Design of a Single Stage Centrifugal Compressor as Part of a Microturbine Running at rpm, Developing a Maximum of 60 kw Electrical Power Output

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1 Amian Jounal of Aopa Engining 07; 4(): 6- oi: 0.648/j.aja ISSN: (Pint); ISSN: (Onlin) Dign of a Singl Stag Cntifugal Compo a Pat of a iotubin Running at pm, Dvloping a aximum of 60 kw Eltial Pow Output unz Shhah Youf Ebai, Quai Zuhai ohmma Al-Haman hanial Engining Dpatmnt, Faulty of Engining, Philalphia Univity, Amman, Joan Aiaft Engining Dpatmnt, Pth Collg, Univity of th Highlan an Ilan, Pth PH 8PD, Sotlan, UK a: mbai@philalphia.u.jo (. S. Y. Ebai), quai.al-haman.pth@uhi.a.uk (Q. Z.. Al-Haman) To it thi atil: unz Shhah Youf Ebai, Quai Zuhai ohmma Al-Haman. Dign of a Singl Stag Cntifugal Compo a Pat of a iotubin Running at pm, Dvloping a aximum of 60 kw Eltial Pow Output. Amian Jounal of Aopa Engining. Vol. 4, No., 07, pp. 6-. oi: 0.648/j.aja Riv: ah 6, 07; Apt: Apil 5, 07; Publih: July 0, 07 Abtat: In thi unt wok, th ign of a ingl tag ntifugal ompo a pat of a omplt mall ga tubin oupl itly to high p pmannt magnt unning at 60000pm an vloping a maximum ltial pow of 60kW i pnt. Th hoi of a aial impll wa oni an th ign wa ba on uing a non-lina optimiation o to tmin th gomti imnion of th impll. Alo, th optimum axial lngth an th flow paag of th impll w foun ba on pib man tam vloity. Th popo o wa vifi an how quit goo agmnt with th publih ata in th opn litatu. Th ign of a vanl iffu an a volut w oni ba on atifying th govning quation of onvation of ma, momntum, an ngy onvation imultanouly. Rult how goo agmnt with th CFD analyi foun in th opn litatu. Thi wok wa motivat by th gowing intt in mio-ga tubin fo ltial pow gnation, tanpot an oth appliation. Kywo: Cntifugal Compo, Vanl Diffu, Impll, an Stam Vloity, Optimization. Intoution Cntifugal ompo a on of th main omponnt of miotubin. iotubin a ga tubin with pow anging appoximatly fom 0 t0 00kW. Th vi an b u in tationay, tanpot an auxiliay pow appliation. In th ompo ign tag, many hoi of ign option n to b oni bfo th final ign. It i ntial that ign ngin bgin to pfom a ompo ign with full untaning of all apt of th ign oniation [ 4]. any ah wok that hav bn it in th opn litatu u iffnt optimization mtho uh a atifiial nual ntwok (ANN) an a gnti algoithm (GA), vlop omput o, an Computational flui mhani (CFD) to ign th ntifugal impll. Th w ba on th ign vaiabl that ontol th hap of th impll [5-]. Howv, th upioity of th ign thniqu oul not b valiat in xpimntal ult u to th iffiulti in poply onuting xpimnt.. Dign Poblm Th a many ign poblm whn aling with ntifugal ompo. Fit poblm i that th flow ini th ompo i omplx bau th flow tak pla againt th poitiv pu gaint; onquntly it lat along th man flow path. Eo in th ign of th impll, fo xampl, may la to xiv pa at of lation in th inu tion; hn pou high lo Ingham an Bhin [3]. Son poblm i th lativ ah numb lo to th inu tip. In a of high-pu atio impll, th inu tip ah numb may ah unity; onquntly om pat of th inlt aa may b hok. Oftn thi poblm i a by utting altnat bla bak, ulting in plitt bla. Howv, it i not ay to nu that flow at in th ulting two hannl woul b qual bau of th pn of jt an wak flow in th

