Advanced seal design for rotating machinery

Transcription

1 AMERICAN JOURNAL OF SCIENTIFIC AND INDUSTRIAL RESEARCH 1 Science Hβ htt://.scihb.rg/ajsir ISSN: X di:1.551/ajsir Adanced seal design fr rtating machiner E. Saber and Khaled M. Abd Mechanical Engineering Deartment Cllege f Engineering Arab Academ fr Science and Technlg Aleandria Egt ABSTRACT Labrinth and mre recentl brsh seals hae been sed etensiel in high seed rtating machiner. Deelment is still in rgress t redce the leakage rate and the frictinal resistance f these seals beside the aareness f their stabilit characteristics. A seal er similar t the brsh seal gemetr is rsed here. It is cmsed f fine stris relacing the ires f the rdinar brsh seal. A simle theretical mdel fr this stri seal is t frard here based n the assmtin that the fl thrgh it is stead laminar and incmressible. A Renlds like eqatin is deised gerning the ressre inside the seal. Calclatins f the leakage rate and the frictin resistance are carried t fr the aris arameters cnsidered and the reslts are resented and discssed in detail alng ith cmarisns ith reis rk. It is shn in this rk that the stri angle has a majr effect n the erfrmance f the seal as ell as n the frictin resistance. It is fnd that the larger the angle the lesser the leakage rate and the larger the frictin frce. The timm ale fr minimm leakage is 9 bt fr mechanical stabilit and drabilit reasns it shld be smaller. It is als fnd that the ider the stris the lesser the leakage rate fr all ales f the stri angle. The site hlds fr the frictin resistance. The sacing beteen the stris has a minr effect n the leakage rate fr small ales f the stri angle bt fr larger ales f the angle the increase in leakage becmes cnsiderable hen increasing the sacing fr angles f rder 7. Cmarisns ith reis rks n different tes f seals shed that the resent seal mdel can satisfactril be imlemented in ractice. Kerds: Nn-Cntact seals Labrinth seals Brsh seals Rtating machiner. INTRODUCTION Seal technlg las an imrtant rle in cntrlling end leakage fl. Althgh the labrinth seal technlg is er ell deeled leakages are still high. The need fr a sealing technlg ith gd leakage sealing erfrmance and cmact sie has risen. Brsh seals hae flfilled sch cnditins. The brsh seals are designed t cntact the rtr. The are seeral times better leakage erfrmance eight redctin and sace reqirements than labrinth seals. Cmared t finned labrinth seals brsh seals can maintain a mch higher ressre difference. The tcme is a mch mre stable and balanced sealing sstem that is nlikel t let leakages take lace. Mllen et al [1] mdeled the tdimensinal fl field in a linear brsh seal cnfigratin and determined the fl field nmericall sing the finite element methd. The stdied the temral distrbance f the stream fl field. The stdied als the effect f tangential fl f the stream bndar. Frm their reslts the calclated fl rates ere in agreement ith reis eerimental reslts. Bran et al [] carried t fl isaliatin in simlated brsh seals sing a shining f a lanar laser sheet f light thrgh the regin f interest in the brsh ths making isible the magnesim ide seed articles that trace the flid fl. Their fl isaliatin techniqe alled definitin f bth lcal fl strctre inside the ids f the rs matri and qalitatie and qantitatie fl descritin at the entr sectin and at the eit f rs matri. The inestigated als the ressre dr beteen single and t seqentiall sitined brsh seals. The intrdced a blk fl mdel and cmared their reslts against blished engine brsh seal data. Schlmberger et al [3] carried t eerimental inestigatins n the effects f eccentricit n brsh seal leakage fr air at ambient temeratre and satrated steam bth at nnrtatinal and l rtatinal seeds. The cmared their reslts ith an annlar seal fr air and standard labrinth seal fr steam. The determined that large eccentricities did nt damage the brsh seal; heer the rtr srface as rn indicating that a

