGrid 1 27 87 39 185367Grid 2 35 107 49 295421Grid 3 43 127 57 435309
Figure 10(b) also present a good match However it seemsthat larger stall margin is obtained by applying less gridnumber In consideration of running safety in the test thegrid plan 3 with smaller stall margin will be selected as areference for design because designers can not just pick theoption with the best evaluation
For adiabatic efficiency of impeller 1D code can presentthe results with and without parasitic losses However CFDdoes not usually include parasitic losses unless the exact prac-tical structure of centrifugal compressor is built That is thereason why Figure 11(a) shows three distribution curves forefficiency In addition to evaluate 1D code through comparingwith CFD without parasitic losses the efficiency includingparasitic losses close to real environment is needed to bepresented as well 1D code shows wider operating rangeand further stall point which means that comparing withCFD 1D code predicts that the centrifugal compressor canrun at lower mass flow rate Itrsquos shown that steady CFDsimulation cannot get an accurate stall point Transientsimulation should be done after steady calculation which isnot completed in this paper According to the comparisonof efficiency CFD has a little bit discrepancy in adiabaticefficiency on the right side of blue line However differencein efficiency becomes bigger and distribution trends showdifferent as mass flow rate continues to be reduced
In Figure 11(b) total pressure ratio from CFD is overpre-dicted but has same distribution trend with 1D predictionSince empirical loss models are used in the code and CFDcannot show the exact results with real values we think1D code works well and has the function to finish the per-formance evaluation within acceptable discrepancy Furthervalidation with more impellers needs to be carried out in thefuture to see if a constant coefficient for total pressure ratioexists between 1D code and CFD And if this is the case theprediction accuracy of 1D code can be further improved
Note Equation (6) presents the efficiency without parasiticlosses However parasitic losses are taken into account in(7) As mentioned before these two equations are used to becompared with CFD and test data respectively
Relative Mach number distributions at 10 50 and90 spans are shown in Figure 12 It is very clear that alow velocity region exists near pressure surface and becomessmaller gradually as blade span increases Because high staticpressure near pressure surface accompanies low velocity thelow magnitude area can be expected near pressure surfaceMoreover narrow passage introduces large viscous effectsand the typical velocity distribution of the bend comes upjust before the leading edge of the impeller which makes itobvious why Figure 12 presents relative Mach number like
that Fortunately no flow separation is found in the flow fieldof the impeller
Figure 13 shows 119881119898distribution on the meridional view
No low flow region and separation bubble exist whichindicates that this design is rational It is seen in Figure 13that velocity is gradually increasing from hub to shroud inthe extended inlet region which is a typical flow distributionin the bend High velocity means low static pressure andvice versa High pressure static pressure near hub regioncreates centripetal force to balance centrifugal force In orderto reduce the effect of this kind of flow distribution onthe incidence angles along the span of impeller inlet lowercurvature of shroud in the extended inlet region which cancause higher flow area and reduce hub-to-shroud velocitygradient should be applied for performance optimization inthe future Figure 14 presents the idea that static pressuredistribution is smooth through the impeller as expected