2 7 unz Shhah Youf Ebai an Quai Zuhai ohmma Al-Haman: Dign of a Singl Stag Cntifugal Compo a Pat of a iotubin Running at pm, Dvloping a aximum of 60 kw Eltial Pow Output impll flow paag. Stahl [4] invtigat th fft of inu lativ tip ah numb on ffiiny uing val Boing ompo. Th ult w pnt iniat th pnalty that may b pai fo th ina in. Effiiny fall off apily fo gat than 0.8. Thi poblm i th aial vanl iffu whih may b oni a majo ou of inffiiny in ntifugal ompo u to non-unifom flow laving th impll; thfo, mot of th wok it in th opn litatu wa it to tuy th flow an fin mtho to pit th lo in th vanl iffu in an attmpt to ina it ffiiny, [5-0]. Aoing to thi, aful ign i a to th vanl iffu to pou ffiint ompo. Bttni at l. [] pnt th ign po fo a ntifugal ompo that will b pat of montativ mio-ga tubin plant. Th ign mthoology vlop at Dimt ha bn u fo th flui ynami ign of a ntifugal ompo fo a mall mio ga tubin plant. Zah an Bayomi [] pnt th vlopmnt of a pliminay ign mtho fo ntifugal ompo. Th ign po tat with th aoynami ign an it lian on mpiial ul limiting th main ign paamt. Thi pou an b appli to th ompo fo th pu atio of.5, 3.0 an 5.0. Dign oniation of mhanial t fo th impll an minimum inlt ah numb w takn into oniation. In thi ah wok, th autho ha on th pliminay ign in whih th wok input an ompo ffiiny wa oni. Th impll ign at iffnt pu atio ha bn on. afat t al. [3] pnt th ign pou of multi-tag ntifugal ompo, by oniing on imnional flow ign. Th ign pou tat fom alulation of impll inlt an it i ontinu fo th oth tion inluing impll xit, iffu an volut. Th total ffiiny, tag ffiiny, otion fato an lakag a alulat. Fom th pou. it wa val that th a ntial paamt uh a tip p ah numb, flow o-ffiint at inlt an iamt of impll whih will play majo ol in tmining ompo polytopi ha an onquntly ompo polytopi ffiiny. Th ign volut i iffnt than that th f on. Th iimilaity i on th goun that th mntion mtho oni minimum optimum valu ath than mot ffiint on, whih la to an onomial ign. Kuauhi an Baboa [4] pnt th ign of a ntifugal ompo fo natual ga in 3 tp in whih th fit tp ha -D pliminay ign havily ba on mpiial ata, th on tp i th flow analyi in th miional plan an th lat tp involv th CFD analyi to hk if th -D mthoology i aquat. Th point of patu fo th ntifugal ompo ign wa appopiatly lt following Vava' uggtion. Li t al. [5] pnt an optimization ign mtho fo ntifugal ompo ba on on imnional alulation an analyi. It onit of two pat whih a ntifugal ompo gomty optimization ba on on imnional alulation an math th optimization of th van iffu with an impll ba on th qui thoat aa. Gui t al. [6] ib a ign an xpimntal ffot to vlop mall ntifugal ompo fo aiaft ai yl ooling ytm an alo fo mall vapo ompion figation ytm. Sval low-flow-at ntifugal ompo whih a fatu with th-imnional bla hav bn ign, manufatu an tt in thi tuy. An xpimntal invtigation of ompo flow haatiti an ffiiny ha bn onut to xplo a thoy fo mini-ntifugal ompo. Th fft of th numb of bla, ovall impll onfiguation, an th otational p on ompo flow uv an ffiiny w tui ooz t al. [7] pnt a mtho fo ntifugal an mix typ ompo flow path ign ba on a uniqu intgat onptual ign nvionmnt. Th appoah povi in th pap giv th ign th oppotunity to ign axial, aial an mix flow tubo-mahiny uing th am tool. Bowa an Paahka [8] pnt a tp by tp guian to ign a aial typ van pofil. In aial typ van, th van pofil i a uv that join th inlt an outlt iamt of th impll whih an b on in infinit numb of uv an o it i qui to fin pop hap of th van. In thi pap, impl a, oubl a, iula a an point by point mtho w tat. It an b onlu fom pviou wok that th i no tana pou of ign alulation of ntifugal ompo in vy ngin li on om mpiial lation. Alo, publih pap on omplt ign of ntifugal ompo a pat of a omplt mall ga tubin oupl itly to high p pmannt magnt unning at 60000pm of 60kW pow output i till a. Thfo, thi motivat th wok in thi pap to pnt a omphniv ign of a ingl tag ntifugal ompo, whih inlu th impll, th vanl iffu, an th volut a pat of a miotubin fo pow gnation unning at unning at pm, an vloping a maximum of 60 kw ltial pow output. Futhmo, vloping a ign mtho fo alulating th numb of bla N b an th axial lngth Z axial woul off a ignifiant ontibution. In aition to that, th ign of bla pofil an flow hannl ba on pib man vloity i a nw appoah a fa a th autho i awa off. Th pou of th popo ign of th ntifugal ompo i ib haft. PROPOSED DESIGN PROCEDURE Th ign pou of a ntifugal ompo wa ivi into th following two tag: Stag (): Fitly, th tmination of th optimum gomti imnion an numb of bla of th impll. Sonly, th optimization of axial lngth an paag gomty fo a pib o aum man-tam vloity. Stag (): Th ign of th vanl iffu an th volut fo whih th govning quation of ma, momntum an ngy quation mut b atifi imultanouly.

3 Amian Jounal of Aopa Engining 07; 4(): Impll Dign... Optimiation of th Pinipal Dimnion of th Impll Th tminology u to fin th omponnt of a ntifugal ompo i hown in Fig. an th pu i ao it i pit in Fig.. An nthalpy ntopy iagam i plott to how th ompion po pogion in th ompo tag a hown in Fig. 3. Figu. Componnt of ntifugal ompo. It houl b not that th po pat fom intopi ompion u to lo au by fition, viou ag an oth. In gnal, th impll of a ntifugal ompo may b oni a a gnaliz flui hanling ytm an Figu. Pu i ao th ompo tag. Tabl. ain paamt of a ntifugal ompo impll. th vaiabl whih will ompltly ib th ign an pfoman of thi ytm may b ivi into th goup a hown in Tabl. Contol vaiabl Dign vaiabl Pfoman quimnt Inlt pu Tip iamt an bla with a flow at Inlt tmpatu Inu an hub iamt Intopi ffiiny Rotational p Axial lngth, bla angl Pu atio Popti of woking flui ah numb Spifi p, Diffuion atio an Flow offiint

