THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 89-GT-233 345 E. 47 St., Ne York, N.Y. 117 CS The Society shll not be responsible for sttements or opinions dvnced in ppers or in dis- Cussion t meetings of the Society or of its Divisions or Sections, or printed in its publictions. M Discussion is printed only if the pper is published in n ASME ournl. Ppers re vilble ]ri[ O from ASME for fifteen months fter the meeting. Printed in SA. Copyright 1989 by ASME Industril Centrifugl Compressors: The Influence of the Impeller Diffusion on the Stge Performnce KLAS LODTKE Mnger Aerodynmics Turbocompressors BORSIG GmbH, Berlin,.-Germny ABSTRACT The meridionl convergence of n unshrouded inducer type impeller ith 3 bckrd lening bldes s modified by reducing the exit idth by 22 %. The vneless diffuser s chnged ccordingly, heres the impeller eye opening s kept constnt. Performnce curves sho tht the loer diffusion leds to enhnced surge limit, loer hed t incresed efficiency. Choke point remins unchnged nd the extension of the rotting stll rnge is reduced. The rnge of tip speed Mchnumbers tested s.6 to 1.17. Test vlue nlysis, broken don into components, is bsed on the to-one model impeller exit evlution procedure detecting clerly the cuses of performnce mp chnges. NOMENCLATRE A net impeller exit re b 2impeller exit idth ( ss - ps)/av blde lod fctor Blod c bsolute velocity cu tcircumferectil velocity component cm 2meridionl velocity component c pspecific isobric het cpcity d 2impeller outer dimeter k-r h =RTot ^[( Pot) K?P-, pol. hed, totl-to-totl m mss flo M 1 inducer tip reltive Mchnumber M 2. = 2./ krt 2iidel reltive exit Mchnumber M 2. = 2j / krt 2. jet reltive exit Mchnumber MR 2 = M 1 /M 2jrel diffusion rtio MR 2i idel diffusion rtio = M1/M2i Mu g = u 2 / krt Ot tip speed Mchnumber N rottionl speed p Pressure R gs constnt Re Reynolds number s 2 impeller blde exit thickness T thermodynmic temperture T 2i idel (isentropic) sttic exit temperture T 2j jet sttic exit temperture u 2 impeller tip speed V volume flo red = V R T 1 /RT 1reduced volume flo V ot/v impeller volume rtio 2i idel (blde congruent) rel, exit velocity 2j jet reltive exit velocity number of impeller bldes h pred = hp (R T /RT ) reduced pol.hed R = 28%5 k/kgk reference gs constnt T 1 = 288.15 K reference suction temp. h specific enthlpy B1s - 13 inducer tip incidence ngle i l k = cp/cv specific het cpcity rtio L ork Presented t the Gs Turbine nd Aeroengine Congress nd Exposition une 4-8, 1989 Toronto, Ontrio, Cnd Donloded From: http://proceedings.smedigitlcollection.sme.org/pdfccess.shx?url=/dt/conferences/smep/8335/ on 7/15/218 Terms of se: http://.sme.org/bo
B mixed-out bs. flo ngle inducer tip flo ngle 13 Is inducer tip blde ngle f3 2j jet flo ngle mixed-out flo ngle f3 2 flo exit ngle 2s 13 A h e impeller blde exit ngle mixed-out rel. flo ngle specific enthlpy difference = A/A 2ke re rtio 9 dynmic viscosity 7 p polytropic efficiency (totl-to-totl ps polytropic efficiency (totl-to-sttic) A 2 mixed-out sirl prmeter = cu/cm = cu 2 /cm 2sirl prmeter u = cu /u 2mixed-out slip fctor density, rection 4V/ (11 d 2 2 u 2 ) inlet flo coefficient impeller exit flo coefficient 922 cm2/u2 mixed-out exit flo coefficient