Due to the even absolute flow angle distribution atimpeller exit shown in Figure 15 vaneless or vaned diffuserhas perfect inlet condition and can be easily designed ifneeded Blade loading at 10 50 and 90 spans distributesreasonably which can be checked out in detail in Figure 16The blank area between pressure and suction surface staticcurves represents the load that blade withstands which doesnot vary too much through the blade at different spans Thatis what designers expect
The main performance parameters comparison at designpoint is listed in Table 3 The power calculated by CFD isapproximately in the middle of these two values computed by1D code Compared to CFD the efficiency is overpredictedby 152 in the 1D code which is really satisfying The totalpressure ratio in CFD is 305 higher than 1D code Inaddition parasitic losses drop efficiency a lot based on 1Dprediction
5 Conclusions
1D code is developed in this paper and divided into two partswhich are used to design and analyze Based on the code alowflow coefficient centrifugal compressor is designed and itsperformance is predicted In comparisonwith 1D code steadyCFD simulation has been carried out and provides flow fielddetails in the impeller
Comparing to 1D code CFD overpredicts total pressureratio of impeller but shows the same distribution trend whichis encouraging Further validations through more impellershave to be done in the future to confirm if a constantcoefficient for total pressure ratio exists between CFD and1D code For adiabatic efficiency 1D code without includingparasitic losses matches very well CFD in the operating rangeof near design point and choke point However 1D code isoverpredicted between near design point and stall point Thedifference of mass flow rate at choke point between CFDand 1D code is less than 2 Compared to steady CFD 1Dcode presents stall point at lower mass flow rate No flowseparation is found in the flow field of impeller and even theabsolute flow angle distribution at impeller exit is shownThe
10 International Journal of Rotating Machinery
02 03 04 05 06 07 08 09 10 1100
02
04
06
08
10
CFD1D (with parasitic losses)1D (without parasitic losses)
120578
mmchoke
(a) Adiabatic efficiency
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 10 11
CFD
120587to
t
1D code
mmchoke
(b) Total pressure ratio
Figure 11 Impeller performance curves
0 01 02 03 04 05 06
(a) 10 span (b) 50 span (c) 90 span
Figure 12 Relative Mach number map
120
100
80
60
40
20
0
Vm
Figure 13 Meridional velocity and streamline distribution
15E + 07
145E + 07
14E + 07
135E + 07
155E + 07
13E + 07St
atic
pre
ssur
e
Figure 14 Static pressure distribution
0
5
10
15
20
25
30
0Axial length (mm)
minus9 minus8 minus7 minus6 minus5 minus4 minus3 minus2 minus1
1205722
(∘)
Figure 15 Absolute flow angle distribution at impeller exit
International Journal of Rotating Machinery 11
0Axial length (mm)
10 span50 span90 span
10E + 07
11E + 07
12E + 07
13E + 07
14E + 07
15E + 07
16E + 07
Pst
(Pa)
minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2
Figure 16 Blade loading distribution at different spans
Table 3 Performance comparison between CFD and 1D code atdesign point
CFD 1D(no parasitic losses)
1D(parasitic losses)
Power 1778400W 1656740W 1857339W120587tot 121 11731 11731120578 902 9172 8257
blade loading at three different spans distributes smoothly asexpected
Since the low flow coefficient centrifugal compressordesigned in this paper is not the usual type and empiricalequations used are based on medium flow coefficient com-pressors further research on the improvement and validationof 1D code needs to be done by experiment and CFD toincrease prediction accuracy
Nomenclature
119860 Area (m2)AR Area ratio (119860
2sin(1205732119887)1198601sin(120573th))
119886 Sonic velocity (ms)119861 Fraction area blockage119887 Blade height (m)119862119901 Specific heat at constant pressure(Jkg K)