4 9 unz Shhah Youf Ebai an Quai Zuhai ohmma Al-Haman: Dign of a Singl Stag Cntifugal Compo a Pat of a iotubin Running at pm, Dvloping a aximum of 60 kw Eltial Pow Output availabl of; (a) th inlt tagnation pu an tmpatu; th tana atmophi onition a oftn appliabl, (b) th g of p-whil; h it will b aum that th flow nt th inu with zo p-whil, () th ma flow at of th woking flui, an () it will b aum that th flow nt unifomly o that th i no vaiation of axial vloity with aiu. In aition uing th momntum, ontinuity an ngy quation, val aoynami an gomtial xpion of th flow mut b iv to valuat th pinipal imnion fo th inu an th a: N a. Sp paamt CpaT 0 Coniing th flow at th inu man iamt, p paamt i givn by: N C T pa 0 ( P P ) 0 0 = π η ϕ ( w u)( ) () Figu 3. Gnali H-S iagam fo a ntifugal ompo. Fo a givn t of pfoman quimnt, th ign appoah ntail th alulation of omplt gomtial paamt of th impll, in aition, it i nay to intify th ontaint uh a inu ah numb, tmpatu an t limit. Th gomti hap of a typial aial flow impll inluing th vloity tiangl, auming zo wil at impll inlt, a hown in Fig. 4. b. Rlativ flow ah numb at inu tip iamt ( ) Rf to inlt vloity iagam at inu tip in Fig. 4 pnt abov, th following xpion an b wittn a: πn CpaT 0 = πn ( ) in β + CpaT 0 () Wh: N C T pa 0 ( P P ) 0 0 = π η ϕ ( w u)( ) (3) mɺ CpaT 0. a flow paamt P 0 Uing th ontinuity quation at inu inlt fo ma flow at giv: mɺ CpaT0 π h in β = ( ) ( ) Bf P ( ) + ( in β) (4) Figu 4. A ntifugal impll with th inlt an outlt vloity tiangl.. Inu tip to impll tip iamt atio( ) an hub to impll tip iamt atio ( h ) (i). Impll Inlt Dign Paamt Bfo ommning any ign pou, pio knowlg of om paamt mut b availabl, whilt oth mut b aum. Fo an inu ign, pio knowlg i uually

5 Amian Jounal of Aopa Engining 07; 4(): 6-0 ( ) o β = πn + in β C pat0 + ( ) ( in β ) = π ( Bf ) ( in ) β 4 mɺ CpaT 0 + P0 h Wh: (5) (6) B f n( t ) ( ) + ( ) th = π h (ii). Impll Outlt Dign Paamt a. Diffuion atio paamt ( v v ) in β + v in β ( P0 P0 ) = π ( ϕ ) v o β in β π η ϕ b. Bla tip with to impll tip iamt atio xpion ( b ) (7) mɺ CpaT 0 P 0 N + b 0 0 P η P πϕ C pat = Bf P o π ϕ 0 N α ( tan ) P α 0 P + 0 CpaT 0 η P0 ( ) (8) Wh: lina o non- lina quality an inquality ontaint, i.. B f π t = n gi( x ) = 0 i =,... q (9) g j( x) 0 j = q +,... m (0)... Optimization Pou Fo a givn t of ign onition a lit in Tabl, th optimum gomti imnion of th impll w foun by olving Eqn. () to (8) within th pifi ang of th ontaint vaiabl. Th olution an b obtain by uing a uitabl optimiation algoithm. In viw of thi, numial optimiation thniqu an b a uful tool to poblm involving a lag numb of vaiabl. Tabl. Compo input ata at ign point. Dign Vaiabl Dign Valu a flow, mɺ a Pu atio, P0 P 0 4/ Inlt tagnation tmpatu, T 0 Rotational p, N Avag bla thikn at impll inlt, t / th Avag bla thikn at impll outlt, t th 300 K 60,000 pm.0 mm.0 mm Th autho u th algoithm all optimiation uing uiv quaati pogamming OPRQP vlop by Bigg [9, 30]. Th optimiation pogamm tat by aigning iffnt valu to a t of paamt X, X, X,... 3 X n. Thfo, an objtiv funtion not by F( X ), wh X i a vto with lmnt, X, X, X,... 3 mut b fomulat an th aim i to tmin th valu of th vto X, whih will fin th optimum valu of th funtion F( X ). Thi funtion may b ubjt to poibl X n Wh: g i an g j pnt non-lina quality an inquality ontaint, ptivly. Th ubipt i an j f to th numb of ontaint. (i). Containt Optimiation Thniqu Pou Th fam iz an wight of ntifugal ompo i oftn an impotant paamt oniation, in viw of thi, th iz of th impll play an impotant ul in tmining th ovall iz of uh a ompo. Thfo, th aim i to minimi th impll tip iamt an thi an b oni a ontaint optimiation poblm. Th pou to olv uh a poblm i ib blow: a. Sltion of main pinipal paamt of a tubin oto Th hoi of lting th pinipal paamt of a ompo impll to olv thi optimiation poblm i givn by th matix: = X() X() = β = X(3) = X(4) h = X(5) X = α = X(6) b = X(7) v v = X(8) β = X(9) = X(0) β = X() ()