2 Am. J. Sci. Ind. Res. 11 (1): harder srface as reqired. Shaft rtatin did nt affect brsh seal erfrmance in air bt it significantl increased leakage in steam. The brsh seal had ler leakage rates than thse redicted fr cmarable annlar and labrinth seals. Hendricks et al [4] discssed design similitde f brsh seal ith a blk fl mdel based n fls in rs media and rb srface cating. Their fl calclatins ere the sm f leakage fl thrgh the bristles the clearance at the interface beteen the srface and bristles and the clearance beteen the srface and backing late. Their reslts f fl calclatins ere in agreement ith the reis eerimental reslts. Carlile et al [5] inestigated the leakage erfrmance f a brsh seal ith gases rking flids; air helim and carbn diide fr seeral bristle /rtr interference b sing a taered rtr at static and l rtr seed cnditins. The cnclded that the brsh seal redced the leakage in cmarisn t the annlar seal t 9.5 times. Additin f a lbricant redced the leakage b.5 times hen cmared t a nn-lbricant brsh seal. Dler et al [6] resented a mdel f bristle bed cnsisted f a heagnal circlar clinder arrangement in rder t std the cratre effects n the leakage fl thrgh the brsh seal. The sed a single arameter effectie brsh thickness t crrelate the leakage fl thrgh the brsh seal. The effectie brsh thickness as defined as a cnstant beteen the jrnal diameter and the mean diameter f the brsh. The cmared their reslts against aailable eerimental data fr the same mdel frm different srces. The demnstrated that the mdel effectiel accnts fr the effect f the seal cratre and the signal arameter as indicatr f brsh seal leakage effectieness. Ch and Dler [7] carried t eerimental inestigatins n a single stage and mlti stage brsh seals and ne reference labrinth seal t determine the erfrmance characteristics f brsh seals fr alicatin in limited-life gas trbine engines. The designed and bilt an eleated temeratre rtating test rig t test labrinth and brsh seals in simlated sbsnic and sersnic engine cnditins. The reslts frm their tests demnstrated that brsh seals leaked less cmared t labrinth seals eseciall fr sbsnic limited-life engine alicatins. Ths reslting in significant engine erfrmance imrements. Bale and Lng [8] carried t eerimental and theretical stdies f the fl and ressre distribtins in a brsh seal. Their mdel assmed laminar and cmressible fl thrgh rs media. Their measrements f the mass fl rate tgether ith radial and aial distribtins f ressre ere taken n a nn-rtating eerimental rig. The sed the eerimental data t estimate the seal rsit. The assmed the erall rsit cnstant ith a ariatin in the bristle matri. Cmarisn beteen these t cases shed sme difference in the distribtin f ressre in the bristle matri. Their cmarisns beteen measred and redicted fls thrgh the seal as generall gd cnsidering the erall simlicit f their theretical mdel. Handericks et al [9] carried t eeriments n dal brsh and labrinth cmressr discharge seals in a T-7 engine test.. The test cnditin inclded cmressr discharge ressre t 1 MPa temeratres 47C erating seeds t 43 rm and srface seeds t 16 m/s ith dr ambient air as the rking flid. The fel cnsmtin as less fr the dal brsh than fr the labrinth seal. The cnclded that the brsh seal leaked less than the labrinth seal. Che et al [1] deeled a mdel f brsh seal in hich the bristle ack as treated as an aismmetric anistric rs medim ith nnlinear rs resistance cefficients. The eqatins ere sled sing cnentinal cmtatinal flid dnamics techniqes t gie redictin f fl rate ressre distribtin elcit field and bending frces n the bristles. The bristle aerdnamic frces ere sed in a searate calclatin t estimate bristle bending and reactin frces n the shaft and backing late. Their redictin fr the brsh seal ere in agreement ith eerimental bseratins. Frm their reslts a nnlinear rs resistance la gae better agreement ith measrement than the linear Darcian treatment. Sharatchandra and Rhde [11] resented a nmerical std f the effects f rtr indced sirl elcit n the erfrmance f brsh seals. The sed the Naier-Stkes eqatins in a tdimensinal analsis t btain the elcit and ressre fields fr an idealied brsh seal cnfigratin here the inclinatin f the bristles as neglected. Their cmtatins ere in gd agreement ith measrements fr the similar fl acrss tbe banks. Sharatchandra and Rhde [1] inestigated the aerdnamic bristle frce distribtins in brsh seals sed in aircraft gas trbine engines. These frces ere resnsible fr the nset f bristle ti lift-ff frm the rtr srface hich significantl affected brsh seal erfrmance. In rder t achiee that the sed Naier-Stke fl simlatin in a streamise eridic mdle f bristles crresnding t the staggered sqare cnfigratin. The stdied als the effect f bristle sacing and bristle inclinatin angle. The fnd that the lifting 59