119890 Impeller mean line radius ratio119863 Diameter (m)119863eq Equivalent diffusion factor119896 Ratio of specific heatsΔℎ Enthalpy increase (Jkg)119868119861 Blade work input coefficient
120590(1 minus 119898cot(1205732119887)((120588211986021198802)(1 minus 119861
2))) minus
119880111986211990611198802
2
119871119885 Impeller axial length (m)
119871119861 Length of blade mean camberline (m)
119872 Relative Mach number119898 Mass flow rate (kgs)119873 Rotation speed (rpm)119873119904 Specific speed
119875 Pressure (pa)119877 Gas constant (J(kgsdotK))119879 Temperature (K)119880 Blade speed (ms)119881 Absolute velocity (ms)119882 Relative velocity (ms)Δ119882 Average blade velocity difference (ms)119885 Number of the blades
Greeks
120572 Absolute flow angle from tangential (∘)120573 Relative flow angle from tangential (∘)120578 Adiabatic efficiency120582 Workenthalpy coefficient Δℎ119880
2
2
120587 Pressure ratio120588 Gas density (kgm
3)
120590 Slip factor120593 Inlet flow coefficient119898(120588
111988021205871198632
24)
Ψ Inlet head coefficient(8544119863
2)21198621199011198791((11987521198751)((119896minus1)119896)
minus 1)
Δ120596 Total pressure loss coefficientΔ1199010(1199010minus 119901)
Subscripts
0 Total condition1 Impeller inlet2 Impeller outlet3 Diffuser inlet4 Diffuser outlet
119887 Bladebl Blade loading119888 Criterionchoke Choke pointdf Disc frictiondif Inducer diffusionℎ Impeller inlet hubhs Hub-to-shroudinc Incidenceis Isentropic119897 Leakagelim Limit119898 Meridional componentmax Maximummin Minimummix Wake mixing119904 Shroudst Staticth Impeller throat
12 International Journal of Rotating Machinery
sf Skin frictiontot Total-to-total119906 Tangential componentvld Vaneless diffuser
Superscripts
lowast Correct value1015840 New valueand Value relative to rotating frame of reference
Conflict of Interests
The authors declare that they have no financial and personalrelationships with other people or organizations that caninappropriately influence their work there is no professionalor other personal interest of any nature or kind in anyproduct service andor company that could be construed asinfluencing the position presented in or the review of thepaper
Acknowledgment
This work is supported by the National Natural ScienceFoundation of China under Grant no 51010007 and theChina Scholarship Council (CSC) The authors would like tothank Dr Marco Vagani and Christopher D Bolin for theirdiscussion and advice
References
[1] T Sato J M Oh and A Engeda ldquoExperimental and numericalinvestigation of the flow in a vaneless diffuser of a centrifugalcompressor stage Part 1 experimental investigationrdquo Proceed-ings of the Institution of Mechanical Engineers C vol 219 no 10pp 1053ndash1059 2005
[2] R H Aungier Centrifugal Compressor A Strategy for Aerody-namic Design and Analysis ASME Press New York NY USA2000
[3] V Rusak ldquoDevelopment and performance of the wedge-typelow specific speed compressor wheelrdquo Tech Rep 82-GT-214ASME 2009
[4] M V Casey P Dalbert and E Schurter ldquoRadial compressorstages for low flow coefficientsrdquo in Proceedings of the IMechEInternational Conference on Machinery for the Oil and GasIndustries 1990
[5] T Koizumi ldquoExperimental studies on performance of centrifu-gal compressors with very small flow coefficientrdquoMitsui ZosenTechnical Review vol 117 pp 28ndash39 1983
[6] J Paroubek J Kyncl and V Cyrus ldquoExperimental investigationand performance analysis of six low flow coefficient centrifugalcompressor stagesrdquo Transactions of the ASME Journal of Turbo-machinery vol 117 no 4 pp 585ndash592 1995
[7] J-L Di Liberti Design and development of low-flow coefficientcentrifugal compressors for industrial application [PhD thesis]Michigan State University 1998