6 unz Shhah Youf Ebai an Quai Zuhai ohmma Al-Haman: Dign of a Singl Stag Cntifugal Compo a Pat of a iotubin Running at pm, Dvloping a aximum of 60 kw Eltial Pow Output b. Fomulation of th objtiv funtion Th objtiv funtion i to optimi th oto tip iamt an it an b fomulat a follow: inimiz. Fomulation of quality an inquality ontaint a. Equality ontaint a. F( X) = = X() () mɺ CpaT0 π h in β g() = ( ) ( ) Bf P ( ) + ( in β) (3) a. g() mɺ CpaT 0 P + 0 ( ) + b 0 0 P η P + = π B f P 0 inα P 0 (4) a.3 v in β ( P0 P0 ) = π g(3) v ( ϕf ) in β + o β in β π η ϕ f (5) a.4 g(4) ϕ b N f = b 34.4 tanα (6) b. Inquality ontaint b. 0.0m : Thi i govn by th iz of th ompo b...0 quimnt g(5) = 0.0 (7) : Spifi by th uboni flow g(6) =.0 (8) b.6 α 7 : Contoll by iffuion atio b.7 b atio b.8 v v 0.55 impll paag g(0) = α 7 () : Govn by lakag lo an iffuion g() = b (3) : Govn by flow paation in th g() = v v 0.55 (4) b.9 β 60 : Spifi by iffuion atio quimnt b.3 β 5 : Spifi by maximum flow at inu inlt g(3) = β 60 (5) g(7) = β 5 (9) b : Govn by th lativ ah numb b.5 h 0.40 numb of bla. g(8) = 0.55 (0) : Spifi by t limitation an g(9) = 0.40 h () b : fix by lativ flow angl at impll xit g(4) = 0.95 (6) b. β 35 : Govn by inu an hub iamt g(5) = β 35 (7) (ii). Optimiation Pogamm Th optimiation uing uiv quaati pogamming Fotan pogamm, oubl piion, OPRQP i u to olv

7 Amian Jounal of Aopa Engining 07; 4(): 6- a gnal non-lina pogamming poblm uing th uiv quaati pogamming algoithm an a uuppli gaint. Th iption of th OPRQP pogamm i foun in Rf. [9-3]. Th only unuual fatu i th u of th impll tip iamt a an optimiation vaiabl an an objtiv funtion. Howv, uh a hoi houl not afft th woking of th pogamm.th objtiv funtion an th quality an inquality ontaint with thi fit ivativ a int into th pogamm into two ub-outin all, all funtion an all gaint...3. Optimiation Rult Th optimiation pogam wa un fo a numb of bla anging fom to 0. Th numb of bla wa pifi within thi ang in aoan with th aum ffiiny η, blokag B f an bla loaing fato Cw u. Fig. 5 how th impll tip iamt an th impll tip with b plott againt th numb of bla N b. A on woul xpt, th tip with ina a th iamt i u fo th bla numb fom to 5, thn th hang fo both an b i faily mall. Th ign outlt an inlt vloity iagam ba on optimiation thniqu a hown in Fig. 6a an 6b. Alo, th omplt ult of th ign a givn in Tabl 3a an 3b, ptivly. Tabl 3a. Rult ata () fo th impll ba on numial optimization. Dign Paamt mɺ a N 0 0 = 0.566kg = 60000pm P0 = 4.0 P T t p = 300K = 88.6 K = 0.87ba 3 ρ =.05kg m Gomtial Dimnion = 5.9m b = 0.64m t th th = 0.m = 6.387m = 3.038m h = 8.506m t = 0.m Flow Angl at Impll Inlt an Exit α =.0 β = 68 α = 90 α = 90 h α = 90 β = h β = β = 30 Pfoman Paamt S = 0.77 P p m = 0.34 η = 0.83 u = 0.33 v v = 0.67 Figu 5. Plot of impll tip iamt an tip with againt Th numb of bla. Figu 6a. Outlt vloity tiangl ba on numial optimization thniqu. Tabl 3b. Rult ata () fo th Impll ba on numial optimization. Flow Vloiti at Impll Exit m w v v m v w = m = 58.8m = 4.3m = 70.7m = 58.8m = 63.95m Flow Vloiti at Impll Inlt = 54.9m w h w h = 0.0 m/ = 54.9 m/ = 54.9 m/ v = 53.0m v v = 00.65m = 80.89m v = m/ Bla Sp at Impll Inlt an Outlt u = m/ u = 9.8 m/ u = 95.8 m/ h u = 76.4 m/ ah Numb at Impll Inlt an Exit =.4 h = 0.65 = = 0.53 = = Figu 6b. Inlt vloity tiangl ba on numial optimization thniqu... Optimization of Paag Gomty an th Choi of Axial Lngth To fin th paag gomty of th impll, th axial lngth of th impll i almot a p-quiit. Thfo, a pib man tam vloity itibution appoah wa u to optimiz th paag gomty an th axial lngth of th impll. Th lativ vloity vto V at any point ini th

8 3 unz Shhah Youf Ebai an Quai Zuhai ohmma Al-Haman: Dign of a Singl Stag Cntifugal Compo a Pat of a iotubin Running at pm, Dvloping a aximum of 60 kw Eltial Pow Output impll paag, a hown in Fig. 7, an b olv into th bai omponnt along th axial, aial an tangntial ition, V z, V an V w, H V m i th vloity vto along th man tamlin in th hub-to-hou plan, hn V = V z + V + V w (8) Th bounay valu of th omponnt of th lativ vloity a known fom th inlt an outlt vloity tiangl, whih ult fom th pviou optimiation. Th bounay valu a givn a follow: At impll inlt: Vz = ( Vz) max V 0, = At impll xit: V z = 0, V = ( V) max, an Vw = ( Cw U) U Fom Fig. 7, th following lation a hol Th angl ( α, β an θ ) a lat to ah oth by ombining th abov lationhip a follow: tan β = tanθoα (3) Th patial iption of th man tamlin an b foun itativly by auming a tating valu fo th miional lngth z m, an th itibution of th lativ vloity vto. Figu 8 ib th vloity omponntv, V z an V w fo on aum valu of Z = 0.06m. At th tat, all th figu a ba on th aumption that th vaiation of th lativ vloity vto V i lina. A omput pogam wa wittn to pfom th itativ alulation to hk thi lina lationhip vaiation of lativ vloity vto along th man tamlin an th flow anglα an β. Th output ult a plott in Fig. 9 an 0, an a flow hat ba on thi pogam i hown in Fig.. an Vm = V + Vz, V = Vz + V + Vw, V = Vw + Vm (9) Vw = V in β, V = Vm inα, Vm V Vz = Vm oα, β = in (30) Th angl hown in Fig. 7 abov an b xp in tm of th vloiti a hown: Vw Vw Vz But,: tan β =,tanθ =, anoα = V V V m z m Figu 8. Aum lina lationhip of lativ vloity vto man an it omponnt fo an aum Z = 0.06m. Figu 9. Pib lativ vloity itibution along tamlin fo an aum miional lngth of z = 0.06m. m Figu 7. Shmati fo th lativ vloity vto an it omponnt. Figu 0. Atual valu of th flow angl α an β along man tamlin of a miional lngth of z = 0.06m m

