computer-aided analysis ofcentrifugal compressorsF. MOUKALLED, N. NAIM and I. LAKKlS, Faculty of Engineering andArchitecture, Mechanical Engineering Department, American University ofBeirut, Beirut, Lebanon
Received 15th January 1993Revised 28th June 1993
This paper describes computer-aided analysis of centrifugal compressors (CAACC), a microcomputer-based, interactive, and menu-driven software package for use as an educational tool bymechanical engineering students studying radial flow compressors. CAACC is written in the Pascalcomputer language and runs on IBM PC, or compatible, computers. 1n addition to solving for anyunlawwn variables, the graphical utilities of the package allow the user to display a diagrammaticsketch of the compressor and to draw velocity diagrams at several locations. Furthermore, theprogram allows the investigation and plotting of the variation of any parameter versus any otherparameter. Through this option, the package guides the student in learning the basics ofcentrifugalcompressors by the various performance studies that can be undertaken and graphically displayed.The comprehensive example presented demonstrates the capabilities of the package as a teachingtool.
NOTATION
Cp specific heat at constant pressureCw whirl component of velocityPOI inlet stagnation pressureP03 exit stagnation pressureTOl inlet stagnation temperatureT03 exit stagnation temperatureV impeller tip speedVe average speed of impeller eyeVer speed of impeller eye rootVet speed of impeller eye tipWe compressor worka slip factorljI power input factor
INTRODUCTION
The centrifugal compressor is usually introduced to mechanical engineering students in a seniorcourse which concentrates on the application of thermodynamics to gas turbines. No attempt will be
0306-4190/94/0004-245 $0.00 international Journal 01Mechanical EngiMerIng EducatJon Vol 22 No 4
246 F. Moukalled, N. Nairn and I. Lakkls
made here to fully describe it; rather, a brief description will be given in the next section. Forfurther details of the subject the reader is referred to textbooks [1-7].
A large number of parameters affect the performance of centrifugal compressors and, dependingon the known variables, the inter-parametric relations may not be given via simple functions. Insuch cases, one has to solve nonlinear equations in order to obtain the values of the parameters inquestion. Performing this task by hand is tirne-consuming. This limits the number of cases that canbe considered by students and prevents them from exploring the effects of design parameters oncompressor performance.
With advances in computer technology, microcomputers are not only becoming more and morereliable in both speed and accuracy, but are also now within the reach of the majority of engineering students. Therefore, if given the tool, students may exploit microcomputers in solving timeconsuming problems. Through their use, students can solve more problems and conduct moreanalyses of a given type than when using hand-calculation. This in turn, leads students into a deeperunderstanding of the basic principles governing a particular application.
The aim of this paper is to present a program developed to provide the mechanical engineeringstudent with a tool that allows him to explore the effects of design changes on the performance ofcentrifugal compressors without the boredom of performing hand-calculations.
PRINCIPLE OF OPERATION AND THEORETICAL PERFORMANCE
The centrifugal compressor consists of an impeller rotating within a stationary casing. Duringoperation, gas is sucked into the impeller eye and whirled round at high speed by the vanes of theimpeller disk. While flowing, the fluid receives energy from the vanes resulting in an increase inboth pressure and absolute velocity. At any point in the flow through the impeller, the centrifugalacceleration is obtained by a pressure head, so that the static pressure of the gas increases from theeye to the tip of the impeller. The remainder of the static pressure rise is obtained in the volutecasing surrounding the impeller or in flow through fixed diverging passages known as the diffuser,in which, the very high velocity of the fluid leaving the impeller tip is reduced to somewhere in theregion of the velocity with which it enters the impeller eye. Friction in the diffuser causes some lossin stagnation pressure. Unless otherwise specified, CAACC performs computations assuming halfof the pressure rise occurs in the impeller and the other half in the diffuser.
Since no work is done on the gas in the diffuser, the energy absorbed by the compressor isdetermined by the conditions of the fluid at inlet and outlet of the impeller. Designating theconditions at impeller inlet, impeller exit, and compressor outlet by subscripts 1, 2, and 3 respectively, the work absorbed by the compressor and the stagnation pressure rise of the gas across thecompressor are given by
where
U = Uer +Uele 2
(1)
(2)
(3)
and l/f, Cp, U, Cw l and 0' being the power input factor, the specific heat, the blade tip velocity, thewhirl velocity component at inlet, and the slip factor respectively.
