Design of Helium Cryogenic Turboexpander

Transcription

1 IJSRD Intrnatonal Journal for Scntfc Rsarch & Dvlopmnt Vol. 1, Issu 11, 2014 ISSN (onln): Dsgn of Hlum Cryognc Turboxpandr Rnu Kushwah 1 Prof. N.V. Bora 2 1,2 Mchancal Engnrng Dpartmnt, 1,2 L. D. Collg of Engnrng, GTU, Ahmdabad, Gujarat, Inda Abstract Th xpanson turbn consttuts th most crtcal componnt of a larg numbr of cryognc procss plants ar sparaton unts, hlum and hydrogn lqufrs, and low tmpratur rfrgrators. Prsnt day cryognc gas turbns ar n mor popular as thy mt th growng nd for low prssur cycls. Th prsnt study s amd at th dsgn of hlum cryognc turboxpandr of mxd flow mpllrs wth radal ntry and axal dscharg. To dtrmn th prncpal dmnsons of th turbn whl, optmum opratng spd has bn takn from dsgn charts basd on Smlarty prncpls. Th man dmnsons, thrmodynamc proprts at dffrnt stats, vlocty and angls at ntry and xt of th turbn whl wr workd out. A modst attmpt has bn mad to undrstand, standards and documnt th dsgn of cryognc turboxpandrs. Kyword: Cryognc, turboxpandr, mxd flow turbn, flow angl, flow vlocty I. INTRODUCTION Th turboxpandr or xpanson turbn consttut th most crtcal componnt of larg numbr of cryognc procss plants lk sparaton unt, hlum lqufrs and low tmpratur rfrgrators. Th prmary functon of ths unt s to produc coolng by xpandng a prcoold hgh prssur gas stram whr powr s xtractd from th flud and nthalpy of gas dcrass. Compard wth othr xpanson dvcs th us of turboxpandr offrs gratr conomy, safty and flxbty. Fg 1: Schmatc of an xpanson turbn assmbl 1.Turbn whl 2.Brak comprssor.shaft 4.Nozzl 5.Journal Barngs 6.Thrust Barngs 7.Dffusr 8.Barng Housng 9.Cold nd housng 10.Warm nd housng 11.Sals Fg. 1: NOMENCLATURE Th turboxpandr ssntally conssts of a turbn whl and a brak comprssor mountd on a sngl shaft, supportd by th rqurd numbr of journal and thrust barngs. Ths basc componnts ar hld n plac by an approprat housng, whch also contans th flud nlt and xt ducts.othr. It conssts of a shaft wth th turbn whl fttd at on nd and th brak comprssor at th othr. Th hghprssur procss gas ntrs th turbn through ppng, nto th plnum of th cold nd housng and, from thr, radally nto th nozzl rng. Th flud acclrats through th convrgng passags of th nozzls. Prssur nrgy s transformd nto kntc nrgy, ladng to a rducton n All rghts rsrvd by

2 Dsgn of Hlum Cryognc Turboxpandr statc tmpratur. Th hgh vlocty flud strams mpng on th rotor blads, mpartng forc to th rotor and cratng torqu. Th nozzls and th rotor blads ar so algnd as to lmnat suddn changs n flow drcton and consqunt loss of nrgy. 1) Turbn whl: Th turbn whl s of radal or mxd flow gomtry,.. th flow ntrs th whl radally and xts axally. Th blad passag has a profl of a thr dmnsonal convrgng duct, changng from purly radal to an axaltangntal drcton. Work s xtractd as th procss gas undrgos xpanson wth corrspondng drop n statc tmpratur. 