THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 91-GT-77 3 5 E 7 S ew Yo k Y 1 17
e Socie y s a o e es o si e o s a eme s o o i io s a a ce i a e s o i is- ES cussio a mee i gs o e Socie y o o i s i isio s o Sec io s o i e i i s u ica io s M iscussio is i e o y i e a e is u is e i a ASME ou a a e s a e a ai a e ] ® om ASME o i ee mo s a e e mee i g i e i USA Copyright © 1991 by ASME Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT1991/78989/V001T01A025/2400405/v001t01a025-91-gt-077.pdf by guest on 30 September 2021 e E icie cies o Si g e-S age Ce i uga Com esso s o Ai c a A ica io s
C O GE S Ae o e mo a Co ce ua esig C ie Su s a owe Sys ems Sa iego CA 9 1
A S AC s S eci ic S ee e us o mos ece a a ces i si g e—a wo—s age q Wo k ac o ce i uga com esso ec o ogy y e ae os ace commu i y as ee mo i a e y i e es i i c easi g ai ea i g essu e o u sio sys em owe e si y, a im o i g s eci ic ue Gas Co s a co sum io wi ig e s age essu e a ios. A a ces i e e ey o s um e as eca e a e ma e i a o ia e o e iew e ma o esig parameters influencing the efficiency levels of single—stage T Total Temperature centrifugal compressors for aircraft applications. U Impeller Tip Speed A simple efficiency correlation was derived for advanced W Flow Rate single—stage centrifugal compressors. It was based upon four critical parameters: A Difference
• Inlet Specific Speed ° Density • Impeller Tip Diameter Tl Efficiency (Total—static) y Specific Heat Ratio • Inducer Tip Relative Mach Number v Kinematic Viscosity • Exit Discharge Mach Number The correlation was shown to predict attainable (0 Angular Velocity state—of—the—art efficiencies within a band width of ± 2 % points. k Shock Loss Constant This was considered acceptable for preliminary compressor and engine design work. Flow coefficient = Cm1 /U2 SUBSCRIPTS NOMENCLATURE 1 Impeller Inlet C Velocity 2 Impeller Tip CFS Volume Flow (based on inlet stagnation density) ad Adiabatic Cp Specific Heat at Constant Pressure c Compressor D Diameter e Diffuser Exit g Gravitational Constant h Hub J Joules Equivalent m Meridional H Isentropic Head s Shroud M Mach Number u Tangential N Rotational Speed pol Polytropic
ese e a e I e a io a Gas u i e a Ae oe gi e Co g ess a E osi io O a o u e 3- 1991 1.0 INTRODUCTION
The correlation of efficiency levels of low and high pressure ratio centrifugal compressors and pumps with specific speed, have 0 produced relatively great uncertainty concerning the D'" . 0. state-of-the-art in maximum attainable efficiency potential. C This was demonstrated in Reference 1. This uncertainty was _w 80 caused by the practice of extrapolating the published U performances of widely differing impeller and diffuser designs. Ui Other factors were differences in determination of efficiency U Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT1991/78989/V001T01A025/2400405/v001t01a025-91-gt-077.pdf by guest on 30 September 2021 measurement and computation, and basic data uncertainty and 0 repeatability. w t Reference 1 showed that improved efficiency correlation 80 could be achieved if the impeller and diffuser performances of centrifugal compressors and pumps could be separated. This allowed the impeller performance potential to be correlated separately in terms of peak polytropic efficiency versus specific 0 speed, based upon average flowpath density.