9 Amian Jounal of Aopa Engining 07; 4(): Lo ol Sval mol a availabl in th publih litatu Dallnbah [3] an Rog [33] whih tak aount of th lo. Th lo mol w aopt fo th impll a givn in Eqn. 3 an 33, ptivly. A tail viw an ivation of th lo mol a outi th op of thi pap, but it houl b mntion that any lo mol might b intgat into th pogam a ub-outin..3.. Skin Fition Lo Skin fition lo xpion at any tion X a a imnionl quantity i givn by: 0 b ( ) ( 0.444) ( ) 4 av l V q R SFL = x R hy u x x x (3) v x πin β πu ( q) 0.05 DBL = x + + v l x lv x (33).3.3. Shok Lo Th lo a igno a th flow i uboni. Th nxt tp wa to optimiz th axial lngth Z by minimizing th lo of tagnation pu in th flow hannl. Thfo, a omput pogam wa wittn to optimiz th axial lngth an th flow paag ba on th lation lit h. H th aiu of th man tamlin in th miional plan an b pnt uing Lam oval lationhip a: 3 z z = ( ) + m m zm zm (34) Th fit an on ivativ of z a givn in Eqn. 35 an 36, ptivly: 3 l z z z z z j z z m m = m m m m z m = + zm zm zm zm (35) (36) Th lngth of th tamlin i givn by: zm zm L = + zm z (37) m Th tmpatu at any tion X ini th paag u x Tx = T0 + CpaT 0 (38) Th pu at any tion X ini th paag P ϕ P x T x = 0 T0 (39) Th nity at any tion ini th paag vx Px ρx = CpT x RTx (40) Th hou ontou at any tion X ini th paag Figu. Flow hat fo lativ vloity vto vaiation along man tamlin..3.. Combin Diffuion an Bla Loaing Lo Combin iffuion an bla loaing lo xpion at any tion X a a imnionl quantity i givn a: mɺ a oα x = ( ) + π ρ v B x m x x mx Th hub ontou at any tion X ini th paag hx m x x fx (4) = ( ) (4)

10 5 unz Shhah Youf Ebai an Quai Zuhai ohmma Al-Haman: Dign of a Singl Stag Cntifugal Compo a Pat of a iotubin Running at pm, Dvloping a aximum of 60 kw Eltial Pow Output It an b n fom Eqn. 7 an 8 that thy an b u to alulat th hou an th hub ontou at any tion X ini th bla paag, hn th final hap of th bla paag an b fin. A flow iagam fo optimiing th axial lngth an flow paag of th impll i givn in Fig.. Th output ult a pnt gaphially. Fig. 3 how a plot of impll intnal lo, that i, kin fition lo q SFL an iffuion an blaing lo qdbl v. miional lngth of a ntifugal impll. A on woul xpt that q SFL i lowt fo th mallt axial lngth an ina a th axial lngth i ina whil qdbl i hight fo th mallt axial lngth an a a th axial lngth i ina. Figu 4 how a plot of total pu lo ini th paag v. miional lngth of a ntifugal impll. It an b n that th optimum miional lngth wa foun to b 4.5mm fo minimum pu lo in th paag. Figu 3. Vaiation of impll intnal lo along th impll paag. Figu 4. Ovall impll intnal lo along th impll paag. Figu 5. Th imnional oli mol of th ign impll. Figu. Flow hat fo th ign of th flow paag an optimizatio of th miional lngth. Figu 6. Dtail ign awing of miional tion of th ign impll.