C = cm/u2 p = 2h p /u 2 2 pol. hed coefficient SBSCRIPTS N BEP SMP MDP SL opt mx ss ps AV ide stge (high b ), high diffusion impeller nrro stge (lo 6 2 ), lo diffusion impeller best efficiency point scroll mtching point mximum diffusion point surge limit stge optimum (= BEP) choke point blde suction side blde pressure side = ss + psblde verge ke j jet t totl Rotor impeller Sttor diffuser + scroll + conicl diffuser SR disk friction i idel; internl (gs ork) u circumferentil m meridionl o impeller inlet, gross 1 impeller inlet, net (incl. blde blockge) 2 impeller exit, net (incl. blde blockge) mixed-out, impeller exit, gross (infinitesiml fter impeller exit) 4 diffuser exit 7 exit flnge, fter conicl diffuser effects of the re rtio on the sttor, i.e. diffuser, return chnnel or scroll. So the designer of industril centrifugl compressors ho is expected to design complete stges from the suction to the dischrge nole still does not kno ll the nsers to questions like: Ho cn the operting rnge of stge be incresed nd ht re the pertining efficiency nd hed trdeoffs? Are there conventionl mens to mintin poer consumption nd pressure rtio for given impeller tip speed being dictted by stress limits hen enhncing the surge limit? If the impeller diffusion is reduced by nrroing the exit idth including the prllel lled diffuser idth: ht ctully hppens to the impeller nd diffuser efficiencies nd ht is the mechnism tht brings bout ider operting rnge? TEST CONFIGRATIONS To shed some light on these interreltions nd to come up ith prcticl solutions for the designer of industril stges tests ere conducted on vrious xil inlet overhung type unshrouded impellers equipped ith vneless prllel lled diffusers nd offset type volutes ith circulr crossections folloed by exit diffusers, see Fig. 1. Geometricl nd opertionl test dt see Fig. 2 nd tble A. The to impellers tested ll hve identicl blde surfces mde up of stright line elements, ith only the meridionl shpe being chnged. The flo chnnels ere 5-xis NC-milled from solid hub forging. The mteril is.5 % crbon, 13 % chrome nd 4 % nickel. Impeller N s directly derived from impeller by blde cut-bck. These stges re being extensively used for single stge ter vpor pplictions (so-clled mechnicl vpor recompression systems), for single nd multistge integrl ger compressors for ir nd industril gses nd lso, ith slightly higher hub-tip rtios, s first stges in single-shft multi-stge compressors for the chemicl industry to tke dvntge of the incresed flo nd hed potentils of these semi-open impellers compred to shrouded heels. L_1 r_ INTRODCTION Much hs been published during the lst 1 yers ith regrd to impeller diffusion, re rtio, blde loding nd velocity distribution, e.g. Miuki et l. (1974), Mishin nd Nishid (1983), Schumnn nd Clrk (1986). Most of these ppers hoever concentrted on the impeller itself ithout investigting the Fig. 1 Compressor crossection 2 Donloded From: http://proceedings.smedigitlcollection.sme.org/pdfccess.shx?url=/dt/conferences/smep/8335/ on 7/15/218 Terms of se: http://.sme.org/bo