Although the improved correlation of impeller efficiency 0.2 0. 0.4 0. .0 . 2.0 provided a more accurate definition of optimum impeller s S ECI IC S EE ( og sca e s _oI features, its inherent shortcoming was that it did not quantitatively rate the efficiency potential of the overall stage, igu e 1 Es ima e S age E icie cies e e e ce 1 that is, of the impeller plus stationary diffusion system (diffuser). Furthermore, the average density specific speed of the impeller cannot be readily calculated. It requires iteration of the impeller The thrust of recent advances in single-stage centrifugal tip vector triangle. pr r t hn l h b n t v t d b th r p community in the interest of increasing power density through If it is assumed that the impeller and diffuser performances higher airflows per unit frontal area (higher specific speeds) and n b p r t d, nd th t th r p rf r n r n t improved thermal performances at higher (air) stage pressure interdependent, it is possible to apply the extensive data ratios. Single-stage pressure ratios of 15.0 with very reasonable generated for two-dimensional and conical diffusers to evaluate efficiency and adequate operating range, have been achieved by overall stage performance potential. Canadian Pratt & Whitney. Excellent performance for a small 4.0-inch diameter impeller at a pressure ratio of 6.0 is reported in Component separation works reasonably well for the impeller Reference 4. In parallel with aerodynamic improvements, (with undistorted inlet flow). This is not the case for the improved materials and structural design techniques are used, downstream diffuser. Here, as expected, the single most providing the capability of operating at higher tip speeds, with dominant parameter affecting the performance of a particular increased cyclical life. diffuser geometry is the inlet blockage. Therefore, diffuser The application of axial compressor transonic blading design performance with a centrifugal compressor or pump depends techniques to centrifugal compressor inducers has resulted in upon the particular impeller discharge flow conditions. further performance improvements. These include choke-flow capabilities, and also efficiency at inducer tip relative Mach Representative attainable compressor stage performances in numbers (Mis) exceeding approximately 1.2. The significance of 1980 were generated in Ref I by using the impeller data combined M 1 s on centrifugal compressor characteristics, particularly surge, with an assumed maximum diffuser static pressure recovery of has been shown in References 5 and 6. It is a critical design 0.78. This provided the results presented in Figure 1. The general parameter influenced by selection of specific speed and inducer efficiency trends of Reference I are still valid to date, but do not hub diameter ratio. reflect further improvements which have taken place in the last decade. These include: These advances in the last decade have made it appropriate to review the major design parameters influencing the attainable efficiencies of single-stage centrifugal compressors. • Extensive work of NASA (Ref 2), and Casey (Ref 3) on the effect of Reynold's number. 2.0 AIRCRAFT GAS TURBINE APPLICATIONS The simplicity and reduced cost features of the single-stage • The use of impeller shroud bleed, which generally increases compressor are ideal assets for small gas turbine auxiliary power efficiency between one and two percent points, together units (APUs); small, expendable turbojets; and small turboprop, with the more important attribute of increased flow range. turboshaft engines. The most prevalent applications are in engines up to approximately 500-hp output. Larger power • Extension of Centrifugal Compressor Technology to higher engines in the 500-3000 hp range feature two-stage centrifugal pressure ratios and Mach numbers. compressors, or combined axial centrifugal compressors, in single— or two—spool arrangements. Extensive small gas turbine cycle optimization studies, using single—stage centrifugal compressors and single—stage radial inflow turbines, were presented in Reference 7, and indicated that:
• Optimum cycle SFC, and minimum cost/power occur at different specific speeds.