2) Dffusr: Th dffusr s a dvrgng passag and acts as a comprssor that convrts most of th kntc nrgy of th gas lavng th rotor to potntal nrgy n th form of gan n prssur. Thus th prssur at th outlt of th rotor s lowr than th dscharg prssur of th turbn systm. Th xpanson rato n th rotor s thrby ncrasd wth a corrspondng gan n cold producton. ) Brak Comprssor: A loadng dvc s ncssary to xtract th work output of th turbn. Ths dvc, n prncpl, can b an lctrcal gnrator or a cntrfugal comprssor. II. DESIGN OF HELIUM TURBOEXPANDER Th basc nput paramtrs: Workng flud : Hlum Turbn nlt tmpratur : 11 K Turbn nlt prssur : 14 bar Turbn outlt prssur : 2.2 bar Mass flow rat : 60 g/s A. Turbn whl dsgn: Th dsgn of turbn whl has bn don followng mthod by Balj [] and Kun & Sntz [8]. Spcfc spd and spcfc damtr unquly dtrmn th major dmnsons of th whl and ts xt vlocty trangls. Spcfc spd (n s ) and spcfc damtr (d s ) ar dfnd as Spcfc spd n s Spcfc damtr d s ( h ) h For stmatng th thrmodynamc proprts at dffrnt stats along th flow passag, th softwar packag ALLPROPS 4.2 s usd. Tabl 1 rprsnts th thrmodynamc stats at th nlt of th nozzl and th xt of th dffusr accordng to nput spcfcatons Inlt (Stat In) Ext stat (x,s) Prssur (bar) Tmpratur (K) Dnsty (kg/m ) Enthalpy (kj/kg) Entropy (kj/kg K) Tabl 1: thrmodynamc stats at th nlt of th nozzl and th xt of th dffusr accordng to nput spcfcatons Usng data from abov tabl, Q x x 10 m /s Kun and sntz [8], howvr suggst two mprcal factors k 1 and k 2 for valuatng ths paramtrs. Th factors k 1 and k 2 accou fo h dff c b w h a a d causd by prssur covry and consqunt rs n tmpratur and dnsty n th dffusr. Followng th suggston of Kun and sntz [8], k & k kg/m Q k 1.Q x 1.11 x x x 10 m /s h ns k 2 (h 0,n h x,s ) 1.0x( x 10 ) J/kg From Balj[] th pak ffcncy of a radal nflow turbn corrsponds to th valu of : n s 0.54 and d s.4 Put ths valu n q. (1) rspctvly Rotatonal spd Whl damtr 15,256 Rad/sc 1,45,684 RPM D 2 16 mm Tp spd U m/s Spoutng vlocty C 0 h C m/s Vlocty Rato, 0.67 Accordng to Kun and Sntz[8], th vlocty rato U 2 / C 0 n a radal nflow turbn gnrally rmans wthn 0.65 and Th rato of xt tp damtr to nlt damtr should b lmtd to a maxmum valu of ξ D tp 10.8 mm Fg 2: Stat pont of turboxpandr Accordng to Balj[] th xt to tp damtr rato All rghts rsrvd by

3 Dsgn of Hlum Cryognc Turboxpandr should mantand abov a valu of 0.4 to avod xcssv blad blockag and nrgy loss. Hub a o λ mm For small turbns, th crcumfrnc at xt and damtr of mllng cuttrs avalabl dtrmn th numbr of blads. In ths dsgn numbr of blads (Ztr) ar chosn to b 10, and th thcknss of th blads to b 0.6mm. 1. A convrgng scton or shroud 2. A short paralll scton. Dvrgng scton Th convrgng porton of th dffusr acts as a casng to th turbn. Th straght porton of th dffusr hlps n rducng th nonunformty of flow. In th dvrgng porton, th prssur rcovry taks plac. (a)inlt vlocty trangl (b) Ext vlocty trangl Fg. : Vlocty trangls of turbn whl From vlocty trangl n fg. a β man a Comparng both quatons a a a m/s From gomtrcal consdratons, A ( ) Now, by wrtng quaton n th form of Q rsults: Q A C Whr Z tr 10 and t tr 0.6mm & Q x 10 m /s C 58.8 m/sc Put ths valu n q.