1 b 1r STAGE bz STAGE N STRAIGHT LINE BLADE ELEMENTS Fig. 2 Schemtic stge geometry 3 Pcl 1-' Pst (b) u u I V 6 7718 9 Pstld) ^ 11 liltolinl`" 5 GP GP >P,]P (nl (g) Itl (e) it i' srdp Gi',^ T^xPt,;` I -_^^,^ i^^t, 2xTti^^I 1 Pst STATIC PRESSRE Pt TOTAL PRESSRE Tt TOTAL TEMPERATRE APDIFFERENTIAL PRESSRE Q PIEZZO QARTZ (SRGE DETECTION) MV MOTOR OPERATED VALVE Fig. 3 Test set-up 1 AXIAL INLET 2 IMPEER loth) 3 VANELESS DIFFSER 4 VOLTE 5 DISCHARGE NOZZLE 6 CARBON RING SEAL PI') 7 RADIAL BEARING 8 AXIAL BEARING 9 COPLING 1 GEAR BOX 11 ELECTRIC DC -MOTOR (),(b),(c) PRESSRE BETEEN HB DISK AND CASING (c )STATIC PRESSRE AT IMPEER EXIT (d),(e),(f),(g),(h) STATIC PRESSRE ALONG DIFFSER (i),(j),(k),(i),(m) STATIC PRESSRE ALONG SCRO AZIMTH OGAGE OTRANSMITTER I:IORIFICE 3 IMPEER/DIFFSER (IDE) N (NARRO) d2 IMPEER DIA. mm 355 355 b2 EXIT IDTH 175 13.6 d seye DIA. 196 196 dr, HB DIA 72.4 72.4 L LENGTH 79 79 CI CLEARANCE COLD.55.55 S BLADE THICKNESS TIP INLET 26 2.6 Z BLADE NMBER 18 18 P1 TIP INLET ANGLE o 33 33 P2S EXIT ANGLE 6 6 d4diffser O.D. mm 64 64 A5 VOLTE AREA mm2 15725 15725 L1 LENGTH CON. DIFFSER mm 75 75 DN S SCTION NOZZLE DIA " 25 25 DNd DISCH NOZZLE DIA. " 25 25 N ROT SPEED rpm 11 3 11 24 - i- 18 3 18 4 - "- 2 44 2 44 -"- 21 6 21 6 M2 TIP SPEED MACHN..614.69 -t^-.994.998 Tble A TEST SET-P AND MEASRING STATIONS 1.19 1.11 1.175 1.165 Test medium s tmospheric ir. An electric vrible speed DC-motor ith integrl ger s used s driver. Besides the flnge-to-flnge pressure nd temperture mesurements the flo rte s mesured in the suction nd the dischrge pipe. Three sttic pressure tps ere locted in the bck-plte opposite the hub disk (for thrust clcultion; the outer tp for impeller efficiency). Four ll pressure tps ere plced in the diffuser rer ll nd five sttic pressure tps ere oriented long the scroll imuth to check for circumferentilly even pressure distribution. The sttic pressure t the impeller exit s mesured t one loction only (see Fig. 3). This tp s plced t 18 from the scroll tongue to keep it y from the normlly uneven pressure dis tribution ner the tongue. Mesurements of the peripherl pressure distribution long the scroll revel tht the scroll mtching point flo coefficient, i.e. the operting point ith circumferentilly constnt sttic pressure, is beteen ero nd 18 %, i.e. n verge of 1 % greter thn the stge optimum flo coefficient. The excessive scroll re increses the sttic pressure tords the scroll exit hich in turn cuses someht uneven pressure distribution long the impeller outer perimeter for the stge optimum. Hoever, the scroll pressure distribution curves revel n lmost liner grdient so tht the pressure tp t 18 from the tongue is stisfctory mid-point loction beteen minimum nd mximum impeller exit pressure, hich serves ell to reltively compre the erodynmics of the to configurtions. The onset of surge s determined by pieo-qurt instlled in the compressor dischrge line. The het loss of the uninsulted rig s clculted to be pprox..5 %. Donloded From: http://proceedings.smedigitlcollection.sme.org/pdfccess.shx?url=/dt/conferences/smep/8335/ on 7/15/218 Terms of se: http://.sme.org/bo