• The optimum compressor specific speed for minimum cost /A U and weight is approximately unity. Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT1991/78989/V001T01A025/2400405/v001t01a025-91-gt-077.pdf by guest on 30 September 2021 • Optimum compressor specific speed for minimum SFC is approximately 0.7. • Cycle pressure ratios above 7.0 show diminishing gains in SFC and reduced cost. The weight and cost contraints of small intermittent duty APUs and short duration expendable turbojets usually mandate the selection of Ns close to unity. Specific fuel consumption ( O /S A becomes more important in the design of longer duration small turboprops and turboshaft engines. In these cases, two axial turbine stages are typically selected, one to drive a higher pressure ratio (8.0) single—stage centrifugal compressor with a specific speed close to 0.7, and the second turbine stage to drive the propeller, or rotor. The three major avenues of single—stage centrifugal compressor technology for aircraft gas turbine applications are: i WO S AGE
• APUs and Expendable Turbojets (Specific speeds of approximately unity with moderate pressure ratios of 4.0 to 5 • Small Turboprop and Turboshaft Engines (Specific speeds of approximately 0.7, with pressure ratios up to 8.0 as constrained by structural limitations.) • High Pressure Spool or Second —Stage Compressors (Applications require moderate specific speeds and pressure ratios, with larger inducer hub diameter ratios.) igu e Ce i uga Com esso o Typical examples of such applications are shown in Figure 2. Ai c a A ica io s Note that in the first two applications, the consequence of high specific speed and moderate pressure ratio, or moderate specific speed and high pressure ratio can produce M1s levels greater that The shortfall of this approach was the need to define impeller tip 1.2. Efficient inducer design is critical in both applications. conditions in order to target the projected efficiency goal. Impeller tip vector conditions cannot be generated prior to 3.0 PERFORMANCE PARAMETERS engine cycle optimization, unless an iterative engine and component optimization technique is available. Targeting the The attainable total—to—static efficiency levels of single—stage initial compressor efficiency goal is normally accomplished by centrifugal compressors with ambient sea level (air) suction either scaling from an existing stage characteristic, or by use of conditions is largely dependent upon four parameters: inlet specific speed charts. Examples of these charts are shown in Reference 8. • Inlet Specific Speed N S • Impeller Tip Diameter D2 The two common forms for specific speed based on inlet stagnation conditions used in the gas turbine industry are: • Inducer Tip Relative Mach Number Mls C • Exit Mach Number M e NS Dimensional Specific Speed = (Had)314 (1) The importance of each of these four parameters is discussed in the following sections. C NS Non-Dimensional Specific Speed = ^Had)'14 (2) 3.1 Inlet Specific Speed As mentioned previously, Reference 1 presents extensive The non-dimensional form will be used in this paper to avoid conversion factors. research on the effect of specific speed on centrifugal compressor impeller efficiency. It's objective was to identify the role of the The importance of the specific speed efficiency relationship, impeller geometry in shaping the specific speed efficiency curve. and the design parameters selection that enables optimum
e o ma ce o e a ai e a o g e eak e icie cy ocus, a e e co es o i g a ia a ic e icie cy c(a was o ai e a amou ec o ogy o success u com e i i e esig s. om: E e wi is i o ma io , goo esig , ma u ac u i g, a es e e o me ac ice a e s i ecessa y o ac ie e eak e icie cy e e . e e o e, c oosi g s eci ic s ee "a io i" is -1] (3 o a u co i io a gua a ee o ma imum e o ma ce. c (A =[ ( y ] [ (p, ) e ese a i e im e e geome ies co e i g a wi e a ge o s eci ic s ee s a e s ow i igu e . A ow s eci ic s ee s, e h d t r n d r d r pr nt t v f rr nt
equi a e y au ic a ius o e assage is sma . is com esso s wi e o owi g ea u es: Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT1991/78989/V001T01A025/2400405/v001t01a025-91-gt-077.pdf by guest on 30 September 2021 eci i a es ig ic io a osses, w i e a ig s eci ic s ee s e l r r p rv t r pr p t t n r d l nd th • Sea e e S a a Suc io : e . 0 7 o e ia o s ou se a a io . A ic io a im e e • ig A ea a io i use s, wi e e e ce e i Mac mea s eam i e ow mo e was ese e i e e e ce , a com a e o e e ime a es a a o a wi e a ge o im e e um e : Me 0. geome ies. ese esu s we e a s a e i o cu e • Mi imum C ea a ces (a a a e coa i gs s a e o e a , ai c a y e, si g e s age ce i uga • I uce u Im e e i iame e : 0. com esso e icie cies o a ase i e ey o s um e o . 0 a a e igi i e e ow e sus o e a s age o y o ic • Su ge ma gi o a eas % e icie cy • i ackswee > 0 eg ees ( om a ia
S ECI IC S EE E SUS ASE I E O Y O IC E ICIE CY MA h,(p l = 0.88 = . x 0 Me = 0.1
0 0.2 0.4 0.6 0.8 .0 .2 .4 2.0 r M x 0.2 0.682 0.8 8 0. 8 .0 0. 82 0. 0. 2 0.