[8] Y I Biba D A Nye and L I U Zheji ldquoPerformance evaluationand fluid flow analysis in low flow stages of industrial centrifu-gal compressorrdquo International Journal of Rotating Machineryvol 8 no 5 pp 309ndash317 2002
[9] M R Galvas ldquoFortran program for predicting off-designperformance of centrifugal com-pressorsrdquo Tech Rep TN D-7487 NASA 1973
[10] K H Ludtke Process Centrifugal Compressors Basic FunctionOperation Design Application Springer Berlin Germany 2010
[11] F J Wiesner ldquoA review of slip factors for centrifugal compres-sorsrdquo Journal of Engineering for Power Transactions of theASMEvol 89 pp 558ndash572 1967
[12] R H Aungier ldquoMean streamline aerodynamic performanceanalysis of centrifugal compressorsrdquo Transactions of the ASMEJournal of Turbomachinery vol 117 no 3 pp 360ndash366 1995
[13] S L Dixon Fluid Mechanics and Thermodnamics of Turboma-chinery Butterworth-Heinemann 4th edition 1998
[14] Y Senoo and Y Kinoshita ldquoLimits of rotating stall and stall invaneless diffusers of centrifugal compressorsrdquo Tech Rep 78-GT-19 ASME 1978
[15] S Lieblein ldquoLoss and stall analysis of compressor cascadesrdquoASME Transactions Journal of Basic Engineering vol 81 pp387ndash400 1959
[16] H Krain and B Hoffmann ldquoFlow physics in high pressure ratiocentrifugal compressorsrdquo in Proceedings of the ASME FluidsEngineering Division Summer Meeting June 1998
[17] G Eisenlohr and H Krain ldquoInvestigation of the flow througha high pressure ratio centrifugal impellerrdquo in Proceedings of theASME Conference Proceedings 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
10 International Journal of Rotating Machinery
02 03 04 05 06 07 08 09 10 1100
02
04
06
08
10
CFD1D (with parasitic losses)1D (without parasitic losses)
120578
mmchoke
(a) Adiabatic efficiency
100
105
110
115
120
125
130
02 03 04 05 06 07 08 09 10 11
CFD
120587to
t
1D code
mmchoke
(b) Total pressure ratio
Figure 11 Impeller performance curves
0 01 02 03 04 05 06
(a) 10 span (b) 50 span (c) 90 span
Figure 12 Relative Mach number map
120
100
80
60
40
20
0
Vm
Figure 13 Meridional velocity and streamline distribution
15E + 07
145E + 07
14E + 07
135E + 07
155E + 07
13E + 07St
atic
pre
ssur
e
Figure 14 Static pressure distribution
0
5
10
15
20
25
30
0Axial length (mm)
minus9 minus8 minus7 minus6 minus5 minus4 minus3 minus2 minus1
1205722
(∘)
Figure 15 Absolute flow angle distribution at impeller exit
International Journal of Rotating Machinery 11
0Axial length (mm)
10 span50 span90 span
10E + 07
11E + 07
12E + 07
13E + 07
14E + 07
15E + 07
16E + 07
Pst
(Pa)
minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2
Figure 16 Blade loading distribution at different spans
Table 3 Performance comparison between CFD and 1D code atdesign point
CFD 1D(no parasitic losses)
1D(parasitic losses)
Power 1778400W 1656740W 1857339W120587tot 121 11731 11731120578 902 9172 8257
blade loading at three different spans distributes smoothly asexpected
Since the low flow coefficient centrifugal compressordesigned in this paper is not the usual type and empiricalequations used are based on medium flow coefficient com-pressors further research on the improvement and validationof 1D code needs to be done by experiment and CFD toincrease prediction accuracy
Nomenclature
119860 Area (m2)AR Area ratio (119860
2sin(1205732119887)1198601sin(120573th))
119886 Sonic velocity (ms)119861 Fraction area blockage119887 Blade height (m)119862119901 Specific heat at constant pressure(Jkg K)
119890 Impeller mean line radius ratio119863 Diameter (m)119863eq Equivalent diffusion factor119896 Ratio of specific heatsΔℎ Enthalpy increase (Jkg)119868119861 Blade work input coefficient
120590(1 minus 119898cot(1205732119887)((120588211986021198802)(1 minus 119861
2))) minus
119880111986211990611198802
2
