ADARSHA H G. EDUSAT PROGRAMME 15 Turbomachines (Unit 3) Axial flow compressors and pumps

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1 EDSA PROGRAMME 5 urbmacines (nit 3) Axial flw cmressrs and ums Axial flw cmressrs and ums are wer absrbing turbmacines. ese macines absrb external wer and tereby increase te entaly f te flwing fluid. Axial flw turbmacines use large quantity f fluid cmared t mixed and centrifugal tye f turbmacines. Hwever, te ressure rise er stage is lwer in case f axial flw turbmacines tan mixed and centrifugal flw turbmacines. Axial flw cmressrs are used in aircraft engines, stand alne wer generatin units, marine engines etc. Design f axial flw cmressrs is mre critical tan te design f turbines (wer generating turbmacines). e reasn is tat, in cmressrs te flw mves in te directin f increasing ressure (adverse ressure gradient). If te flw is ressurized by sulying mre wer, te bundary layers attaced t te blades and casing get detaced and reverse flw starts wic leads t flw instability leading t ssible failure f te macine. Hwever, in turbines te fluid mves in te decreasing ressure (favurable ressure gradient). transfer a given amunt f energy mre number f stages are required in cmressrs tan in turbines. Generally, te fluid turning angles are limited t 0 in cmressrs and is 50 t 65 in case f turbines. us te ressure rise er stage is limited in case f cmressrs. Fluid flws in directin f increasing ressure, tis increases te density f te fluid, tus te eigt f te blade decreases frm te entrance t te exit. Axial flw cmressrs ave inlet guide vanes at te entrance and diffuser at te exit. Figure sws te flw trug te cmressr and fig. sws te crresnding inlet and exit velcity triangles. Generally fr a cmressr te angles are defined wit resect t axial directin (knwn as air angles). It can be seen tat te fluid turning angle is lw in case f cmressrs. Figure 3 sws te flw trug te turbine blade and fig. 4 te crresnding inlet and exit velcity triangles fr a turbine.

2 Fig. Flw acrss a cmressr blade Fig. Inlet and exit velcity triangles

3 Fig. 3 Flw acrss a turbine blade Fig. 4 Inlet and exit velcity triangles fr turbine

4 Exressin fr degree f reactin fr axial flw cmressr Degree f reactin is definedd as a measure f static entaly rise tatt ccurs in te rtr exressed as a ercentage f te ttal static entaly acrss te rtr. Assumtins: Static R Static. e analysis is fr -dimensinal flw. e flw is assumed t take lace at a mean blade eigt were blade erieral velcities at inlet and utlet are same and tere is n flw in te radial directin 3. It is cmmn t exress blade angles w.r.t. axial directin in case f axial flw cmressr (air angles) 4. Axial velcity is assumed t remain cnstant Figure sws te inlet and exit velcity triangles fr axial flw cmressrs. ( u tan tan (tan tan )- - a a 0 a 0 a(tan tan 3 ) entaly rise in rtr entaly rise in stage ) u 3 tan tan tan tan0 3 4 R r ( 0 r 0 5 )

5 0 u r r r a a r tan a ( a a (tan tan tan (tan and Substituting eq. 6 and 7 in eq.5 R 0 0 a a 3 u 3 ) u tan tan a (tan tan (tan tan 0 a tan ) 7 ) ) tan tan tan 3 tan0 ) 6 a 3 0 a (tan tan R (tan tan a a(tan tan ) R 8 a R (ctβ ctβ ) 9 a R ( ) tanβ tanβ a tanβ tanβ R ( tanβ tanβ ) ) 0 ) 0 4

6 ( ) ( ( WD E R r r r ) ) ( ) r r r

7

8 Prblem In a mixed flw um abslute fluid velcity at te inlet is axial and equal t radial velcity at te exit. Inlet ub diameter is 80 mm and imeller ti diameter is 50 mm. Pum seed is 3000 rm. Find te degree f reactin and te energy inut t te fluid, if te relative velcity at te exit equals te inlet tangential blade seed.e fluid leaves te rtr in te radial directin Given: a rd ; D 80 mm, D 50 mm, N3000 rm, R?, WD?, r e next ste is t draw te velcity triangles r.57m/s;.57m/s; rd E WD - R R 0.5 Prblem u ( ) KJ/kg ( E r r r 4.3m/s 7.78m/s r ) e ttal wer inut at a stage in an axial flw cmressr wit symmetric inlet and utlet velcity triangles (R0.5) is 7.85 kj/kg f air flw. If te blade seed is 80m/s trugut te rtr, draw te velcity triangles and cmute te rtr blade angles. D yu recmmend te use f suc cmressr?. Assume te axial velcity cmnent t be 0m/s.