a+
1 S age S age E S age s= 51 s= 73 s =1 3 9 5- 3
igu e 3 Im e e Geome ies 3.2 Impeller Tip Diameter terms, the efficiency decrement due to high inducer shroud Within the limited range of typical aircraft gas turbine relative Mach numbers greater than unity may be represented by centrifugal compressors (ambient suction, and Ns = 0.7 to 1.2), impeller tip diameter reflects the relative Reynolds number. I 0 ?lc = A (M,, - 1.0) (8) I Larger diameter impellers exhibit higher efficiency levels and vice versa. When initially evaluating efficiency potential, it is Here the shock loss constant X is on the order of 0.10, for zero necessary to know the approximate impeller size. For a given shroud bleed. rotational speed pressure ratio and efficiency, the impeller tip It can be shown for typical inducer tip/impeller tip diameter diameter can be assessed using the following work factor Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT1991/78989/V001T01A025/2400405/v001t01a025-91-gt-077.pdf by guest on 30 September 2021 expression: ratios that the air angle resulting in minimum relative Mach number for zero prewhirl is approximately 60 degrees, which q gJCpAT (4) corresponds to an inlet flow coefficient of approximately 0.3. The U, constraints between minimum Mach number, and tolerable shroud curvatures necessitate a compromise in inlet design flow where U, = n D,N/720 (5) coefficient for higher specific speeds. This is represented by the expression: Impeller work factors for small gas turbine impellers are discussed in Reference 9 being basically dependent upon impeller discharge angle and diffusion factor. Typical values are: =0.2+0.iNs (9) Impeller Tip Blade Angle Degree: 60 40 20 0 Given the inlet flow total pressure and total temperature Work Factor: 0.65 0.72 0.86 0.88 conditions, it is possible to assign a corresponding inlet area using the above flow coefficient relationship. Further, by defining Dlh/D2, the inducer shroud diameter and relative Mach number The representative Reynolds number for centrifugal M1s, can be computed, assuming one dimensional flow compressors is defined in this correlation by: conditions.
U (6) These approximations permit an evaluation of an efficiency e decrement due to inducer tip relative Mach number operation greater than unity with state-of-the-art transonic inducer inlet The effect of Reynolds number on efficiency used in the blade designs. The approximations can be tailored to suit test correlation is: results by appropriate selection of the shock loss constant "k".
1.5x,o- )nl Combined axial-centrifugal compressor configurations, A7c _ 0 -rl) t _ ( 7 particularly high pressure ratio two spool arrangements, restrain e ( the aft centrifugal stage to relatively large Dlh/D2 diameter ratios as shown in Figure 2. This results in relatively small equivalent where the exponent n is on the order of 0.20 impeller passage hydraulic radii and high shroud curvatures, Although it is preferred to use a Reynolds number based upon normally deleterious to the attainment of high efficiency. impeller tip width, this parameter is not available in early engine Surprisingly good performance was obtained for a test case to be cycle analysis, without the previously mentioned determination of presented later. the impeller tip velocity triangle. 