TEST EVALATION PROCEDRE fr,'ernr.!r_rsr: Pot, rot, P7t,T7t, P2, m, N, R Assumptions: T2t1 i = I4tM = T7tj P2=P2u=P2u; rn /ri,=o.2 (,) primry one = isentropic Clcultion Totl pressure impeller exit: rn(h7t - ht)=rr, Lh =LufLsP ^ L u =rcu2 u2 (2) Cue= (^I1-h5 /u2 ; cm2 = t»rt2/p2a2 1/2 (3) A2=b( 7T_12 - s2/sin 13 2s), C2=(Cm2t"Cu2) (4) )2 /oh - hsr ) T = '2t I P / 2 cp - I cc2, 2cp (S) _I 1l2 / r r R lz 1 (h h\2 ' /2^4A2 + A 2A I A lp2a2/ 2Cp'B = t t 2 12p k (6) PPt - P2(T2t/T )' _' (7) Mi L, fc -+I,,., TEST RESLTS AND DISCSSION Overll results Fig. 4 shos on the bsis of reduced hed nd volume flo direct comprison of the to overll stge performnce mps. The stge ith the loer diffusion impeller (N) chieves ider opertionl rnge thru reduced rotting stll nd surge limits, higher pek efficiencies especilly t high Mchnumbers nd less efficiency drop for prt nd overlod opertion. Ho cn this globl result be nlied in detil? hpr- 1 4 [k/kgl ROTATING STA ^.^ } 9 STAGE N 8 7 6 = 5-4 m ^t4 2 STAGE SRGE h _ o.o /B^,td2Y 3 u d2 4 sr Re.2 1 2) Z 2m / Re= Z 2 (8) 1 Polytropic impeller efficiency u+ 1.5 2 2.5 t^ nlt Po) Dot)n LI /PRotor ) 9psRotor 1 (9) ^PRef CP ^ Tot CPR r t' l / r --- STAGE ^^^ STAGE.9 n'=ln Tot llf pt n"= (n Tt/Ln Pot p (o) N \ I M 2 L L totl - to-totl totl-to-sttic O.61 O 1. O 1.1 As 1.16 \ I Polytropic stge efficiency: '7P k1 In 7t t)totl-to-totl (u) [n (T7t/ot) 1.8 I- C) -i 1 I.5 1 1.5 2 2.5 3 RED. INLET VOLME FLO Vred [m 3/s] Polytropic sttor efficiency: sttor = vneless diffuser + volute + conicl diffuser ^p =hp /oh = (hprotor-^ ^ZZ 2 +hpsrotor-hp)]1h A (12) _ ^PPotor + ( hp-hpsrotor)/ -/](i E) (l3) =(off - c /2)/h u4) I Psttor = I - (gp Rotor -I 7P)/(i - S') (f 5) Clcultions, to-one model: ll relevnt formuls re given by pikse (1985). Fig. 4 Performnce mp comprison stges nd N Detiled results Comprisons of the to stges cn be crried out in different mnners. One y ould be to compre on the bsis of similr velocity tringles t the inlet nd exit, hich implies compring for constnt flo coefficients. Since especilly exit flo coefficients differ considerbly for both impellers this ould led to compre lo inlet flos for the nrro impeller ith high inlet flos for the ide impeller. The designer of these industril compressors hoever is normlly interested in either designing high-hed-stge for given tipspeed or iming t ide operting rnge. Since either trget cn be chieved ith only slightly differing stge efficiency, the designer of course nts to kno ho vrious erodynmic prmeters of the to stges compre for the best-efficiency-point (BEP) for the stge, hich in most cses is the contrctully 51 Donloded From: http://proceedings.smedigitlcollection.sme.org/pdfccess.shx?url=/dt/conferences/smep/8335/ on 7/15/218 Terms of se: http://.sme.org/bo
greed gurntee point. He is especilly interested in flo nd hed coefficients. Therefore it is thought to be meningful y to compre vrious prmeters for the BEP of the stge t the rnge of Mchnumbers tested. The folloing comprison nd nlysis therefore is solely relted to the stge-bep (Figs.5,6,7). 