9 Given: Symmetric velcity triangles wit R 0.5; P 7.85 kj/kg f air flw; 80m/s; a0m/s; β? and β?; D yu recmmend suc cmressr? Draw te velcity triangles. Since te R0.5 and velcity triangles are symmetrical αβ; αβ; r and r WD ( u 54.7m/s X.64 Prblem 3 u X β β tan tan β β ) 7850kJ/Kg u ; X ( u )/ e axial cmnent f air velcity at te exit f te nzzle f an axial flw reactin stage is 80m/s, te nzzle inclinatin t te directin f rtatin is 7. Find te rtr blades angles if te degree f reactin is 50% and te blade seed is 80m/s. Als, fr te same blade seed, axial velcity and nzzle angle find degree f reactin, if te abslute velcity at te rtr utlet suld be axial and equal t axial velcity at te inlet. Given: ) a80m/s, α 7, R 50%, 80m/s, β?, β? ) 80m/s, a80m/s, α7, R?, if aa Sl: ) R 50%, r, r, αβ and αβ Inlet velcity triangle is swn in te figure

10 sinα csα β α β r R tan β 80; 73.6m/s β m/s Frm te exit velcity triangles 45, m/s r 80 r ( ) ( 54.55m/s r r m/s 80m/s r ) urbines- tilizatin factr.tilizatin factr is defined nly fr PGM- urbines.adiabatic efficiency is te quantity f interest in turbines 3.Overall efficiency is rduct f adiabatic efficiency and mecanical efficiency 4.Mecanical efficiency f majrity f M s is nearly 00% 5.erefre, verall efficiency is almst equal t adiabatic efficiency 6. Hwever, adiabatic efficiency is rduct f utilizatin factr (diagram efficiency) and efficiency assciated wit varius lsses. 7.tilizatin factr deals wit wat is maximum energy tat can be btained frm a turbine witut cnsidering te lsses in te turbine 8.tilizatin factr is te rati f ideal wrk utut t te energy available fr cnversin t wrk 9.nder ideal cnditins it suld be ssible t utilize all te K.E. at inlet and increase te K.E.. due t reactin effect

11 0. e ideal energy available fr cnversin int wrk.e wrk utut given by Euler s urbine Equatin is. tilizatin factr is given by. tilizatin factr fr mdern M s is between 90% t 95% Relatin between utilizatin factr and degree f reactin tilizatin factr is given by e degree f reactin is given by Substituting te value f X in te exressin fr utilizatin factr and simlifying ( ) ( ) [ ] w r r a ( ) ( ) ( ) [ ] ( ) ( ) ( ) [ ] ( ) ( ) [ ] r r r r a r r w w ε w ( ) ( ) ( ) [ ] ( ) ( ) [ ] r r r r a w w ε ( ) ( ) ( ) ( ) ( ) ( ) ( ) E R r r r r r r ( ) ( ) ( ) ( ) R R X X X R X r r ( ) ( ) R ε

12 e abve equatin is valid fr single rtr under te cnditins were Euler s turbine equatins are valid. e abve equatin is invalid wen R. e abve equatin is valid in te fllwing range f R 0 R < tilizatin factr is given by ε Maximum tilizatin factr tilizatin factr maximum if te exit abslute velcity is minimum. is is ssible wen te exit abslute velcity is in axial directin Maximum utilizatin factr is given by ε ε ε m m m ( ( R sinα cs α Rsin α cs α Rsin α ) ) R sin sin α α ε wen α m 0

13 Maximum tilizatin factr fr imulse turbine Fr an imulse turbine R 0, tus m Frm te velcity triangles OAB and OBD are similar. us AB, csα csα Seed α is made as small as ssible(5-0 ) Maximum tilizatin factr fr 50% reactin turbines 50% reactin turbines ave r, r, αβ and α β and fr maximum utilizatin must be in axial directin. e crresnding velcity triangles are ε m R 0.5, Als, cs α Rsin α ε csα csα m cs α 0.5sin φ seed Rati φ α rati ε cs α