C ENIs Ho<wood Ud. Hemel Hempsllllld. England
Computer-alded analysis of centrifugal compressors 247
Usually, the stagnation conditions (ambient conditions when the working fluid is air) are knownat the compressor inlet. The package exploits this information and starts iterations, wheneverneeded, using these values as an initial guess in order to compute the inlet axial velocity and staticconditions. Further, in calculating the required depth of the impeller channel at the periphery, someassumptions regarding the radial component of velocity at the tip and the division of losses betweenthe impeller and the diffuser must be made in order for the density to be evaluated. The usualdesign practice is to choose the radial component of velocity equal to the axial velocity at inlet tothe eye. Unless otherwise instructed, the program follows this practice. In addition, if the losses inthe impeller and diffuser are not specified, the package divides the total loss equally between them.Once the radial component of velocity at impeller tip and the isentropic efficiency of the impellerare known, all fluid properties at that location are found by using the isentropic relations.
The current trend in compressor technology is towards high-performance compressors usingbackswept curved vanes. The use of such vanes in the impeller imply less stringent diffusionrequirements in both the impeller and diffuser, tending to increase the efficiency of both components and to widen the compressor operating range. CAACC permits the user to explore the effectsof changing the vane backswept angle on the overall performance of the compressor.
After leaving the impeller and before entering the diffuser, gas flows in a vaneless space. In thisgap, no energy is supplied to the fluid whose angular momentum remains constant (neglectingfriction). From this condition, the whirl component of the velocity at diffuser inlet is determined.The radial component of the velocity is calculated from the continuity equation using a guess-andcorrect procedure. The velocity decreases during flow in the vaneless space and as such somediffusion takes place. This is to advantage since it decreases the amount of diffusion needed in thediffuser. Knowing the velocity components at diffuser inlet, the angle of the diffuser vane leadingedge is easily determined. The throat width of the diffuser is calculated by an iterative procedureusing continuity and isentropic relations. For any required outlet velocity, knowing the total loss forthe whole compressor, the final density is easily calculated and hence the flow area required atoutlet. The length of the passage after the throat then depends on the chosen angle of divergence.
DESCRIPTION OF THE PROGRAM
CAACC is written in Pascal using the Turbo Pascal compiler version 6 [8] which includes apowerful debugger and facilitates enhanced graphics options. The package runs on any IDM PCXT/AT or compatible which includes at least 640 Kbytes of main memory, a colour monitorequipped with a Video or Enhanced Graphics Adaptor card (VGA or EGA), and an optional mathscoprocessor.
The software is divided into three major modules. The first one consists of procedures forgenerating menus and data entry windows. The role of the second module which is composed ofseveral procedures, is to solve for unknowns. An iterative solution procedure is adopted. Theiterative process consists of repeatedly executing the solving routine until no further changes in thenumber of known variables is noticed. The purpose of the third module is to view, print, and plotresults. The second and third modules are intercorrelated owing to the need for repeatedly solvingfor unknowns while plotting the variation of one quantity versus another. The program allows theplotting of the variation of three quantities at a time.
The menu structure of the program, depicted in Figs I and 2, is designed in such a way as toprovide a user-friendly environment. The main menu offers five entries. By selecting the appropriate task from this menu, one can input data, solve for unknowns, optimize the compressor performance, or use the graphics screen as a window through which a schematic of the compressor or ofvelocity diagrams may be seen or printed. The user starts by choosing entry INPUT which allows
International Journal 01Mech8nIcaI~ Education Vol 22 No 4
248 F. Moukalled, N. Nairn and I. Lakkls
Fig. 1. Hierarchical menu structure of CAACC.
them to enter the values of the known quantities. As depicted in Fig. 2, the menu-driven structure ofthe package facilitates this task by guiding the user throughout the data-entering procedure. Havingentered all data, the user may store them into a file that can be read by the program at any time.This option is included to permit easy correction of wrongly inputted or missing data. Afterinputting all data, a solution is obtained by choosing the SOLVE entry. Results may be viewed andprinted by going to the OUTPUT entry (Fig. 2). The effect of varying a parameter on the overallperformance of the compressor is studied as shown in Figs I and 2, in the GRAPH entry. Thisallows a comprehensive analysis of the different parameters involved. A diagrammatic sketch ofthe compressor and velocity diagrams at several locations may be seen from the DIAGRAM entry.To increase the usefulness of the package and to facilitate its usage, a HELP option, accessablefrom any level during execution, is included. Hard copies of the compressor and velocity diagramsmay be obtained by using the 'print-screen • command with a suitable graphics printer via anymemory-resident mM graphics module.