'P ROTOR'PSROTOR Q9 ^P Ref np Ref o Stge efficiency. The results re s follos: As s expected the nrro stge is better dpted to the high Mchnumbers: t M = 1.17 pol. stge efficiency is 1 1/2 points higher 2 thn for the ide stge (Fig. 6). Hoever stge N designed for high M ug does not hve its highest stge efficiency there: rip increses for decresing M so tht stge N is superior over lmost for the complete Mchnumber rnge tested. The brek-don into rotor nd sttor prt yields the folloing results: Impeller efficiency. For ll Mchnumbers tested impeller N loses 1 point totl-to-totl nd 2 points totl-to-sttic over impeller, the resons being: - The reltive jet Mchnumber M 2 is up to 17 % higher for N resulting in cor1siderbly higher friction losses in the heel exit region (Fig. 6). - Incidence ngles t the inducer inlet of impeller N re 2 higher thn of, cusing someht higher inlet losses (Fig. 6). - These to negtive effects re prtly offset by positive one: the ke re E is 1 to 17 % smller for impeller N leding to reduced mixing losses, hich in this flo model re ssigned to the impeller (Fig. 6). Loer diffusion mens loer blde loding (compre Figs. 8, 9), smller ke re, smller difference beteen flo ngle nd blde ngle, expressed by greter jet nd greter mixed-out reltive flo exit ngles. ' 12 1. ^-' 1]8 11 1.14 P 1.12- -- -- STAGE ---E-_ STAGE N lit i^ -^ Z N 1 M R, O.7 6r A4 7 8.9 1. 11 TIP SPEED MACHNMBER Mu g Fig. 5 Stge best-efficiency-point comprison stges nd N The lck of efficient diffusion of impeller N leds to too lo sttic pressure levels in the impeller resulting in loer impeller efficiency. Similr findings for vrious impeller convergence vritions re reported by Schumnn nd Clrk (1986). Another mens of ssessing n impeller performnce is the diffusion rtio chrt, Figs. 1 nd 11. This plot compres on reltive Mchnumber bsis ctul jet flo diffusion to the idel diffusion hich is keless nd blde congruent. S Q ^P Ref L u_ cc n cc F- _ u/ --- -- T ^^_ V.7 T 71P STATORv\ ^P Ref --)--- STAGE o --4 STAGE N ^^ 3.3+ 55 /32 Z O 4 ' I cc M 4 iii----i +--- + 1 F.7.8.9 1. 1.1 TIP SPEED MACHNMBER Mu g Fig. 6 Stge best-efficiency-point comprison stges nd N The higher the chieved diffusion MR t given idel diffusion MR the better the impeller ficiency. ef The reference bnd (s published by pikse nd Osborne (1986)) represents the stte-of-the-rt, i.e. the region of the highest diffusion nd efficiency levels ttined so fr. ith regrd to diffusion, impellers cn be ssessed s follos: - Mximum diffusion points (MDP) re best efficiency points (BEP) of the impeller. For these prticulr Donloded From: http://proceedings.smedigitlcollection.sme.org/pdfccess.shx?url=/dt/conferences/smep/8335/ on 7/15/218 Terms of se: http://.sme.org/bo
8 O MR2 34 off' 3: Q3 F.24 ^ 1.5 ---_ STAGE ~ ---D- STAGE N -.pl 1.4 Q CREARE X1.2+ REF.BAND Di r C-) 1 Q.8 f yy' STAGE BEP STAGE Mug O.61 O TO Di 11 O 1.16 1.2 Vot/V i[a MR2 F2.8+ _ 24.^ 1 X 2 4 + vii 2+-i i.7.8.9 1 11 TIP SPEED MACH NMBER Mu 2 Fig. 7 Stge best-efficiency-point comprison 1. II! V =274 m3/s ^.9 Mug =1 11 N =2418 rpm.8 C 31E SHROD.7 + HB X MID. SECTION.6 N 5 Impeller blde loding, Q4 stge.3 Fi g. 8.2 of co 1 = 2.7 m3/s 9 = 1.11 _,8 = 2431rpm 4 SHROD 7 HB o MIDSECTION ij.6 Cr D u).5.4 Q Di.3 Di.2.si INPA Impeller blde CREARE ol.2t REF,BAND Di 1 loding, stge N stge, sttor nd rotor efficiencies vs. the mixed-out irl prmeter stge shos tht the stge...1.2.3.4.5.6.7.8.9 To 72 REL BLADE COORDINATE Sre i Fig. 9 6 f \ STAGE BEP 1.5 2 2.5 3.5 IDEAL MACHNMBER RATIO MR 2 i Fig. 1, 11 Impeller diffusion rtio STAGE N M u2 O.61 O 1 O 1.1 116 configurtions they re identicl ith the surge points of the stge (solid points in Fig. 1, 11 ). Mximum diffusion for impeller (: 1.6) is higher thn for impeller N (,^ 1.4) thus explining the higher efficiency for impeller. Lines of best efficiency points for the stge (stge optimum) sho mximum diffusion of 1.35 for nd of 1.15 for N (Fig 1,11 nd 6). Here e hve nother indiction hy impeller is more efficient in the stge optimum thn N. The MDP' s of both stges ccur t round 1. tip speed Mchnumber suggesting tht for the stge optimum both impellers hve their highest efficiency t round this Mchnumber, s cn be seen in Fig. 6. Diffuser efficiency. The reson hy the stge efficiency of stge N is superior to stge inspite of ll these impeller shortcomings must be ttributed to the sttor (i.e. diffuser plus scroll). According to Fig. 6 the sttor efficiency of stge N gins beteen 3.5 nd 8 points over stge. Fig. 12, displying optimum does not 2coincide t ll ith the sttor optimum: Donloded From: http://proceedings.smedigitlcollection.sme.org/pdfccess.shx?url=/dt/conferences/smep/8335/ on 7/15/218 Terms of se: http://.sme.org/bo
1. 71 P ROTOR np Ref.9 I- Of O 7Z P STA 71 P Ref cc TI P } _ - T T PRef.8 6.5.8 TR.7.6 STAT R BEP.5.4.8 STAGE BEP Q 7 STAGE BEP 6 5 C M2 STAGE 4 O 61 O 1. 3 11= ^PROTOR O 1.16 ^P Ref mx S LID PTS+ SRGE 1 2 3 4 5 SIRL PARAMETER 3' p ip P^Ref^.9 Li 8 cc 7 o'.6.5.8t PSTATOR 'f P Ref..7 Cr 6 F-.5.4.9t r; OE - u_ E CD X.4 R.3 STATOR BEP STAGE BEP Mu g STAGE BEP O.61 STAGE N G 1. O 1.1 ^p A 116 7 (PRef 7ZP R OTOR mx S LID PTS: SRGE 2 3 4 5 SIRL PARAMETER 2' Fig. 13 Polytropic efficiencies, stge N Fig. 12 Polytropic efficiencies, stge t = 3.1 for the stge nd /l opt = 1.7 for 2 the st?rr (verge vlues). By nrroing impeller exit nd diffuser idth the impeller sirl prmeter is reduced by 3 % pproximtely due to meridionl velocity increse. This shifts the rotor efficiency curves including choke points to smller 71 2 A-vlues, compre Fig. 12, 13. The loss mechnism of the diffuser rects differently: the sttor efficiency curves shift to only 1 % smller A -vlues compre Figs. 12 b, 13 b. The chnge of the impeller- by 3 % nd of 7 the sttor- by 1 % of course mens tht the summtion of rotor nd sttor efficiencies cc. to formul (15) cuse the reduction of the optimum stge- 2A,1 from 3.1 (verge) of stge to 2.3 of stge N. Thus for N t the stge optimum the sttor opertes very close to its on BEP. Although the impeller optimum ( = 3.5 to 4.5 pproximtely) is fr y from the sttor optimum (see Figs. 12, 13) it is less pronounced mximum ith the impeller efficiency being constnt for very ide sirl prmeter rnge The ide stge sees lrge devition beteen stge nd sttor optimum The differing loctions of stge nd diffuser optim sem to hold the potentil for n improvement of the overll efficiency in cse the diffuser BEP could be shifted to higher sirl prmeters. One could superficilly dr the conclusion to pinch the diffuser to chieve better mtching. Shifting hoever ould be ccompnied by reduction of the mximum sttor efficiency level thru higher bsolute velocity in the diffuser, leding to incresed friction nd lso higher dumping losses in the scroll due to higher meridionl velocity dissiption. The effects of vrious degrees of diffuser pinching ere reported erlier by the uthor (1983): in ll cses pinching yielded