14 Cmarisn between Imulse and 50% reactin turbine at maximum utilizatin A) Wen bt ave same blade seed Let I and R be te blade seeds f imulse and 50% reactin turbines. e velcity triangles fr maximum utilizatin are E Frm E Fr E But E I I R R 50% velcity R I u R u u reactin R triangle turbine Cmaring eq. and, it is clear tat imulse turbine transfers twice te amunt f energy er unit mass tan 50% reactin turbine fr te same blade seed wen utilizatin is maximum. Hwever, 50% reactin turbines are mre efficient tan imulse turbines. But 50% reactin turbines transfer alf te energy cmared t imulse turbines. If nly 50% reactin turbines are used mre stages are required r if nly imulse turbines are used stages are less but efficiency is lw. In steam turbines were large ressure rati is available it is cmmn t use ne r tw imulse stages fllwed by reactin stages. u I

15 Cmarisn between Imulse and 50% reactin turbine at maximum utilizatin b) Wen bt ave same energy transfer E R R R E c) Wen and α are same in bt M s Seed rati fr imulse and 50% reactin stage fr maximum utilizatin I I R I R Prblem I φ I I csα φ csα I 6.44 I 3 ; ; R I csα csα I 4 5 Find an exressin fr te utilizatin factr fr an axial flw imulse turbine stage wic as equiangular rtrr blades, in terms fixed inlet blade angle and seed rati ф. Given: Equiangular rtr blades ββ, axial flw turbine, Imulse turbine R 0, rr, find exressin fr utilizatin factr in terms f α and ф. Frm te velcity triangles r r r r csβ ( ) cs 80 β

16 4rcsβ ( csα ) 4 ε ε ε 4φ R (csα ( 4 csα φ) were, φ Prblem Fr a 50% degree f reactin axial flw turbmacine, te inlet fluid velcity is 30m/s; utlet angle f inlet guide blade 30 ; inlet rtr angle 60 and te utlet rtr angle is 5. Find te utilizatin factr, axial trust and te wer utut/unit mass flw. Given: R50%; 30m/s; α30 ; β60 ; β5 ε?; Fax?; P? Altug R 50%, α β; as a a Inlet and exit velcity triangles are drawn a r sinα a sinβ csα R r r r 5m/s 3.8m/s r r ( ) ( r r r m/s csβ r r r r 3.8m/s 3.8 r r ) csβ )

17 R ε 6.36m/s r ( ) ( ) s kg N 6.8 m F sinβ Sinα m F m rust Axial ax r a a ax a a & & & ( ) ( ) 37KJ/kg/s m P 78.9m/s csβ 99.98m/s csα m P r u u u u & &

18 NI 4 ermdynamics f fluid Snic velcity and Mac number.snic velcity is te seed f ragatin f ressure wave in a medium..e seed f sund in a fluid at a lcal temerature fr isentric flw is given by were is te rati f secific eats.4, R is caracteristics gas cnstant 87 J/kg K and is te lcal temerature in kelvins. At 5 te seed f sund is 340 m/s. c R 3.As altitude increases temerature decreases and seed f sund decreases. 4.Mac Number is defined as te rati f lcal velcity f fluid t te snic velcity f sund in tat fluid M c R 5. Many turbines and cmressrs exerience ig Mac numbers 6.Hig Mac numbers give rise t sme secial rblems suc as sck waves wic leads t irreversibility and cause lss in stagnatin ressure and increase in entry 7.sing cntinuity equatin, Euler s equatin and isentric equatin fllwing tw equatins are derived d d M da d M A M 8.e abve equatins decide te variatins in velcity, ressure and area fr different Mac numbers 9.e tree basic classificatins are a) Subsnic flw M< b) Snic flw M c) Suersnic flw M>

19 Classificatin fluid flw based n Mac number a) Subsnic flw (M<) : Nzzle wen d da is negative A is negative area decreases and velcity increases Diffuser d wen is increases da A sitive area increases and velcity decreases is d d M da d M A M

20 b) Suersnic flw (M>) : Divergent nzzle wen area d is negative increases and velcity increases Cnvergent Diffuser wen area d is sitive da A da A sitive decrease and velcity decreases is is negative d da A d M d M M