C EMIs HoIwood lid, Hemel Hempstead. England
Computer-alded analysis of centrifugal compressors 249
IMP Tin
Diffuserenera araMe ers
IMpeller- El;Je Root
IMPeller- El;Je Tip
I Lrrp e I Le r El;Je Genet-a!
, IMPeller- Tin
Di t t uae r inlet
'h'·q·W-'ii++U
Inlet
'., 1-
I tlPUT
III!W' pm,@'I II ..",el Ie' T .p
I
I~:::-----hIL---~
ReI Uel ower npu ac Dr
Abs Radial Vel
Ahs Whi,-I Uel
Tan Uel
S lIP Factor
Ls.errt r-op i o Eff
y---------i % 1055 at l nne l t e r
V.Space Radial Width
Diff t ru-oa t R Mean
Diff Passage Deptt, I[Pg On] I
Lrtpe Ll e r- Eff
tio. of IMp Vanes
lPg On]
FI-Help F6-S t ore F7-Load F8-Pr- int F9-tiew Alt-X Exit
Fig. 2. Main menu and several illustrative submenus of CAACC.
REPRESENTATIVE GRAPHICAL PLOTS
The capabilities of the program are demonstrated in this section by presenting a comprehensivestudy of a test problem. The centrifugal compressor in question is considered to be part of anaircraft engine. It is required to determine the performance of the compressor at take-off (sea-levelaltitude and zero forward velocity). Records of input and output data are presented in Table 1.while graphical output results are shown in Fig. 3. Figs 4 to 7 reveal the compressor responses tovariation in its parameters.
In Fig. 3. the velocity triangles at impeller eye root (Fig. 3(a». impeller eye tip (Fig. 3(b»,impeller tip (Fig. 3(c», and diffuser inlet (Fig. 3(d» are presented. The variation of the variousvelocities as gas flows through the compressor are easily depicted.
The effect of varying any parameter on the overall performance of the compressor may bestudied through the GRAPH option. Such analysis was undertaken here and results are presented inFigs 4 to 7.
The influence of compressor isentropic efficiency on the overall pressure ratio and diffuser inletMach number is depicted in Figs 4(a) and 4(b) respectively. As expected, the overall pressure ratioincreases with increasing the isentropic efficiency of the compressor owing to the decrease instagnation pressure loss. The decrease in the diffuser inlet Mach number is attributed to an increasein the static temperature and a decrease in the absolute velocity. In Figs 5(a), 5(b), 6(a), and 6(b)
Internatlonal Journal 01Mechanical EngIneering Education Vol 22 No 4
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252 F. Moukalled, N. Nairn and I. Lakkls
I,IPUT SOLVE OUTPUT GRAPH
uec t c r Dlag,-an at (no_II.," Ey. Root (Intak.'............................................ 'On',R'
IMP Tip
o t (fuser-
II • l:lll 7
U '197 5
C •• ""2 9
velocities are in m/s.
FI-Ilelfl F6-Stor-. F7-Lollrl F8-Pt' iot F!l-H~u Ot t -)( ExJ t I
Fig. 3(a). Velocity diagram at impeller eye rool
SOLVE OUTpur GRAPH
COHD. 0"',1uec t o r 01""9"-0'1'" .t I,",n~ 11f'1'- E'JI! Tin.................................. M''&'
TI Eye Root
" ,\.U,...l-I..., I'D
Diffus.,..
Utan
~,U -273 3
";'~ .•.U -30n 3
C ·1""2 .9
velocities are in m/s.
FI-H.l" Fa-Storlt F7-Load Fa-Print F9-H4!" Alt-X Exit I
Fig. 3(b). Velocity diagram at impeller eye tip.
C EN" Ho<wood ltd, Heme! Hempetead, EngIllnd
Computer-alded analysis of centrifugal compressors 253
I IHPUT SOLVE OUTPUT GRAPH ""\Air.gl ]
Vector Dhgr.", .t l"p.118,.. Tip..............................
~c=1Uten
U -"S5.5
U ·149 7
C ....3 ... t
velocities are in m/s.
FO-S to,.. F7-Lo.d F8-P'" Int F9-H."
EW. Root
Eye T tp
Alt-X EMI t I
Fig. 3(c). Velocity diagram at impeller tip.
Vector Ol.gl'a" e t OJ(rU~.H'' Inlet
IHPUT SOLVE OUTPUT GRAPH 1""1r!;fN']COMP. Olag
1'P"'3'
Eve Root
E..,. Tip
lnp Tip.
U -546.8
V .226 I;
C -355 0
velocities are in m/s.