(2) tan β man a β man 45.6 B. Dffusr dsgn: It plays an mportant rol n th ovrall procss. Th dffusr convrts ths mpartd kntc nrgy nto prssur rs. For dsgn purposs, th dffusr can b sn as an assmbly of thr sparat sctons opratng n srs: (2) Fg. 4: Dffusr nomnclaturs Th gomtrcal spcfcatons of th dffusr hav chosn somwhat arbtrarly. Damtr of dffusr nlt s qual to damtr of th turbn nlt. Damtr of throat of dffusr s dpndng on th shroud claranc. Th rcommndd claranc s 2% of th xt radus, whch s approxmatly 0.2 mm for whl. For damtr of dffusr xhaust, Balj[]suggstd xt vlocty of th dffusr should b mantand nar about 20 m/s wth half con angl 5.5. Agan by followng Ino t. Al [6] th bst sutd dffusng angl (tan 1 (damtr/2xlngth)) s 5 to 6 dgr whch mnmz th loss n prssur rcovry and th aspct rato lngth/damtr of 1.4 to.. Wth th abov rcommndd suggstons, th dmnsons ar slctd as, Damtr of dffus nlt, D nd 16.5 mm Damtr of throat of dffusr, D thd mm Damtr of dffusr xhaust, D xd 20 mm Dffusng angl 5.0 Gvng: Cross sctonal ara at throat, A thd mm2 Dscharg cross sctonal ara, A xd 14 mm2 Lngth of th dvrgng scton, L dd 50 mm C. Thrmodynamc stat at whl dscharg (stat ): At th xt of th dffusr, Qx x 10 m /s and A x 0.14 x 10 m 2 Ext vlocty C x 7.8 m/s Ths vlocty s blow 20 m/s as suggstd by Balj[] Ext stagnaton nthalpy h 0x h x + Ext stagnaton prssur kj/kg P 0x P + x C x x x bar All rghts rsrvd by

4 Dsgn of Hlum Cryognc Turboxpandr Nglctng losss n th dffusr, th stagnaton nthalpy at turbn xt, h 0 h 0x 7.6 kj/kg From th stagnaton nthalpy, h 0 and stagnaton prssur P 0x, th ntropy s s stmatd by [9] S kj/kg.k And statc nthalpy h h kj/kg Tp crcumfrntal vlocty U tp Rlatv vlocty at y tp 82.8 m/s W tp m/s Hghst Mach No a β tp Β tp 5.55 Whr C s s th vlocty of sound for th corrspondng stat ponts as shown n tabl. Hub crcumfrntal vlocty U Rlatv vlocty at y W W m/s a β β m/s D. Thrmodynamc stat at whl dscharg (stat ): For computng th thrmodynamc proprts at whl nlt (stat 2), th ffcncy of th xpanson procss tll stat 2 s assumd. Sxsmth[24] has obsrvd that th nozzl ffcncy nds to b btwn 0.9 and Followng Kun a d S z[ ] ozzl ffc cy η a u d Anothr mportant paramtr s th raton of nlt to xt mrdonal vlocts Cm2/Cm. Balj[87] suggsts valus btwn 1.0 to 1.25 for ths paramtr. Followng Kun and Sntz[29], ths rato s assumd to b 1.0, ladng to Cm2 Cm C 58.8 m/s Th mportant assumpton rlats th gas angl at nlt of th rotor to th corrspondng blad angl. W2 Cm m/s Thn th absolut vlocty at nlt: C m/s Th ncdnc angl: α Th ffcncy of th nozzl alongwth th vanlss spac s dfnd as η n h h h h 0.9 Snc h 01 h 0n h n kj/kg as nput paramtr, nthalpy at th xt of turbn whl: h 2 h kj/kg Thus h 2s h n h h kj/kg Th nput paramtr for ntropy s xprssd as: s n s 1 s 2s kj/kg.k Usng proprty data [], th corrspondng prssur s calculatd from h 2s and s 2s as: p 2s p 2. bar From th valus of p 2 and h 2, th othr proprts at th pont 2 s calculatd [] as: T K, kg/m and s kj/kg.k Corrspondng to ths thrmodynamc condtons: Vlocty of sound C s m/s, Spcfc hat C p kj/kgk From contnuty quaton, th blad hght at ntranc to th whl s computd as: b 2 ( ) mm ( ) E. Nozzl dsgn Fg. 5: Major Dmnsons of nozzl and nozzl van 0.8 An mportant forcng mchansm ladng to fatgu of th whl s th nozzl xctaton frquncy. As th whl blads pass undr th jts manatng from th statonary nozzls, thr s prodc xctaton of th whl. Ths All rghts rsrvd by