21 da A area C) Snic flw (M) : is is zer cnstant and velcity is snic d da A d M d M M At te trat rtin f te cnvergent divergent nzzle te velcity is snic. Static and Stagnatin states urbmacines invlve te use f cmressible and incmressible fluids. In cmressible M s fluid mve wit velcities mre tan Mac ne at many lcatins. In incmressible M s te fluid velcities are generally lw, wever, K.E. and P.E. f te mving fluid are very large and cannt be neglected frmulate equatins based n actual state f te fluid based n laws f termdynamics tw states are used. e states are static state and stagnatin states. Static State If te measuring instrument is static wit resect t te fluid, te measured quantity is knwn as static rerty. e measured static rerty culd be ressure, velcity temerature, entaly etc.,. e state f te article fixed by a set f static rerties is called static state. Stagnatin State It is defined as te terminal state f a fictitius, isentric wrk-free and steady flw rcess during wic te final macrscic P.E. and K.E. f te fluid article are reduced t zer. Real rcess des nt lead t stagnatin state because n real rcess is isentric. Stagnatin rerty canges rvide ideal value against wic te real macine erfrmance can be cmared. It is ssible t btain stagnatin rerties in terms f static rerties by using te definitin f stagnatin state. Cnsider te steady flw rcess given by te first law f termdynamics.

22 i q gz i w i q w ke e gz Static state is te initial state in a fictitius isentric wrk free, steady flw rcess and te stagnatin state is te terminal state in wic te ke and e are reduced t zer, ne can define a stagnatin state at te initial static state. q 0; q w ke w 0; ke 0; e e In te abve eq. subscrit reresents stagnatin state and subscrit i reresents initial static state If subscrit i is remved frm te initial static state us stagnatin state as been exressed as te sum f tree static rerties. Since te rcess is isentric, te final entry is same as initial entaly. Final entry is stagnatin and initial entry is static. Any tw indeendent rerties at a secific state is sufficient t fix te state f simle cmressible substance by using termdynamic relatins. a) Incmressible Fluid: (Density is cnstant) d vd d 0; ( ke e ) i i i ( ke e) ds 0 s s ds d vd but ρ d because s s Final state is stagnatin wit subscrit and initial state is Static witut subscrit i

23 ρ( gz) us stagnatin ressure f an incmressible fluid is exressed in terms f static ressure, velcity and eigt abve a datum line. d 0; us using termdynamic relatins stagnatin ressure, Stagnatin ressure, stagnatin temerature and stagnatin internal energy are fund. Prblem ρ ρ ds 0 dv 0 Als, ρ ( ) ( ) ( ke e ) ds du dv as du dv du 0; s ρ cnstant u du C s u v d Liquid water at standard density flws at a temerature f 0, a static ressure f 0 bar and a velcity f 0m/s. Find te ttal ressure and ttal temerature f te water. Given: 0, 0 bar and 0m/s,? and P?, Water is incmressible wit ρ 000 kg/m3 ρ( gz) bar 0 5

24 Prblem A turbmacine andling liquid water is lcated 8m abve te sum level and delivers te liquid t a tank lcated 5m abve te um. e water velcities in te inlet and utlet ies are m/s and 4m/s resectively. Find te wer required t drive te um if it delivers 00 kg/min f water. Given: z8m; z5m; m/s; 4m/s; mass flw rate00 kg/min Find te Pwer P? b) Perfect gas w q w ρ ρ 4 w wrk n um 3.6 J/kg Pwer P mw & 386 W c c eliminating c c v R and c c v c v R g ( 8) ( z z ) 3.6 J/kg

25 Substituting te value f c in te abve equatin and simlifying Efficiencies f urbmacines Efficiency f a turbmacine is given by ( ) M ( ) ( ) M v v M v v v v v v a m m a m a 00% almst are efficiency mecanical efficiency; adiabatic were,

26 e adiabatic efficiency f a M can be calculated frm te -s diagram fr bt te exansin and cmressin rcess. e ideal wrk inut r utut can be using eiter static r stagnatin states. a) Pwer Generating urbmacines (PGM) Actual wrk utut fr PGM e rer equatin is determined by te cnditins f urbmacine in questin. Fr examle in a turbine if te inlet ke is negligible and exit ke is used fr rductin f mecanical energy smewere else, ten static t ttal definitin is used. If te exit ke is wasted ten static t static definitin is used. Let 50; t t 0 0' 0 0 s t 0' 48; 0; 0' 5; w w w w t t t s st ss 0 0 0' ' 0' ' t t t s st s-s ; % 66. t s 0 ' ' % s -s 69.76% 43 ' 0' 0 '.67% 0 0' 0 ' 0