3 Am. J. Sci. Ind. Res. 11 (1): bristle frce increased ith redced intra-bristle sacing and increased inclinatin angle. The rimar effects f decreasing the bristle inclinatin angle ere a decrease in the tangential frce cmnent and a slight increase in the aial frce cmnent. Shrt et al [13] carried t eeriments n a single stage brsh seals in rder t increase ressre caabilit er stage redce bristle ti cntact ressre and insring stable leakage erfrmance f brsh seals. The deeled a design fr the seal ith thicker bristle diameter ider bristle ack and ider clearance beteen back late and bristles ack. Hendricks et al [14] stdied and tested a set f inner diameter /ter diameter bidirectinal brsh seals t redce the leakage lsses in case f the leakage fl changed directins. Frm their data the indicated that the brsh seals ere caable f sealing sitie r negatie ressre drs ith resect t the aial directin and the erfrmance f the machine increased frm 3% t 1%. Che and hgg [15] deeled a mdel fr redicting leakage fls thrgh the bristle ack f a brsh seal. The treated the bristle ack as a rs medim. Their redictins frm a ne-dimensinal mdel ere in agreement ith a ide range f eerimental data aailable frm literatre fr seals ith a bristle ack t rtr interference fits. The als redicted a reasnable estimatin f the bristle ack thickness and cnclded that the leakage fl increased rrtinal t the area aailable beteen the backing ring and shaft. O Neill et al [16] carried t eeriments n different designs f brsh seal mltile seals and a single brsh seal in rder t std the effect f instabilit n sealing erfrmance hen mltile seals ere erated in series at high ressre lading. Demirgl et al [17] resented a - D laminar fl analsis sing the finite element analsis. Their mdel redicted fl rate erss ressre dr fr a gien fl regin. The brsh seal fl dmain as diided int reresentatie smaller cells in hich simlatin takes lace. The cells ere chsen sch that tgether the can reresent the hle seal. A cell is laced in the beginning a secnd ne in the middle and fr cells at each crner f a sqare. Then ther cells ere added in rder t etralate the reslts fr a fll seal. In arallel t the nmerical rk the deeled a simle analtical mdel. This simlified sltin f the -D laminar Naier-Stkes eqatin redicted ressre dr acrss t bristles. Their reslts frm the nmerical rk ere als cmared t their analtical sltin. Their reslts shed that the resented mdel as caable f analing bristles cnfigratins ith realisticall small inter-bristle gas and in a staggered fashin. The mdel shed reasnable accrac hen cmared ith aailable eerimental data. It cld be sed t ealate aris seal designs befre an eensie testing rcess. The mdel redictins cnfirmed the trend f linear ressre dr acrss the seal thickness. Trner et al [18] resented eerimental inestigatin and a CFD mathematical mdeling f clearance brsh seals ith the rtr t measre the distribtin f aial and radial ressre and their leakage characteristics. The sed.7mm and.75 mm clearances ith ressre ratis t 4 ith the seal fl ehasting t atmsheric cnditins. Their mdel treated the bristle ack as an aismmetric anistric rs regin. The calclated frm the CFD analsis the aerdnamic frces n the bristles the bristle mements stresses and bristle and rtr lads. The reslts shed that the fl thrgh a brsh seal as er deendent n the sitin f the bristles. If a brsh seal as bilt ith a clearance the aerdnamic frces ill tend t me the bristles tards the rtr. The mement as er deendent n the balance beteen the nrmal aerdnamic frces and the frictin leels in the brsh ack. Their stdies cnfirmed that the se f a nn-darican arach gae better agreement t eerimental reslts. Las et al [19] described a recentl deeled hbrid brsh cket damer seal that cmbines high daming ith l leakage. The main bjectie f their eeriments as t measre the daming and leakage f brsh hbrid seals and si-bladed labrinth seals f the same rking dimensin fr cmarisn. Their test rig as cnnected t an electrmagnetic shaker. The shaker cntains an imedance head that tts acceleratin and frce signals in time t ecite the seal jrnal. The fl rate as cntrlled sing a nematic cntrl ale in the ressre range frm 1 t 9. bars. The cnclded that the brsh hbrid cket damer seal leaked less than the labrinth seal hile rdcing t t three times mre daming than the riginal cket seal. The aim f the resent rk is t design a ne te f nn-cntact seal intrdced as stri seal. The seal is er similar t the brsh seal gemetr. MATHEMATICAL MODEL Fig.1 shs the stri seal gemetr and crdinate sstem. In Cartesian crdinate and the Naier-Stkes and the cntinit eqatins fr stead laminar incmressible and is-iscs fl are 6