119871119885 Impeller axial length (m)
119871119861 Length of blade mean camberline (m)
119872 Relative Mach number119898 Mass flow rate (kgs)119873 Rotation speed (rpm)119873119904 Specific speed
119875 Pressure (pa)119877 Gas constant (J(kgsdotK))119879 Temperature (K)119880 Blade speed (ms)119881 Absolute velocity (ms)119882 Relative velocity (ms)Δ119882 Average blade velocity difference (ms)119885 Number of the blades
Greeks
120572 Absolute flow angle from tangential (∘)120573 Relative flow angle from tangential (∘)120578 Adiabatic efficiency120582 Workenthalpy coefficient Δℎ119880
2
2
120587 Pressure ratio120588 Gas density (kgm
3)
120590 Slip factor120593 Inlet flow coefficient119898(120588
111988021205871198632
24)
Ψ Inlet head coefficient(8544119863
2)21198621199011198791((11987521198751)((119896minus1)119896)
minus 1)
Δ120596 Total pressure loss coefficientΔ1199010(1199010minus 119901)
Subscripts
0 Total condition1 Impeller inlet2 Impeller outlet3 Diffuser inlet4 Diffuser outlet
119887 Bladebl Blade loading119888 Criterionchoke Choke pointdf Disc frictiondif Inducer diffusionℎ Impeller inlet hubhs Hub-to-shroudinc Incidenceis Isentropic119897 Leakagelim Limit119898 Meridional componentmax Maximummin Minimummix Wake mixing119904 Shroudst Staticth Impeller throat
12 International Journal of Rotating Machinery
sf Skin frictiontot Total-to-total119906 Tangential componentvld Vaneless diffuser
Superscripts
lowast Correct value1015840 New valueand Value relative to rotating frame of reference
Conflict of Interests
The authors declare that they have no financial and personalrelationships with other people or organizations that caninappropriately influence their work there is no professionalor other personal interest of any nature or kind in anyproduct service andor company that could be construed asinfluencing the position presented in or the review of thepaper
Acknowledgment
This work is supported by the National Natural ScienceFoundation of China under Grant no 51010007 and theChina Scholarship Council (CSC) The authors would like tothank Dr Marco Vagani and Christopher D Bolin for theirdiscussion and advice
References
[1] T Sato J M Oh and A Engeda ldquoExperimental and numericalinvestigation of the flow in a vaneless diffuser of a centrifugalcompressor stage Part 1 experimental investigationrdquo Proceed-ings of the Institution of Mechanical Engineers C vol 219 no 10pp 1053ndash1059 2005
[2] R H Aungier Centrifugal Compressor A Strategy for Aerody-namic Design and Analysis ASME Press New York NY USA2000
[3] V Rusak ldquoDevelopment and performance of the wedge-typelow specific speed compressor wheelrdquo Tech Rep 82-GT-214ASME 2009
[4] M V Casey P Dalbert and E Schurter ldquoRadial compressorstages for low flow coefficientsrdquo in Proceedings of the IMechEInternational Conference on Machinery for the Oil and GasIndustries 1990
[5] T Koizumi ldquoExperimental studies on performance of centrifu-gal compressors with very small flow coefficientrdquoMitsui ZosenTechnical Review vol 117 pp 28ndash39 1983
[6] J Paroubek J Kyncl and V Cyrus ldquoExperimental investigationand performance analysis of six low flow coefficient centrifugalcompressor stagesrdquo Transactions of the ASME Journal of Turbo-machinery vol 117 no 4 pp 585ndash592 1995
[7] J-L Di Liberti Design and development of low-flow coefficientcentrifugal compressors for industrial application [PhD thesis]Michigan State University 1998
[8] Y I Biba D A Nye and L I U Zheji ldquoPerformance evaluationand fluid flow analysis in low flow stages of industrial centrifu-gal compressorrdquo International Journal of Rotating Machineryvol 8 no 5 pp 309ndash317 2002
[9] M R Galvas ldquoFortran program for predicting off-designperformance of centrifugal com-pressorsrdquo Tech Rep TN D-7487 NASA 1973