27 b) Pwer Absrbing urbmacines (PAM) Actual wrk inut fr PAM 0 0 Prblem Air as a erfect gas flws in a duct at a velcity f 60 m/s, a static ressure f atm., and a static temerature f 300 K. (a) Find ttal ressure and ttal temerature f air at tis int in te duct. Assume rati f secific eats as.4. (b) Reeat te rblem wit a flw velcity f 500 m/s. Given: (a) 60 m/s, atm., 300K (b) 500 m/s, atm., 300K Find (a)? and? (b)? and? Slutin: Equatins used are c K M 0.78 R bar w w w w t t t s st ss 0' ' ( ) M 0' ' 0 0 t t t s st s-s ' 0 0 0' 0' '

28 K M.44 R bar 0 Prblem Air enters a cmressr at a static ressure f 5 bar, static temerature f 5 C and flw velcity f 50 m/s. At exit, te static ressure is 30 bar, static temerature f 00 C and flw velcity f 00 m/s. e utlet is m abve te inlet. Find a) isentric cange in ttal entaly and b) Actual cange in ttal entaly. Given: 5 bar; 88K; 50 m/s; 30 bar; 00 C; 00m/s; z- zm. Find a) Isentric cange in ttal entaly, b) Actual cange in ttal entaly Slutin: Plt te -s r -s diagram as swn in fig. 5 bar; 88K; 50 m/s; 30 bar; 00 C; 00m/s; z-zm Isentric cange in ttal entaly 0' c ' 0 ' c ( c 0' gz c ; 0 c ( 0' 0 0' ' ) c 35.07K gz c 0' 0 ) KJ/kg 0

29 Actual cange in ttal entaly 0 c 0 c c ( ) 0 gz c 0 0 c 0 0 c 0 gz c Finite stage efficiency. A stage wit a finite ressure dr is a finite stage. In a multi-stage turbine alng wit te verall isentric efficiency te efficiencies f individual stages are imrtant 3. On accunt f large ressure dr and assciated termdynamic effect te verall isentric efficiency is nt a true index f aerdynamic r ydraulic erfrmance f macine 4. Different stages wit te same ressure dr lcated in different regins f -s lane will give different values f wrk utut Effect f Reeat (urbines) Cnsider fur number f stages between tw states as swn in fig. It is assumed tat te ressure rati and stage efficiency are same fr all te fur stages. x x y y z Wa Overall efficiency Ws e actual wrk during exansin frm state t state is W a W s 0 ( ) KJ/kg z Cnstant

30 e values f ideal r isentric wrk in te stages are W s, W s, W e ttal value f actual wrk dne in tese stages are Wa Wa W a W st Equating eq. and eq. 3 W a st s W 4 s i WW W s st e sle f cnstant ressure lines n -s lane is given by 5 s si, s3 W s4 ( W W W W ) 4 i s W si 4 s s3 s4 3

31 e abve equatin sws tat cnstant ressure lines must diverge twards te rigt 4 Wsi i > W is makes te verall efficiency f te turbine greater tan te individual stage efficiencies e quantity ne. 4 W i W s > s st si is knwn as reeat factr and is always greater tan Reeat is due t te reaearance f stage lsses as increased entaly during cnstant ressure eating rcess. RF st > Infinitesimal stage efficiency r Plytric efficiency (urbines) btain te true aerdynamic erfrmance f a stage te cncet f small r infinitesimal stage is used is is an imaginary stage wit infinitesimal ressure dr and is terefre indeendent f reeat effect Fig. sws a small stage between ressures and -d e efficiency f tis stage is actual temerature dr isentric temerature dr d d s

32 Fr infinitesimal isent Exanding te terms n r..s beynd secnd s s d d d d d s d d d d d d But d d s s tric exansin s. using binmial exressin and neglec d d cting terms

33 Integrating te eq. between limits and e irreversible adiabatic (actual) exansin rcess can be cnsidered as equivalent t a lytric rcess wit index n. Wen, n te exansin line cincides wit te isentric exansin. e efficiency f a finite stage can nw be exressed in terms f small stage efficiency. aking static values f and and assuming erfect gas 4 3 lg lg lg lg d d e e e e ( ) 6 n is rcess in actual exansin f index e 5 n n n n indices Equating n n

34 st s ( Pr ) st s r r s if ressure rati r ; ( r ) were Equatins 7 and 8 can give te efficiencies f varius finite exansin rcesses wit different values f ressure rati and small stage efficiency Prblem e verall ressure rati trug a 3 stage gas turbine is 0 and efficiency is 86%. e temerature at inlet is 400 K. If te temerature rise in eac stage is same, determine fr eac stage (a) ressure rati (b) stage efficiency. Given: 400 K; /0; 86%; st cnstant find: ressure rati fr eac stage and st Draw te -s diagram and assume te gas t be erfect gas r r ; st r 8