FB-S tOI"t~ F7-Lo.d F9-Prlnt F9-H.", AIt-)( EMit I
Fig. 3(d). Velocity diagram at diffuser inlet.
International Journal 01Mechanical Englneefing Education Vol 22 No 4
254 F. Moukalled, N. Nairn and I. Lakkls
OIAGRAM
, i" I
OUTPUl
I I
/
i /
I I I I I I I I
~Ijr SULVE
5.064 I , I
,
j. I !4 _591
[---l, ,
i·.q 117 ,
,
r;===================-=-=-= IY OAAI ABLE
I I t I!X VARIABLE
3 643
:.1 170
"2.896o 5 Step
X v/s VI o suo + 0:, t €On }( U USOstatus
Alt-X Exit[21-Heln ~.~~-ston. F7-Load FB-P_'~_in_t__F_9_-_H_eu ----,
Fig, 4(a), Variation of overall pressure ratio with isentropic efficiency,
I V UARI ABLE
s Step
_____ 1
tT' ,-t-il- Ix UARI ABLE
:
' . ,
-t IMY-i--j I I I-;- -H-I ! ,
I ,
'"' --1-
"
"
,
, ,,- ~t---- , , i
I -I- IFIGURE I
, . -+-+--'Lit,?";!,,,
,
-H I ! FIGURE III
.D .u.i.u. _Ll]-----0_853
0,858
o
FjF-1 0.874
I
I::[ 0 BSB
o 863I
X'v/s "1'''2 o 500 + s t ep x 0.080s t a tus,
xy- 100i;
F1-Help F6-S tore F7-Load FB-PI" i n t F9-Hew Alt-X Exit
Fig. 4(b). Variation of diffuser inlet Mach number with isentropic efficiency,
C Ellis HorwoodUd, Hemet Hempstead, England
Computer-aided analysis of centrifugal compressors 255
111flU1 SOLVE DIOGnAH
• FI GURE II I
l~I_GUnE I I I I
status
xy-(rn)s t eo )( U.UIB() lI1U
, - , -, ,
-l-L
I i I tJ,'-f-j-!,
iI
I
~+H=8-~ -'-1 I·c++ jH-l"-'- ·-tT<-J- ,H-,-,-i-L-I-l l >-'-1 H-t-,,-
96 U56
1U6 625
us 4Hb
14 916
m/s
X v/s VI
r.::;-764 tlJ~-l::jI--H-'++tfR----+H-'-~ : ~:::::~: '-l!, =td ~I?M;~"!!!I!II!!!!I~J
117 t 95
'I
I
I
.1
II
""JAl t -X Exi tF6-S t ore F7-Load Fe-Pr- int F9-Hel.l
-------
Fig, 5(a), Variation of radial velocity at diffuser inlet with vaneless space radial width,
1I
II
II
III
DIAGARN~
IV UAnl ABLE
OUTPUTSOLVE
X UARIABLE
ii¥"'-
I II I
[FIGURE: I
Wp";!"!'I FIGURE III
313 115
353 662
m/s333 389
394 209
II~~;~--L ~ ~
5 Step
X v/s 'y':'" U 01U .. step }{ U Ot8 (rn )s t e t us.
x _IUD.Y
F1-Help F6-S t o re F7-Load F8-PI- int F9-Nel.l Rlt-X Exit
Fig, 5(b), Variation of the whirl velocity at diffuser inlet with vaneless space radial width,
international Journal 01Mechanical Engineering Education Vol 22 No 4
256 F. Moukalled, N. Nairn and I. Lakkls
L IIiPUT SOLVE OUTPUT 01 AGRAN
5 Step
IIY VARIABLE
1 IX UARll-lbLE
i- I I I, le- I
-~ iI
I~i
h -i- I,
$~l_L _
I-I-~+L~ ,= ~= 1--j~r-r-T: 1b - t-ifH
f_l! I1-' i
-I i~!FIGURE II I
-J
'-f-f W,\ild." II FI GURE J I I i
I
lJ _276
() ~'G]
o 250
radian
I: ~:,:Ii
I U "88I
X vis Y2 o 010 + step x 0 018 (rn)status
xy- IOO~
~~~ F6-Stot'e F7-Load F8-P,-int F9-He", Al t -x E><i t
Fig. 6(a). Variation of the diffuser vanes inlet angle with vaneless space radial width.