11 Amian Jounal of Aopa Engining 07; 4(): Valiation of th Optimization Co Th aim of thi valiation i to hk th liability of pnt o to b u with onfin fo th flow analyi. Th ata publih by Ekat [34] an Tough t al. [35] w hon to valiat th pnt o. Ekat [34] pfom maumnt fo tail invtigation of flow fil in a ntifugal impll. Th mau ata hav bn wily u to valiat omputational o an alo quot Tabl 4. Gomti paamt of Ekat impll an Tough t al. [35]. in ibing th flow haatiti along th impll. Tough t al. [35] ai out a CFD analyi to tmin th olution of th flow of a ntifugal impll. Rult of pnt alulation of th gomti paamt in thi wok how quit goo agmnt with th publih wok in th opn litatu [34, 35]. Th ipani btwn th ult an b attibut to th iffnt input paamt of th impll a hown in Tabl 5. Paamt Popo impll Tough t al. [35] Impll (CFD analyi) Ekat [34] impll (omputational o) Inlt tip iamt t = 8.506m t = 5.48m t = 8m Inlt hub iamt h = 3.038m h =.87m h = 9.0m Outlt iamt = 5.9m = 9.5m = 0m Impll xit with b = 0.64m b = 0.3m b =.6m Inlt bla angl β = 37.6 β = 30.0 β = 30.0 Pu atio P = 4.0 P = 4. P = 4.3 a flow at ɺm = 0.566kg ɺm =.45kg ɺm = 5.3kg Inlt total tmpatu 300 K 88 K 88 K Tabl 5. Compaion of ult btwn th popo impll with Ekat [34] an Tough t al. [35] impll. Paamt Popo impll Tough t al. [35] impll Ekat impll [34] Numial ult CFD ult au ult Inlt abolut vloity = 54.9m = 36.30m = 35.90m outlt abolut vloity = m = m = Inlt lativ vloity v = 53.0m v = 68.50m v = 63..0m Outlt lativ vloity v = 70.7m v = 75.40m v = 80.5m Inlt lativ ah numb = = = 0.78 Outlt lativ ah numb = 0.65 = 0.6 = Vanl Diffu Th vanl iffu i oftn aopt a th ol man of pu ovy owing to it impliity an inxpniv ontution, it boa opating ang an it ability to u Figu 7. Dtail ign awing of th ign impll. a oni abolut vloity to a uboni on without th fomation of hok wav. Vanl iffu a vy ommon in automotiv tubohag an figation ompo. Thy hav bn u in tain impotant appliation wh th impll xit kinti ngy i too gat fo atifatoy volut pfoman an wh van iffu

12 7 unz Shhah Youf Ebai an Quai Zuhai ohmma Al-Haman: Dign of a Singl Stag Cntifugal Compo a Pat of a iotubin Running at pm, Dvloping a aximum of 60 kw Eltial Pow Output i unatifatoy. Th vanl iffu may b a vanl pa btwn th impll tip an th bginning of a hannl o aa iffu o it may b un fom th impll ihag to th volut inlt. Analyi in th pviou tion how that th flui ihag fom th impll at high vloity, Tabl 3, an onquntly it i ntial to onvt th kinti ngy ffiintly into tati pu. Th vanl iffu oni in th unt pap i two paalll wall foming an opn paag fom th impll tip to a pifi ihag iamt a hown in Fig. 8. Th following tion ib th ign pou. ω = ω o ω ω = (45) Applying ma ontinuity at any tation along th iffu in lation to impll xit woul giv: mɺ = ρ A = ρa m mɺ = ρ A tanα = ρa tanα (46) ω Combining quation 45 an 46 with th quation of tat A πb p = ρrt an ubtituting fo = an -aanging A πb woul giv an xpion fo tati pu atio in th vanl iffu: m ω p t b tanα = p t b tanα (47) Fo aiabati onition in th vanl iffu, tmpatu atio in th vanl iffu an b xp a: t CpaT = t C T pa 0 0 (48) an fom gnal vloity tiangl, th vloiti an an b xp a Figu 8. Ru with in vanl gap of a ntifugal ompo aing. Vanl Diffu Dign Analyi Th flow at nty to th vanl iffu i xtmly omplx, oniting of jt an wak iuing fom ah paag of th impll Dan an Snoo [9]. Thfo, mixing out ou a th flow lav th impll tip at a finit aial inmnt outi impll known a th vanl gap wh th flow i xpo to un nlagmnt foming i an fition lo. Fih [36] giv a iamt atio of th vanl gap to th impll tip 3 i qual to. to u non-unifomity an noi. Th implt iption of th flow though th vanl iffu an b obtain by oniing th angula momntum quation u fo th impll but appli btwn th impll xit () an th vanl iffu xit (5), (f to Fig. ), that i τ = mɺ ( ) (43) ω5 5 ω Fo th a of an opn paag wh th flow i only tain by th i wall an in th abn of any wall fition fo, th toqu τ xt on th flui i zo an th angula momntum quation abov u to f votx lationhip = (44) ω5 5 ω At any tation along th iffu in lation to impll xit, th abov quation i wittn a: ( ) = ω = ω an oα oα ω = (49) oα Subtituting fo an xpion in Eqn. 49 an ombining with Eqn. 47 an 48 will giv an xpion fo tati pu i atio within th vanl iffu a: ω oα p CpaT 0 b tanα = p b tanα ω oα CpaT 0 (50) Fo paalll wall vanl iffu, th with b = b3 = b5, hn Eqn. 50 bom: ω oα p C pat 0 b tanα = p b 5 tanα ω oα C pat 0 (5) Equation 5 how that th tati pu i in th