35 First stage efficiency is given by 03.K and 06.55K 93.45K same is stage in eac rise emerature K 89.6K 75.K ; y x st ' ' ' ( ) lg lg lg lg x x x x x e e e e 0.8 r were ; r r st x st

36 Pressure rati and stage efficiency f stage is given by y x x 06.55K; y 03.K ( ).4 y x 0.47; y x x y Pressure rati and stage efficiency f 3 stage is given by y y st 03.K; st y st K r r were Prblem In a 3 stage turbine te ressure rati f eac stage is and stage efficiency is 75%. Calculate te verall efficiency and wer develed if te air is initially at a temerature f 600 C and flws trug it at te rate f 5kg/s. Als Find te reeat factr. Given: st75%; 3 stage turbine; ressure rati acrss eac stage; 600 C; mass flw rate 5 kg/s find:?; P?; RF? Draw te -s diagram ; r x y

37 Finite stage efficiency (Cmressr) A cmressr wit a finite ressure rise is knwn as a finite stage Stage wrk is a functin f initial temerature and ressure rati Fr te same ressure rati, a stage requires a iger value f wrk wit iger temerature us cmressr stages in te iger temerature regin suffer n accunt f tis e abve factrs ave a cumulative effect n te efficiency f multistage cmressr ( ) ( ) 73.07% r r st ( ) RF 774.5KW mc P 78.6% st x 3 x y x y x y x y x ' &

38 Effect f reeat (Cmressr) Cnsider a cmressr wit fur stages as swn. It is assumed tat all te stages ave te same efficiencies and ressure ratis. e ttal isentric wrk frm state t s is Ws. e isentric wrk in te individual stages are Ws, Ws, Ws33 and Ws4 e verall efficiency f te cmressr is Ws/Wa Hwever W a but 4 st i 4 i W s st W W si W W si < x s W W xy is makes te verall efficiency f te cmressr smaller tan stage efficiency < st Ws3 Ws4 ; W W s st yz is is due t te termdynamic effect called Pre-reeating ; te gas is nt intentinally eated( reeated) at te end f eac cmressin stage. e reeat in small cnstant ressure rcesses is nly an internal enmena and te cmressin rcess still remains an adiabatic rcess. z W a ( Ws Ws WW s3 W s4 )

39 Infinitesimal r Plytric Efficiency (Cmressr) A finite cmressr stage can be made u f infinite number f small stages Eac f tese infinitesimal stages ave an efficiency called lytric efficiency r infinitesimal stage efficiency It is indeendent f termdynamic effect and is terefre a true measure f te aerdynamic erfrmance f te cmressr Cnsider a stage in wic air is cmressed frm state t state. It als sws an infinite stage erating between ressures and d d d using d d d d s s s s s d d binmial d d exansin

40 Substituting te value f ds int equatin Integrating eq. between state t Assuming te irreversible adiabatic cmressin as equivalent t a lytric rcess wit index n, equatin 3 can be written as e efficiency f finite cmressr stage can be related t small stage efficiency e actual temerature rise is given by d d d d 3 lg lg r lg lg e e e e ( ) 4 n n n n n n 5 r r r were r s s st

41 Prblem A 6 stage axial flw cmressr is t ave a ressure rati f 6.3, wit a stage efficiency f 89.5%. Intake cnditins are 88K and bar. Find (a) Overall efficiency (b) Plytric efficiency ( c) Preeat factr. Assume ressure rati er stage is same. Given: 6 stage axial flw cmressr, ressure rati 6.3, st89.5%, 88K and bar Slutin: cnstant x x 6 x ressure rati er stage.9 st ( r ) ( r ) ( r ) ( r ) Preeat factr ( 6.3) ( 6.3) st / (.9) (.9) / 87.75% Prblem An air cmressr as 8 stages f equal ressure ratis f.3. e flw rate trug te cmressr and its verall efficiency are 45 kg/s and 80% resectively. If te cnditins f air at entry are bar and 35 C determine (a) State f cmressed air at exit (b) lytric efficiency (c) Stage efficiency Given: 8 stages f equal ressure rati f.3, mass flw rate f 45 kg/s, 80%, bar, 35 C find: (a)?,? (b)? (c) st?

42 Stage ressure rati.3; Overall ressure rati (.3) 8.57 ' ' 56K ' 64.6K lg lge bar 8.57 lge lge 308 e st ( r ) ( r ) % 84.88%