--+.---" ~~ X VARIABLE
IW-i
I'-
-rt j i
+Y- -H: I ,
H I i I I i
I
: I FIGURE I
IFIGURE II
I
Ijhlll;" '" Ir Ii~ I
L INPUT
~
I ] 8BO
3 480
bar3.24U
3.021
2 80t
SOLUE OUTPUT
Y VAAl ABLE
5 Step
DIAGRAM J
X vis Y3 0 UIO .step x 0 018 (m)status
X- 100~
Y
FI Hplp F6 Store F7-Load Fa-Pr· iot F9-lielol All X Ex i t
Fig. 6(b). Variation of the air static pressure at diffuser inlet with vaneless space radial width.
C Ellis HorNood lid, Heme! Hempstead, England
Computer-aided analysis of centrifugal compressors 257
the variations of the radial velocity component, the whirl velocity component, the air angle, and theair static pressure at diffuser inlet with the vaneless space radial width are respectively shown. Inaccordance with continuity, velocity and air angle are decreased with increasing values of thevaneless space. Furthermore, since more diffusion is taking place, owing to the decrease in velocity, the static pressure should increase. This is manifested by the results presented in Fig. 6(b).
Finally, the effects of varying the pre-whirl angle on the compressor actual work and theimpeller tip Mach number are presented in Figs 7(a) and 7(b) respectively. As can be seen, thework capacity of the compressor decreases with increasing the pre-whirl angle (Fig. 7(a». Furthermore, increasing the pre-whirl angle decreases both the impeller tip static temperature and absolutevelocity. The rate of decrease in the static temperature, however, is higher than the rate of decreasein velocity. The net effect is an increase in the impeller tip Mach number (Fig. 7(b».
CONCLUSION
A microcomputer-based program for analysing centrifugal compressors was developed. The menudriven structure of the program, along with its HELP utility and enhanced graphical capabilities,allow the mechanical engineering student to easily explore the effect of changing design parameterson compressor performance. The package also provides the user with an efficient educational toolon a low-cost workstation. The capabilities of the package as a teaching tool are demonstrated bypresenting a comprehensive analysis of an illustrative example problem. If hand-calculations arecombined with this educational tool, the user will be able to solve problems more complicated thanthe one presented in this paper very easily. Copies of the package will be provided to users onrequest to the authors.
Ilt~rUl SOLVEI-----~-
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190.578
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OUTPUT
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X VAAl ABLE
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X v/s Y2 0 (Juo t s t eo >< 0 105 (radian)stalus
Ft-He l n FS-S tore F7-Load FB-Pr int F9-He",
_100%
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Fig. 7(a). Variation of the compressor actual work with pre-whirl angle.
Intemaliooal Journal 01Mechanical E"llIn*ring Education Vol 22 No 4
258 F. MoukalJed, N. Nairn and I. Lakkls
DI AGnAtlOUTPUTSOLV-"E _
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P::i::H-t-fI =! r ~-
1._- --!--Lt.J
"TT1+H I :..i-t-+---+-t "---t i'-u ,l-l-j i., r :
'4F, - ffi ",. --; +-;-H-'-'-, , ' i-+i~-+J- t--
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t 103
t t 18
t 122
1 t 10
X v/s 'r'3status
100%
x -y
I',II
I-~,
Alt-X ExitF6-S t o re F7-Lo;:u1 F8-PI- int F9-Npy~n ,~ ~
Fig. 7(b). Variation of impeller tip Mach number with pre-whirl angle.
ACKNOWLEDGEMENTS
This work was supported by the University Research Board of the American University of Beirutunder grant 113040-48756.
REFERENCES
[I] H. Cohen, G. F. C. Rogers and H. 1. H. Saravanamuttoo, Gas Turbine Theory, 3rd edn, Longman Scientific& Technical, Singapore, 1987.
[2] W. W. Bathie, Fundamentals ofGas Turbines, John Wiley, New York, 1984.[3] R. T. C. Harman, Gas Turbine Engineering: Applications, Cycles, and Characteristics, Macmillan, London,
1981.[4] J. K. Jain, Gas Turbine Theory and Jet Propulsion, 5th edn, Khanna Publishers, Delhi, 1985.[5] B. H. Jennings and W. L. Roders, Gas Turbine Analysis and Practice, McGraw-Hili, New York, 1953.[6] D. G. Wilson, The Design of High-Efficiency Turbomachinery and Gas Turbines, MIT Press, Cambridge,
MA (1984).[7] S. L. Dixon, Fluid Mechanics: Thermodynamics of Turbomachinery, 3rd edn, Pergamon Press, Oxford,
1979.[8] Turbo Pascal Owner's Handbook, Borland International, Scotts Valley, CA, 1989.
C EUisHorwoodLtd, HemetHempstead, England
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