13 Amian Jounal of Aopa Engining 07; 4(): 6-8 vanl iffu i a funtion of aiu atio an th abolut flow angl α. Fo an ffiint iffuion, th flow angl α mut b u with inaing aiu atio. Eqn. 5 i plott a hown in Fig. 9 to how th vaiation of pu ovy in th vanl iffu. Figu 0 how th vaiation of both th tangntial an aial vloiti with aiu atio in th vanl iffu. It an b n that both vloiti a aing with inaing aiu atio. Th final ign ata of th vanl iffu paamt at xit a givn in Tabl 6. Figu. Th imnional oli mol of th vanl iffu. Tabl 6. Complt ign ata of vanl iffu. Dign paamt Vanl iffu iamt, 5 Vanl iffu with, b 5 Stati pu at xit, p 5 Flow angl at xit, α 5 Dign valu.06m 0.58m 3.88ba.55 Tangntial vloity at xit, ω m Raial flow vloity at xit, m Abolut flow vloity at xit, m Stati tmpatu at xit, K Dnity at xit, ρ kg m Figu 9. Pu i in th vanl iffu. 4. Volut Dign Th lat bai omponnt of a ntifugal ompo tag i th volut o oll. It i a pial hap houing whih ollt th flow fom th iffu an pa it to a pip at th xit. Dign tho Coniing th flow in th volut to b fitionl an th volut o-tion to b iula, fo impliity an a of manufatu, th ontinuity quation at azimuth angl φ giv: mɺ = ρ A (5) φ φ φ ωφ Figu 0. Vaiation of tangntial an aial vloiti with aiu in th vanl iffu. Th final ign awing of th vanl iffu i hown in Fig. an a th-imnional oli mol of th vanl iffu i hown in Fig.. φ But mɺ φ = mɺ 360 Sin th iffn in vloity at an 5 φ i likly to b mall ompa to th loal vloity of oun, thn th nity atio will b naly on, onquntly; π ρφ = ρ4, ωφ = φ ω an Aφ = 4 Subtituting th abov xpion in Eqn. 5 an -aanging will giv an xpion fo volut o-tion iamt at any azimuth angl a: φ 4 φ mɺ = π 360 ρφ ωφ (53) Figu. Dtail ign awing of th vanl iffu. Fo manufatuing pupo, th volut wa ma of two pat, th volut an it ov. Final ign awing of th volut an it ov a hown in Fig. 3 an Fig. 4 ptivly.

14 9 unz Shhah Youf Ebai an Quai Zuhai ohmma Al-Haman: Dign of a Singl Stag Cntifugal Compo a Pat of a iotubin Running at pm, Dvloping a aximum of 60 kw Eltial Pow Output FINAL DESIGN ODEL OF THE COPRESSOR Final ign awing an th-imnional oli mol an an xplo viw pntation of th ntifugal ompo ambly a hown in Fig. 7, 8 an 9, ptivly. Figu 3. Dtail ign awing of th volut. Figu 7. Shmati iagam of th ntifugal ompo ambly. Figu 4. Dtail ign awing of th volut ov. A th imnional oli mol of th volut an it ov a hown in Fig. 5 an Fig. 6., ptivly. Figu 5. ultipl viw of th- imnional oli mol th volut ov. Figu 8. Explo viw of th ntifugal ambly. Figu 6. ultipl viw of th- imnional oli mol of th volut. Figu 9. ultipl viw oli mol of th ntifugal ompo ambly.

15 Amian Jounal of Aopa Engining 07; 4(): Conluion a) Th ign of a ingl tag ntifugal ompo ompiing an impll, a vanl iffu an th volut ha bn pnt. Th ompo ha bn ign a pat of mio-ga tubin ign fo pow gnation unning at 60000pm an vloping 60kW ltial pow. b) Th pinipal gomti imnion of th impll an th numb of bla w tmin ba on non-lina optimization o vlop fo thi pupo. Alo, th o wa u to fin th optimum axial lngth an optimizing th bla paag. ) Th omput o fo th ign of th impll wa vifi an th ult how quit goo agmnt with CFD analyi publih ata in th opn litatu. ) A pou fo igning th vanl iffu an th volut wa givn ba on th govning quation of ma, momntum, an ngy onvation. Th flow i aum to b intopi an atifi th f votx lationhip. Notation A Aa nomal to man flow ition ( m ) b Bla with ( m ) B Blokag fato f C Abolut flow vloity of ga ( m ) Spifi hat apaity at ontant pu fo ga C p ( kj kgk ) Diamt ( m ) f Fition fato Abolut ah numb Rlativ ah numb mɺ a flow at ( kg ) N Rotational p ( pm) N Numb of bla b P Stagnation pu ( N m, ba ) R Rynol numb Raiu of uvatu ( m ) T Stagnation tmpatu ( K ) t Bla thikn ( m ) u Impll tip vloity ( m ) v, V Rlativ vloity ( m ) W Wok output ( kj ) z Axial lngth ( m ) Gk Symbol α β Abolut flow angl lativ to axial ition (g), angl btwn miional tamlin an axi Rlativ flow angl lativ to axial ition (g), angl btwn lativ vloity vto an miional plan β b Bla angl θ Rlativ angula o-oinat Ratio of pifi hat η Effiiny of a po ρ 3 Ga nity ( kg m ) ψ Bla loaing ϕ Pu lo offiint ϕ Slip fato φ Cntoi ω Angula vloity ( a ) Small inmnt of Subipt 0 Stagnation onition Impll inlt tation at man Impll outlt tation 3 Vanl iffu inlt tation 5 Vanl iffu outlt tation a Ai av Avag Compo Exit onition h Hub hy Hyauli iamt i Inlt onition m an SFL Skin fition lo DBL Bla loaing offiint w Tangntial ition m Root man qua Raial ition x Any tation ini th oto paag Rfn [] Japik, D. Diiv fato in avan ntifugal ompo ign an vlopmnt, in Poing of th Intnational hanial Engining Cong & Expoition, Nov [] Xu C., Amano R. S., Dvlopmnt of a low flow offiint ingl tag ntifugal ompo, Intnational Jounal of Intnational Jounal of Computational tho in Engining Sin an hani, Vol. 0, 009, pp [3] Aungi R. H., Cntifugal Compo A Statgy fo Aoynami Dign an Analyi. ASE P, Nw Yok, NY, USA, 00. [4] Xu C., Dign xpin an oniation fo ntifugal ompo vlopmnt, Poing of th Intitution of hanial Engin, Pat G, Vol., 007, pp [5] Contino R., Alalihi Z., Bambuh V. R. A., Expt ytm fo aial impll optimization. Poing of Euotubo, 00.