5 Dsgn of Hlum Cryognc Turboxpandr prodc xctaton s proportonal to th spd and th numbr of nozzl blads [8]. Th purpos of th nozzl cascad s to assur that th flow should b ncdnt on th whl at corrct angl to avod ncdnc loss. Fg..7 shows a schmatc of th nozzl rng brngng out th major dmnsons of th passags and th vans. Th dsgn of th bladng systm offrd no ral problm as long as th prssur rato across th turbn s not mor than crtcal prssur rato and as long as th tmpratur drop ffcncy dmandd dos not xcd about 80%. F. Thrmodynamc stat at throat and vanlss spac Th proposd systm uss convrgnt typs of nozzls gvng subsonc flow at nozzl xt. Rfrng to fg. 5 th nozzl throat crcl damtr s th outr boundary of th vanlss spac whl th whl damtr s th nnr crcl. If D t s nozzl throat crcl damtr and C mt th mrdonal componnt of th nozzl throat vlocty, th mass balanc quaton ylds, C mt b Whr b 1 s th hght of th passag, assumd to b 0.5 mm. Th vlocty at xt of th throat conssts of two componnts, C mt and C θ. Th mrdonal componnt s prpndcular to th nozzl throat crcl damtr, whch dtrmns th mass flow rat whras th C θ othr componnt s tangntal to th throat. Followng Rf[8], D t 1.08*D mm, ladng to C mt b Smlar to th prsnc of two vlocty componnts at th throat crcl damtr, thr ar two vlocty componnts at th ntry of th turbn whl as shown n fg.. From consrvaton of angular momntum n fr vortx flow ovr th vanlss spac, C θ m/s Thus, h t h 2 + Snc C t conssts of two vlocty componnts prpndcular to ach othr, h t h x 10 + Th rlaton btwn h t a d t gvn and th ntropy consrvaton rlaton gvn blow[9] unquly dtrmns nthalpy and dnsty at that throat. Assumng sntropc xpanson n th vanlss spac, s t s 1 s kj/kg.k From abov rlatons, h KJ g a d t kg/m Usng Rf.[], th othr proprts at that throat ar found to b p t 4 bar; T t 8 K; C st m/s And th vlocts ar obtand from quatons () and () as C t 1.9 m/s; C mt m/s C θ m/s Mach numbr: M t C t / C st 0.85 Ths lads to subsonc opraton wth no loss nrgy. G. Szng of th nozzl vans To comput th dmnsons of th throat, Kun & Sntz[8] usd th consrvaton of momntum & contnuty of flow to gt th corrct throat angl for fnt tralng dg thcknss. Usng th contnuty quaton and th dnsty at th throat, th throat wdth w t a d h h oa a gl α t ar calculatd as follows: For m tr m 0.06 kg/s and b 1 b t w t mm b 1.94 α t a a ( ) 2.49 θ It may b notd that throat nlt angl s dffrnt from th turbn nlt angl and th dscrpancy s du to th drftng of flud n th vanlss spac. Th ntal guss valu of D t s chckd from th consrvaton of angular momntum ovr th vanlss spac, D t mm θ Whch s matchd to th ntal valu of mm. Th blad ptch lngth, p n.62 mm α t s th angl btwn th prpndcular to th throat wdth w t and th tangnt to th throat crcl damtr. From fg. th damtr of th cascad dscharg (th nnr damtr of th nozzl rng) s calculatd as, D n w w co α 17.4 mm III. SUMMARY Sr. No. Paramtr Valus Unt Turbn Whl Dsgn 1 Spcfc spd ns 0.54 Rad/sc 2 Whl damtr D 2 20 mm Inlt & xt chang n h ns Enthalpy J/kg 4 Tp spd U m/s 5 Spoutng vlocty C m/s 6 Vlocty Rato U 2 / C Ey tp damtr D tp 1.5 mm 8 Ey damtr D 6 mm 9 Avrag vlocty of tp U,man and m/sc 10 Numbr of blads Z tr Thcknss of blads t tr 0.6 mm co All rghts rsrvd by 250