[10] K H Ludtke Process Centrifugal Compressors Basic FunctionOperation Design Application Springer Berlin Germany 2010
[11] F J Wiesner ldquoA review of slip factors for centrifugal compres-sorsrdquo Journal of Engineering for Power Transactions of theASMEvol 89 pp 558ndash572 1967
[12] R H Aungier ldquoMean streamline aerodynamic performanceanalysis of centrifugal compressorsrdquo Transactions of the ASMEJournal of Turbomachinery vol 117 no 3 pp 360ndash366 1995
[13] S L Dixon Fluid Mechanics and Thermodnamics of Turboma-chinery Butterworth-Heinemann 4th edition 1998
[14] Y Senoo and Y Kinoshita ldquoLimits of rotating stall and stall invaneless diffusers of centrifugal compressorsrdquo Tech Rep 78-GT-19 ASME 1978
[15] S Lieblein ldquoLoss and stall analysis of compressor cascadesrdquoASME Transactions Journal of Basic Engineering vol 81 pp387ndash400 1959
[16] H Krain and B Hoffmann ldquoFlow physics in high pressure ratiocentrifugal compressorsrdquo in Proceedings of the ASME FluidsEngineering Division Summer Meeting June 1998
[17] G Eisenlohr and H Krain ldquoInvestigation of the flow througha high pressure ratio centrifugal impellerrdquo in Proceedings of theASME Conference Proceedings 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of Rotating Machinery 11
0Axial length (mm)
10 span50 span90 span
10E + 07
11E + 07
12E + 07
13E + 07
14E + 07
15E + 07
16E + 07
Pst
(Pa)
minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2
Figure 16 Blade loading distribution at different spans
Table 3 Performance comparison between CFD and 1D code atdesign point
CFD 1D(no parasitic losses)
1D(parasitic losses)
Power 1778400W 1656740W 1857339W120587tot 121 11731 11731120578 902 9172 8257
blade loading at three different spans distributes smoothly asexpected
Since the low flow coefficient centrifugal compressordesigned in this paper is not the usual type and empiricalequations used are based on medium flow coefficient com-pressors further research on the improvement and validationof 1D code needs to be done by experiment and CFD toincrease prediction accuracy
Nomenclature
119860 Area (m2)AR Area ratio (119860
2sin(1205732119887)1198601sin(120573th))
119886 Sonic velocity (ms)119861 Fraction area blockage119887 Blade height (m)119862119901 Specific heat at constant pressure(Jkg K)
119890 Impeller mean line radius ratio119863 Diameter (m)119863eq Equivalent diffusion factor119896 Ratio of specific heatsΔℎ Enthalpy increase (Jkg)119868119861 Blade work input coefficient
120590(1 minus 119898cot(1205732119887)((120588211986021198802)(1 minus 119861
2))) minus
119880111986211990611198802
2
119871119885 Impeller axial length (m)
119871119861 Length of blade mean camberline (m)
119872 Relative Mach number119898 Mass flow rate (kgs)119873 Rotation speed (rpm)119873119904 Specific speed
119875 Pressure (pa)119877 Gas constant (J(kgsdotK))119879 Temperature (K)119880 Blade speed (ms)119881 Absolute velocity (ms)119882 Relative velocity (ms)Δ119882 Average blade velocity difference (ms)119885 Number of the blades
Greeks
120572 Absolute flow angle from tangential (∘)120573 Relative flow angle from tangential (∘)120578 Adiabatic efficiency120582 Workenthalpy coefficient Δℎ119880
2
2
120587 Pressure ratio120588 Gas density (kgm
3)
120590 Slip factor120593 Inlet flow coefficient119898(120588
111988021205871198632
24)
Ψ Inlet head coefficient(8544119863
2)21198621199011198791((11987521198751)((119896minus1)119896)
minus 1)
Δ120596 Total pressure loss coefficientΔ1199010(1199010minus 119901)
Subscripts
0 Total condition1 Impeller inlet2 Impeller outlet3 Diffuser inlet4 Diffuser outlet
119887 Bladebl Blade loading119888 Criterionchoke Choke pointdf Disc frictiondif Inducer diffusionℎ Impeller inlet hubhs Hub-to-shroudinc Incidenceis Isentropic119897 Leakagelim Limit119898 Meridional componentmax Maximummin Minimummix Wake mixing119904 Shroudst Staticth Impeller throat