loer stge efficiencies t incresed stbility. So there seems to be hrdly ny y to void impeller/diffuser mismtching by vrying the meridionl shpe of the vneless diffuser. In the nrro stge N the reduction of the impeller efficiency is more thn compensted for by the sttor so tht stge nd sttor optimum re plced closer together. Hed coefficient. The penlty for the ider operting rnge of the lo diffusion impeller consists in reduction of the hed coefficient of 4% (verge), 7 Donloded From: http://proceedings.smedigitlcollection.sme.org/pdfccess.shx?url=/dt/conferences/smep/8335/ on 7/15/218 Terms of se: http://.sme.org/bo
C) _ N Co O or. L.L H X I ti I3 I L 4 SIRL PARAMETER -&ZH It u_ Q - CD C 6 C-) 3 - - I- >< Flo coefficient. As cn be seen on Fig. 7 the inlet flo coefficient c2 of configurtion N is for the most prt beteen ero nd 1 % loer thn of stge. This mens tht pplying lo diffusion impeller for given mss flo ould require incresing the meridios kp 12 1.1 1., 9 c STAGE BEP 8 STAGE N 7 Mug O.61 6 1 11 5 1.16 8 7 6 b l 6 5 ` 4 ^p.6.5.4.3.2 1 1 2 3 4 5 SIRL PARAMETER, & Q d Fig. 14 Pol. hed nd flo coefficient, flo ngles, slip-vlues, stge see Fig. 5. This mens tip speed ould hve to be incresed by 2 % in order to rech the required polytropic hed for the given specified dt. This in turn mens 4 % higher impeller stress. In the mjority of pplictions one cn live ith these disdvntges. But in cses of impeller stress limits lredy being reched the high diffusion stge ith the smller operting rnge hs to be selected. As cn be deduced from Fig. 5 the polytropic hed coefficient cn directly be correlted to the diffusion rtio MR 2 : for every percent of hed coefficient increse the diffusion rtio must be rised by three percent. Fig. 15 Pol. hed nd flo coefficient, flo ngles, slip-vlues, stge N nl idth of the impeller inlet nd exit nd of the diffuser by certin common percentge. Other chrcteristic curves for the to stges re given in Figs. 14 nd 15. Surge limit. Fig. 16 shos comprison of the operting rnges of both configurtions in the form of surge flo over stge BEP flo VS L/Vo t nd surge flo over choke flo V SL/V The st rge limit improvements of stge N re i5 >, 5 nd 4 percentge points for Mchnumbers.6, 1., 1.1 nd 1.17 respectively. This cn be highly dvntgeous to cope ith specifictions tht require stringent prtlod opertion. Some surge prmeters re s follos (see lso Fig. 16): 8 Donloded From: http://proceedings.smedigitlcollection.sme.org/pdfccess.shx?url=/dt/conferences/smep/8335/ on 7/15/218 Terms of se: http://.sme.org/bo
u.5 ^ 14 12 u_ ui - F- L r Ln VSO/ Vop + ^j ^ ----E_ ^ -- STAGE ---- STAGE N TIP SPEED MACHNMBER Mug Fig. 16 Surge prmeters stges nd N Stge M.61.99 1.11 1.17 V u2 /V.37.6.67.7 S L mx. 4.69 4.12 4.46 ( 12.1 13.6 12.6 -.83.788.82 - µ Stge N M.61 1. 1.11 1.17.2.51.62.65 SL mx. 7^ 5.6 3.65 3.48 3.77 1.1 15.3 16. 