16 unz Shhah Youf Ebai an Quai Zuhai ohmma Al-Haman: Dign of a Singl Stag Cntifugal Compo a Pat of a iotubin Running at pm, Dvloping a aximum of 60 kw Eltial Pow Output [6] Pihizzi A., Savini., Aoynami an gomti optimization fo th ign of ntifugal ompo. Intnational Jounal of Hat an Flui Flow, Vol. 6, iu, ah 985, pp [7] Al-Zibaiy S. N., A popo ign pakag fo ntifugal impll. Comput an tutu, Vol. 55, iu, Apil 995, pp [8] Xu C., Amano R. S., Empiial Dign Coniation fo Inutial Cntifugal Compo. Intnational Jounal of Rotating ahiny, Vol. 0, 5 pag. [9] Cho S. Y., Ahn K. Y., L Y. D., Kim Y. C., Optimal Dign of a Cntifugal Compo Impll Uing Evolutionay Algoithm. athmatial Poblm in Engining, Vol. 0, pag. [0] Ibaaki S., Sugimoto K., Tomito I., Aoynami ign optimization of a ntifugal ompo impll ba on an atifiial nual ntwok an gnti algoithm itubihi Havy Inuti Thnial Rviw, Vol. 5,, ah, 05. [] Bonaiuti D., Anon A., Emini., Balaa L., Analyi an optimization of tanoni ntifugal ompo impll uing th ign of xpimntal thniqu, GT , 00. [] Vtat T., Alkaloi Z., Van n R. A., ultiiiplinay optimization of a aial ompo fo mioga tubin appliation, Jounal of Tubomahiny, Vol. 3, 3, 00, 7 pag. [3] Ingham, D. R. an Bhin, F. S., Th fft of inu hap on th pfoman of high pu atio ntifugal ompo. ASE pap, No. 74-GT-, 974. [4] Stahl, A. F., Tanoni flow poblm in ntifugal ompo. SAE, ppint No. 68C, Jan. 96. [5] Polikovky, V. an Nvlon,., Th pfoman of a vanl iffu fan. NACA. T 038, 94. [6] Bown, W. B. Fition offiint in a vanl iffu. NACA. TN 3, 947. [7] Bown, W. B. an Bahaw, G. R. tho of igning vanl iffu an xpimntal invtigation of tain untmin paamt. NACA. TN 46, 947. [8] Stantiz, J. D. Som thotial aoynami invtigation of impll in aial an mix flow ntifugal ompo. Tanation of ASE 74:374, 95. [9] Dan, R. C., Snoo, Y. Rotating wak in a aial vanl iffu. ASE., Si D, Spt [0] Johnton, J. R., Dan, R. C. Lo in vanl iffu on ntifugal ompo an pump Tanation ASE, Jounal of ngining fo pow, Vol. 88, No., Jan [] Zah A. H., Bayomi N. N., ISESCO Jounal of Sin an Thnology, Vol. 0, 7, 04, pp [3] afat A., Shahhoini. R., Ahjai. A. "Aapt ign of multitag ntifugal ompo an ompaion with availabl ata", Intnational Jounal of atial, hani an anufatuing. Vol.,, ay 03. [4] Kuauhi S. K. Baboa J. R. "Dign of ntifugal ompo fo natual ga". Vol.,, 03, pp [5] Li P. y., Gu C. W., Song Y. "A nw optimization mtho fo ntifugal ompo ba on D alulation an analyi". Engi. Vol. 8, 05, pp [6] Gui F., Rinat T. R., Saing R. P., Gotthlih J.., "Dign an xpimntal tuy on high p low flow at ntifugal ompo". IECECP, pap No. CT-39. [7] ooz L., Govouhnko Y., Pagu P., Romanko L. "Intgat onptual ign nvionmnt fo ntifugal ompo flow path ign". Poing of IECE, 008. [8] Bowa A., Paahhka C. "A viw of iffnt ign mtho fo aial flow ntifugal pump". Intnational Jounal of Sintifi Engining an Rah (IJSER). Vol. 3, 7, 05. [9] Bigg,. C., Ruiv quaati pogamming mtho fo non-lina ontaint. In Powl,. J. C.,., Nonlina optimization. 98. [30] Bigg,. C., Futh mtho fo nonlina optimization. athmati iviion, Univity of Htfohi, 999. [3] Numial optimization nt. Optima manual. Shool of Infomation in, Hatfil Polythni. Iu No.8, July 989. [3] Dallnbah, Coppag t al. Stuy of uponi aial ompo fo figation an puization. WADC Thinal Rpot 55-57, A. S. T. I. A oumnt No. AD0467, D 956. [33] Rog C., A iffuion fato olation fo ntifugal impll talling, Tan. ASE. J. of Eng. fo Pow, Vol. 00. Ot, 978. [34] Ekat D. Dtail flow invtigation within a high-p ntifugal ompo impll, Tan. ASE, Sptmb, 976. [35] Tough R. A., Toui A.., Ghaffai J., Impoving of th mio-tubin' ntifugal impll pfoman by hanging th bla angl. ICCES, Vol. 4(), pp. -, 00. [36] Fih, F. B., Dvlopmnt of van iffu omponnt fo havy uty il ngin tubohag. I. he, Confn on tubohaging an Tubohag, Lonon, Pap No. C08/86, 986, pp [] Bttini C., Cavo C., Roatlli F., Zito D., "Th Dign of th ntifugal Compo fo a 00kW mio ga tubin pow plant".