12 International Journal of Rotating Machinery
sf Skin frictiontot Total-to-total119906 Tangential componentvld Vaneless diffuser
Superscripts
lowast Correct value1015840 New valueand Value relative to rotating frame of reference
Conflict of Interests
The authors declare that they have no financial and personalrelationships with other people or organizations that caninappropriately influence their work there is no professionalor other personal interest of any nature or kind in anyproduct service andor company that could be construed asinfluencing the position presented in or the review of thepaper
Acknowledgment
This work is supported by the National Natural ScienceFoundation of China under Grant no 51010007 and theChina Scholarship Council (CSC) The authors would like tothank Dr Marco Vagani and Christopher D Bolin for theirdiscussion and advice
References
[1] T Sato J M Oh and A Engeda ldquoExperimental and numericalinvestigation of the flow in a vaneless diffuser of a centrifugalcompressor stage Part 1 experimental investigationrdquo Proceed-ings of the Institution of Mechanical Engineers C vol 219 no 10pp 1053ndash1059 2005
[2] R H Aungier Centrifugal Compressor A Strategy for Aerody-namic Design and Analysis ASME Press New York NY USA2000
[3] V Rusak ldquoDevelopment and performance of the wedge-typelow specific speed compressor wheelrdquo Tech Rep 82-GT-214ASME 2009
[4] M V Casey P Dalbert and E Schurter ldquoRadial compressorstages for low flow coefficientsrdquo in Proceedings of the IMechEInternational Conference on Machinery for the Oil and GasIndustries 1990
[5] T Koizumi ldquoExperimental studies on performance of centrifu-gal compressors with very small flow coefficientrdquoMitsui ZosenTechnical Review vol 117 pp 28ndash39 1983
[6] J Paroubek J Kyncl and V Cyrus ldquoExperimental investigationand performance analysis of six low flow coefficient centrifugalcompressor stagesrdquo Transactions of the ASME Journal of Turbo-machinery vol 117 no 4 pp 585ndash592 1995
[7] J-L Di Liberti Design and development of low-flow coefficientcentrifugal compressors for industrial application [PhD thesis]Michigan State University 1998
[8] Y I Biba D A Nye and L I U Zheji ldquoPerformance evaluationand fluid flow analysis in low flow stages of industrial centrifu-gal compressorrdquo International Journal of Rotating Machineryvol 8 no 5 pp 309ndash317 2002
[9] M R Galvas ldquoFortran program for predicting off-designperformance of centrifugal com-pressorsrdquo Tech Rep TN D-7487 NASA 1973
[10] K H Ludtke Process Centrifugal Compressors Basic FunctionOperation Design Application Springer Berlin Germany 2010
[11] F J Wiesner ldquoA review of slip factors for centrifugal compres-sorsrdquo Journal of Engineering for Power Transactions of theASMEvol 89 pp 558ndash572 1967
[12] R H Aungier ldquoMean streamline aerodynamic performanceanalysis of centrifugal compressorsrdquo Transactions of the ASMEJournal of Turbomachinery vol 117 no 3 pp 360ndash366 1995
[13] S L Dixon Fluid Mechanics and Thermodnamics of Turboma-chinery Butterworth-Heinemann 4th edition 1998
[14] Y Senoo and Y Kinoshita ldquoLimits of rotating stall and stall invaneless diffusers of centrifugal compressorsrdquo Tech Rep 78-GT-19 ASME 1978
[15] S Lieblein ldquoLoss and stall analysis of compressor cascadesrdquoASME Transactions Journal of Basic Engineering vol 81 pp387ndash400 1959
[16] H Krain and B Hoffmann ldquoFlow physics in high pressure ratiocentrifugal compressorsrdquo in Proceedings of the ASME FluidsEngineering Division Summer Meeting June 1998
[17] G Eisenlohr and H Krain ldquoInvestigation of the flow througha high pressure ratio centrifugal impellerrdquo in Proceedings of theASME Conference Proceedings 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