6 Dsgn of Hlum Cryognc Turboxpandr 12 Turbn xt volumtrc flow rat Q x 10 m /sc 1 Turbn whl xt vlocty C 58.8 m/sc 14 Man rlatv vlocty xt blad angl β man 45.6 Dffusr dsgn 1 Volumtrc flow rat at xt of th dffusr Q x x 10 m /sc 2 Dffusr nlt damtr D nd 20.5 mm Dffusr dscharg damtr D xd 20 mm 4 Dffusr throat damtr D thd 1.77 mm 5 Dffusr dscharg cross sctonal ara A xd 14 mm 2 6 Dffusr throat cross A thd sctonal ara mm 2 7 Vlocty at xt of dffusr C x 1.05 m/s Thrmodynamc stat at whl dscharg (stat )and whl nlt (stat 2) 1 Entropy at turbn whl KJ/kgs xt K 2 Enthalpy at turbn whl xt h KJ/kg Tp crcumfrntal vlocty U tp m/s 4 Rlatv vlocty at y W tp tp m/s 5 Hghst Mach No Hub crcumfrntal U vlocty m/s 7 Rlatv vlocty at y W t m/s 8 Tp angl β tp 5.5 Dgr 9 Hub angl β 40.2 Dgr 10 Absolut vlocty at nlt C m/s 11 Incdnt angl α Dgr 12 Nozzl ffcncy η n Vlocty of sound C s m/s 14 Blad hght b mm Tabl 2: SUMMARY A. Nozzl Dsgn 1 Nozzl throat crcl damtr D t mm 2 Hght of th passag b mm Throat vlocty C t 1.9 m/sc 4 Mrdonal nozzl throat C mt vlocty m/sc 5 Vlocty at xt of th throat C θ m/sc 6 Enthalpy at throat h t KJ/kg 7 Dnsty at throat t 0.76 Kg/m 8 Mach numbr M t Throat wdth w t 1.94 mm 10 Throat angl α t 2.49 Dgr 11 Innr damtr of th nozzl rng D n 17.4 mm Tabl : Nozzl Dsgn IV. CONCLUSIONS Small turboxpandrs hav found xtnsv applcaton partcularly n cryognc rfrgraton and lqufacton systms, hlum lqufrs and mrgncy powr packs. Th prsnt work dals wth th dsgn of cryognc turboxpandr for hlum rfrgraton systm. Th papr prsnts a ltratur rvw on major aspcts of cryognc turboxpandr. A comprhnsv mthodology for th dsgn of a turboxpandr has bn prsntd. Th dsgn procdur covrs th turbn whl, dffusr and thrmodynamc proprts at th outlt of turbn whl. Whl som of th dmnsons hav bn calculatd, othrs hav bn slctd basd on ltratur. REFERENCES [1] Balj, O. E. A study on dsgn crtra and matchng of turbomachns: PartA smlarty rlatons and dsgn crtra of turbns Trans ASME J Eng Powr (1972), 8101 [2] Balj, O. E. A contrbuton to th problm of dsgnng radal turbomachns Trans ASME (1952), V74, [] Balj, O. E. Turbomachns John Wly and Sons (1981) [4] Wallac, F. J. Thortcal assssmnt of th prformanc charactrstcs of nward radal flow turbns Trans ASME (1958), [5] Sxsmth, H. Mnatur xpanson turbns, C A Baly (Ed), Advancd Cryogncs Plnum Prss (1971), [6] Ino, N., Machda, A. and Ttsugawa, K. Dvlopmnt of hgh xpanson rato H turboxpandr Advancs n Cryognc Engnrng (1992), V7B, [7] Sxsmth, H., Hasnbn, R. and Valnjula, J. A. A mnatur wt turboxpandr Advancs n Cryognc Engnrng (1990), V5, [8] Kun, L.C. and Sntz, R. N. Hgh ffcncy xpanson turbns n ar sparaton and lqufacton plants. Intrnatonal Confrnc on Producton and Purfcaton of Coal Gas & Spraton of Ar, Bjng, Chna (1985) 121 [9] ALLPROPS 4.2. Computr programs for calculatng thrmodynamc proprts of fluds of ngnrng ntrst [10] Subrata Kr. Ghosh, N.Sshaah, R. K. Sahoo, S. K. Sarang, Computaton of vlocty, prssur and tmpratur profls n a cryognc turboxpandr. 18 th natonal and 7 th ISHMTASME hat and mass transfr confrnc (2006) [11] Subrata Kr. Ghosh, A numrcal modl for th dsgn of a mxd flow cryognc turbn. Intrnatonal Journal of Engnrng, Scnc and Tchnology Vol. 2, No. 1, 2010, pp (2006) All rghts rsrvd by