3.4 Exit Conditions 3.3 Inducer Tip Relative Mach Number The efficiencies of single-stage centrifugal compressors for Selection of inducer tip relative Mach number is probably the aircraft engine applications are commonly quoted based upon most important variable in advanced aircraft gas turbine engine inlet total-to-exit static pressure ratios. These contrast with axial applications, in that it influences both peak efficiency and flow compressors which are conventionally quoted on inlet range. Its effect has been mitigated to some degree by the use of total-to-exit total pressures. The difference between inducer shroud bleed described in References 10 and 11. Its use is total-to-total, and total-to-static efficiencies, becomes small purported to remove the low momentum fluid caused by shock with low exit Mach numbers, (Me). For example, 0.7% for Me = separation near the inducer throat shroud streamtube. It 0.1 and a pressure ratio of 4.0. It is not always feasible to diffuse to subsequently provides reduced blockage out at the impeller tip, such low exit Mach numbers, especially with very high specific with higher work capability. A myriad of shock-loss models have speed configurations and confined diffusion space. The pipe been generated. The most recent is described by Wennerstrom. diffuser and fishtail configuration described in Reference 13 Reference 12. Most models require detailed information relating permits diffuser area ratios up to 8.0 with low exit Mach numbers. to the inlet conditions, cascade geometry, etc., beyond the scope Dual cascade (radial and axial) diffusers (Figure 4) also attempt to of data available in the early design stages. In the most simplistic achieve high area ratios. esc i e com esso s esig e a es e y e au o . e o e sym o s esc i e com esso s om e o e sou ces. e ag eeme is ge e a y qui e acce a e a i g wi i a e o a o wo e icie cy oi s. o o e i o ma io was a ai a e e a i g o e e o ma ce o ig e i uce i Mac um e im e e s o e e e a i i y o e sim e s ock oss mo e . e e o e, a a i io a es case was i c u e o e esea c com esso s ow i ig. 6. is com esso a ai e a eak e icie cy o Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT1991/78989/V001T01A025/2400405/v001t01a025-91-gt-077.pdf by guest on 30 September 2021 8% wi a i uce M s o .42 a s eci ic s ee o 1
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6 I C ES 80 c ES 04 04 igu e a ia a A ia Casca e i use
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I , y e i i io , com esso e icie cy is quo e o c CA C 9 -os o a o s a ic co i io s, e e e icie cy o ig s eci ic s ee com esso s wi imi e i use a ea a ios ca e igu e 5 E icie cy Co e a io esu s co ec e om e ase i e Me 0. co i io y e a o ima e e essio :
t 1 = ( - (Me-o 1 11 + ( Me (1
I , o e am e, e e gi e e e o e co s ai s Me o 0. , e e equi a e ec ease i o a o s a ic e icie cy wou e o e o e o 4 e ce age oi s a a essu e a io o 4.0.
4.0 E icie cy Co e a io ; o es e accu acy o e sim i ie e icie cy e ic io ec ique, a su ey o e mos e icie si g e s age ce i uga com esso s i e o e i e a u e was co uc e . e im o a su ey a ame e s a e is e i a e . ese a e su o e y a ai a e e e e ces i e u ic omai esc i i g e esig ea u es a es e ai s. A esi a e o m o co e a i g a a is usi g i o ma io e a i g o a w o e ami y o im e e s 9 5- e com assi g a wi e a ge o s eci ic s ee s as esc i e i igu e esea c Com esso e e e ce , a oug a owe essu e a ios. .0 S eci ic S ee Cu es e esu s o e su ey a e s ow i igu e , w e e S eci ic s ee cu es we e ge e a e wi e i e o e ic e a es eak e icie cies (wi % su ge ma gi o u a i g e a a o e e e ce 8 ase u o ec o ogica g ea e a e o e agai s eac o e . e s a e sym o s a a ces i e as eca e. ese ma o a a ces a e ee : • Use of Computational Fluid Dynamics (CFD) design 15 I C IA programs q 7 A= 75 M e = 1 8