12 International Journal of Rotating Machinery
sf Skin frictiontot Total-to-total119906 Tangential componentvld Vaneless diffuser
Superscripts
lowast Correct value1015840 New valueand Value relative to rotating frame of reference
Conflict of Interests
The authors declare that they have no financial and personalrelationships with other people or organizations that caninappropriately influence their work there is no professionalor other personal interest of any nature or kind in anyproduct service andor company that could be construed asinfluencing the position presented in or the review of thepaper
Acknowledgment
This work is supported by the National Natural ScienceFoundation of China under Grant no 51010007 and theChina Scholarship Council (CSC) The authors would like tothank Dr Marco Vagani and Christopher D Bolin for theirdiscussion and advice
References
[1] T Sato J M Oh and A Engeda ldquoExperimental and numericalinvestigation of the flow in a vaneless diffuser of a centrifugalcompressor stage Part 1 experimental investigationrdquo Proceed-ings of the Institution of Mechanical Engineers C vol 219 no 10pp 1053ndash1059 2005
[2] R H Aungier Centrifugal Compressor A Strategy for Aerody-namic Design and Analysis ASME Press New York NY USA2000
[3] V Rusak ldquoDevelopment and performance of the wedge-typelow specific speed compressor wheelrdquo Tech Rep 82-GT-214ASME 2009
[4] M V Casey P Dalbert and E Schurter ldquoRadial compressorstages for low flow coefficientsrdquo in Proceedings of the IMechEInternational Conference on Machinery for the Oil and GasIndustries 1990
[5] T Koizumi ldquoExperimental studies on performance of centrifu-gal compressors with very small flow coefficientrdquoMitsui ZosenTechnical Review vol 117 pp 28ndash39 1983
[6] J Paroubek J Kyncl and V Cyrus ldquoExperimental investigationand performance analysis of six low flow coefficient centrifugalcompressor stagesrdquo Transactions of the ASME Journal of Turbo-machinery vol 117 no 4 pp 585ndash592 1995
[7] J-L Di Liberti Design and development of low-flow coefficientcentrifugal compressors for industrial application [PhD thesis]Michigan State University 1998
[8] Y I Biba D A Nye and L I U Zheji ldquoPerformance evaluationand fluid flow analysis in low flow stages of industrial centrifu-gal compressorrdquo International Journal of Rotating Machineryvol 8 no 5 pp 309ndash317 2002
[9] M R Galvas ldquoFortran program for predicting off-designperformance of centrifugal com-pressorsrdquo Tech Rep TN D-7487 NASA 1973
[10] K H Ludtke Process Centrifugal Compressors Basic FunctionOperation Design Application Springer Berlin Germany 2010
[11] F J Wiesner ldquoA review of slip factors for centrifugal compres-sorsrdquo Journal of Engineering for Power Transactions of theASMEvol 89 pp 558ndash572 1967
[12] R H Aungier ldquoMean streamline aerodynamic performanceanalysis of centrifugal compressorsrdquo Transactions of the ASMEJournal of Turbomachinery vol 117 no 3 pp 360ndash366 1995
[13] S L Dixon Fluid Mechanics and Thermodnamics of Turboma-chinery Butterworth-Heinemann 4th edition 1998
[14] Y Senoo and Y Kinoshita ldquoLimits of rotating stall and stall invaneless diffusers of centrifugal compressorsrdquo Tech Rep 78-GT-19 ASME 1978
[15] S Lieblein ldquoLoss and stall analysis of compressor cascadesrdquoASME Transactions Journal of Basic Engineering vol 81 pp387ndash400 1959
[16] H Krain and B Hoffmann ldquoFlow physics in high pressure ratiocentrifugal compressorsrdquo in Proceedings of the ASME FluidsEngineering Division Summer Meeting June 1998
[17] G Eisenlohr and H Krain ldquoInvestigation of the flow througha high pressure ratio centrifugal impellerrdquo in Proceedings of theASME Conference Proceedings 2003
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of