14.8 }l 2ti1.83.781.784.795 The impeller slip seems to correlte best the onset of surge. The surge limits of both configurtions for ll Mchnumbers tested fll into the nrro bnd of =.79 + 1.5 %. It is ssumed tht for proper surge line correltion t lest the folloing prmeters hve to be tken into considertion: flo profile shpe, diffuser inlet blockge, circumferentilly uneven pressure, distribution imposed by the scroll nd pipe volume donstrem of the compressor up to the throttle vlve. SMMARY High-hed-stges or ide-operting-rnge-stges re bsic options for the design of industril compressors depending on the requirements of the speci fiction. These lterntives cn be controlled to certin extent by vrying the impeller diffusion thru chnging the meridionl shpe of the impeller long ith the diffuser, ithout hving to give up the selected impeller blde bck-seep or the vneless prllel lled diffuser configurtion. The tests conducted revel improved surge limit, someht higher stge pek efficiencies but lso loer hed nd fle coefficients for the lo-diffusion impeller. These results re nlysed by mens of the to-one impeller exit evlution method tht mkes possible brekdon into rotor nd sttor efficiencies by utiliing mesured sttic pressure t the impeller exit. The consequences of loer diffusion re: loer impeller but higher sttor efficiency thru better mtching of rotor nd sttor efficiency curves. There is evidence of groing mismtch beteen the rotor nd the sttor ith incresing diffusion, hich cn obviously not be remedied by chnging the meridionl diffuser geometry. From severl possibilities to ssess both stges the one s chosen tht compres vrious erodynmic vlues t the respective best-efficiency-point of the stge in order to sho the necessry prmeters to design n optimum stge either for high hed or ide operting rnge. The described tests nd results re certinly not generlly vlid since they re limited to certin configurtion nd specil operting conditions. But one of the purposes of this pper besides interpreting the effects of certin geometricl chnges is to sho the effectiveness nd perspectives of the pplied nlyticl method tht reches beyond the scope of these investigtions. Bcked up by limited number of conventionl mesurements the method cn serve s mens to crete verstile loss model for vrious compressor components s prerequisite for high prediction ccurcy. ACKNOLEDGEMENTS The uthor ishes to thnk BORSIG GmbH for permission to publish this ork. He lso pprecites the help of his collegue Dr. Dieter Beinecke ho contributed vluble discussions nd ho s responsible for updting nd supplementing the compny's test evlution computer progrms. REFERENCES pikse D.: "Assessment of single- nd to-one modeling of centrifugl compressors studies in component performnce: Prt 3", ASME-Pper No. 85-GT-73 pikse D. nd Osborne C. : "Optimition of industril centrifugl compressors Prt 6 B". ASME-Pper No. 86-GT-222 Ludtke K.: "Aerodynmic tests on centrifugl process compressors - the influence of the vneless diffusor shpe", Trns. ASME ournl of Eng. for poer 1983 nd ASME-Pper No. 83-GT-87 Mishin H. nd Nishid H.: "Effect of reltive velocity distribution on efficiency nd exit flo of centrifugl impellers", ASME-Pper No. 83-GT-74 Miuki S. et l: "Investigtion concerning the blde loding of centrifugl impellers", ASME Pper No. 74-CT-1 43 Schumnn L.F. nd Clrk D.A.: "Effect of re rtio on the performnce of 5.5:1 pressure rtio centrifugl impeller", ASME-Pper No. 86-GT-33 9 Donloded From: http://proceedings.smedigitlcollection.sme.org/pdfccess.shx?url=/dt/conferences/smep/8335/ on 7/15/218 Terms of se: http://.sme.org/bo