• Inducer shroud bleed and treatment - • Use of structural finite element programs to determine the 1 1 dynamic and thermal positions of the impeller, shroud and } 80 U ESSU E diffuser A IO .4 U • Adoption of abradable shroud coatings .6 Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT1991/78989/V001T01A025/2400405/v001t01a025-91-gt-077.pdf by guest on 30 September 2021 W 75 • Laser velocimeter experiments to corroborate the CFD U predictions a Computational results are plotted in Figures 7 and 8 for 0 impeller tip diameters of 15.0 and 6.0 inches. They are presented in terms of predicted adiabatic efficiency versus specific speed with pressure ratio and inducer Mach number M1 s as parameters. The effect of M1s at specific speeds beyond the optimum is 6 observed as an inflexion in the symmetry of curves, especially at 0.2 0.4 0.6 0.8 .0 .2 the higher pressure ratios. This is a direct consequence of the s IME SIO ESS simplistic shock loss model. igu e 7 E icie cy e sus S eci ic S ee The peak efficiency difference between the two sizes of 15 I c Im e e impeller is predicted to be three percentage points, dependent upon the choice of the Reynolds exponent. Inherent in the I C IA efficiency error band is test measurement uncertainty which q = 7 = 75 M e = 1 should not be more than ±0.5% point for compressors with 8 pressure ratios greater than 3.0 calibrated in current test facilities. Efficiencies at the higher pressure ratios are naturally sensitive to the feasibility of operating the impeller with minimum clearance 80 i to avoid excessive rubbing of the abradable shroud coating. 0 - W 0 .2 The three major operating regimes for aircraft engine type U ESSU E M" single-stage centrifugal compressors are superimposed in Figure W A IO 9. Probably the most challenging is the low frontal area U .4 expendable turbojet application, with Ns close to unity and a 1 pr r r t p t .0. r 8 nd t th t rr nt S state-of-the-art efficiencies of 76% are attainable with a 6.0 inch 0 diameter. However, impeller frontal area and cost limitations often necessitate exit Mach numbers higher than 0.3. This results in overall total-to-static efficiencies of less than 73%. The 6 . complete compressor exit dynamic head may not, however, be lost 0.2 0.4 0.6 0.8 .0 .2 or dumped, in turbojet configurations as dependent upon the s IME SIO ESS - particular design of combustor flow path, and fuel atomization technique. igu e E icie cy e sus S eci ic S ee I c Im e e During the typical aircraft engine design process, it is necessary to combine the major components, compressor, combustor, turbine shaft system, and accessories, into an integrated package. This is constrained by weight, volume, cost for specific design cases which impose geometric and and reliability/maintability considerations. Compromises to each manufacturing restrictions. component design are routine in striving for the optimized overall engine design. As mentioned previously, examples of 6.0 Discussion constrained designs are second- stage centrifugal compressors mandating larger hub diameters, and small turbojets imposing a Although the use of Reynolds number based upon impeller tip premium or diffuser radial extent. diameter simplified the efficiency correlation, it is widely recognized that a more representative Reynolds dimension is the Component manufacturing costs also impose design impeller tip blade height. This dimension is particularly relevant constraints to the blade form, fineness, and surface finish, both for for high pressure ratio stages. It would precipitate additional size numerically machined and cast parts (especially smaller size effects not reflected by use of the tip diameter. parts). Ref 10 cites a good example of the effect of blade thickness variations on a 10 lb/sec compressor. Inducer blade thickness is An alternative correlation was studied, using a tip height highly critical in reducing shock losses of high relative Mach based Reynolds number where the tip vector conditions were numbers. The efficiency levels shown in Figs. 7 and 8 represent approximated by the calculation procedure outlined in Appendix minimal restrained designs. Therefore, corrections are advisable . A ey o s e o e o 0. , wi a ase um e o .0 06 com o e i e a s ess co s ai s, e mi s a mo e e i e was ou o o i e a simi a a a ma c . e e ce io was a e o o e ma o e gi e esig isci i es. ig e essu e a ios w e e eak e icie cies a s age essu e a es o 8 a 0.0 we e u o 2 % oi s e ow e e e s s ow o igu es a 8. I wou a ea a use o e sim i ie oce u e cou o i e o imis ic e icie cy e e s a e e ESIG EQUI EME S ig e essu e a ios. Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT1991/78989/V001T01A025/2400405/v001t01a025-91-gt-077.pdf by guest on 30 September 2021 I C IA = 75 M e = 1 CYC E A A YSIS CO S A s 5
Mi 1 COM ESSO I I U I E U S C A s C A W U U U 75 U I- 1 CYC E A A YSIS A IA E I s ESSU E A IO 7 1Q S AGES ® U O O /S A E IMI A Y ESIG O U O E /A U IGU E 0. E GI E CYC E A A YSIS EC IQUE 1 1 s IME SIO ESS
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Im e e i ow A ea = W (A4) Q2 C (1- ockage
A E . CE I UGA COM ESSO E O MA CES ackswe , a e i use , Su ge Ma gi > %, A mos e ic Suc io , Mi i imum i C ea a ce
Mo e e h D2 k m b Me iic test Ns q M s iic ca c PP AO ASME 82 G . 0 . 4.0 8.0 . 2 .0 .0 68.2 0. 0 . 8 48 6 .6 ASME 8 G . 8 . 4.0 8.0 . 2. .02 8. 0. .64 . 6 8 .6 C . 4.0 8.0 . 4 . .0 8 . 0. .64 . 8 .6 . 4.0 8.0 . 6. .0 86.0 0. .6 .68 8 .2 E . 4.0 8.0 . 6 0. . 0 . . . . 8 8 .6 E2 . 4.0 8.0 .68 2. . 6. . . .82 8. 40 G ASME 0 G 8 .2 6. 64.6 4.8 .2 . 8 8.0 0. .6 .2 8.2 ESEA C .28 6.80 64. . 4.64 . 6 8. .02 .6 .42 6. 00 A AA 8 2 0 .2 . 6 0 .0 6.0 0. . 0 8. 0.64 . 4 .0 . 2A ASME E .2 . 2.0 .6 .4 . 2 8 . 0.6 . .0 80.4 o
ASA 0 AIAA 8 4 . 2 2.6 6. .6 . - .4 0. 0 . 6 .2 80. S
A iso C 0 AGA C 282 .2 . 48. 8.0 .2 - 82.0 0.66 . 4 . 8 .6
A iso 00 AIAA 82 20 .24 4.6 86.2 . 0.8 - 8.0 0. 8 . 8 0. 2 .
o s oyce ASME 8 G . . 4. .0 . <. 8 . 0.82 . 2 . 82.0 o s oyce ASME 8 G . 0 . 8 .4 .6 2.6 <. 8 .0 0. 4 . 0. 8 8 .2 o s oyce ASME 8 G .24 . 48. .0 .2 <. .0 0. .68 .20 8 .
Ko e SAE 820 28 .2 02 2 .8 2.6 4. .0 8 . 0. 6 .66 0. 84.4
S ou ee s = 75
10. References . o ge s, C., " e iew o Mi e ow a a ia u i e O io s," AIAA, 0 24 4, 0. . o ge s, C., "S eci ic S ee a E icie cy o Ce i uga Im e e s e o ma ce e ic io o Ce i uga um s a Com esso s," 8. ASME 2 Gas u i e Co e e ce, 80. a e, O.E., " u omac i es," . Wi ey, 8 .
2. Skoc , G. .,Moo e, . ., " wo 0 sec. Ce i uga Com esso s . o ge s, C., "Sma Ce i uga Com esso i ockage E ec s," wi i e e a e a S ou ick esses O e a i g o e a AIAA 8 2 0, 8 . a ge o ey o s um e s," AIAA 8 4S, 8 . 0. C a ma , C., "Mo e 2 0 C 0 C28 Com esso e e o me ," . Casey, M. ., " e E ec o ey o s um e o e E icie cy o AGA C 282, 80. Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT1991/78989/V001T01A025/2400405/v001t01a025-91-gt-077.pdf by guest on 30 September 2021 Ce i uga Com esso s," ASME 84 G 24 . . 4. Yos i aka, ., e ou eau, ., om so , . ., " e e e e ce is e , . ., "A ica io o Ma Wi E a ceme e ices o e ic io a e o ma ce emo s a io o a Ce i uga u oc a ge Com esso S ages," SAE 880 4, 88. Com esso o e M S U," ASME, IG I, 8 . 2. We e s om, A. ., u e aug , S. ., "A ee ime sio a Mo e . Se oo, Y., "E e ime a S u y o ow i Su e so ic Ce i uga o e e ic io o S ock osses i Com esso a e assages," Im e e ," ASME 8 G 2, 8. ASME a s o . 06 84.
6. o ge s, C., "Ce i uga Com esso I e Gui e a es o . Ke y, . . " e is o y a u u e o Ce i uga Com esso s i I c ease Su ge Ma gi ," ASME 0 G 8, 0. A ia io Gas u i es," SAE S 602, 84.
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