4 Am. J. Sci. Ind. Res. 11 (1): (1) μ ρ () μ ρ (3) μ ρ (4) Where and are the elcities in the and directins resectiel. (a) The stri seal cnfigratin and crdinate sstem. (b) The stris and rtr. Fig.1: The stri seal gemetr and crdinate sstem The stri arra f stri seal is inclined t the rtr b an angle. T simlif the eqatins f mtin the Cartesian crdinate can be transfrmed t an bliqe te f crdinates. Fig. shs the bliqe sstem f crdinates. The Cartesian crdinates and ma be ritten in terms f the bliqe crdinates as flls: (5) cs sin The elcit cmnents and in terms f and ma be ritten as. (6) sin cs Fig. Sstem f bliqe crdinates Sbstitting frm the relatins (5) and (6) int Eqns.1 t 4 cnsidering the rder f magnitdes ( ) O 1 θ ( ) O 1 ( ) O 1 ( ) O 1 R b O and () O 1 R L O and neglecting higher rder terms e get the flling dimensinless eqatins: (7) sin θ (8) (9) sin L R Where L b R θ

5 Am. J. Sci. Ind. Res. 11 (1): b and R μ The bndar cnditins f the elcit cmnent are h ωr h k and b Integrating Eqns.7 and 8 tice ith resect t and sing the elcit bndar cnditins e hae 1 sin [ h] k (1) θ h [ h ] (11) 1 R sin L Sbstitting eressins (1) and (11) int the cntinit Eqn.8 and taking the satial aerage b integrating it. r. t. acrss the film e hae θ 3 R h θ L 3 h 6k h k h 1 (1) sin θ sin t And in the absence f an sqeee elcit (stead h state) e can bt. t The flling Renlds-like eqatin gerning the dimensinless ressre distribtin inside the seal is btained 3 R h θ θ L 3 h 6 h sin θ (13) here μ k b ω Eqn.13 is sbject t the bndar cnditins: ( θ) i ( θ1) e (14) ( ) (π ) Where i and e are the dimensinless ressre at inlet and eit resectiel. Becase the shaft ma be eccentric ith the seal ring (casing srface) the ga that eists beteen the shaft and casing srfaces is nt nifrm alng the circmference f the casing. When the idth f the ga is measred alng the casing radis it is referred t as the ga idth h. Figs. 3 and 4 sh the seal ga and the stri shae alng ith the sstems f crdinates. Fig.3 The seal ga and crdinate sstem. Fig.4 Stri shae and crdinate sstem T rder ( e R ) the arimate eressin fr the ga idth in aligned rigid shaft is h g b e cs (15) R Using the transfrmatin: h g h g hg sin and - tan Sbstitting frm (15) int (16) b hg sin 1 c εcs θ hg cs R (16) (17) h g h g b c e c ε are the dimensinless ga b c idth the dimensinless clearance and the eccentricit rati resectiel. The ariatin f the stri idth ma be ritten in dimensinless frm as 6

6 Am. J. Sci. Ind. Res. 11 (1): ( 1 c) φ H sin θ (18) sin here φ is defined as stri shae factr. A small ale f φ leads t a thick stri hile large ne gies a thin stri. The dimensinless film thickness ma then be ritten as h 1 sin 1 cεcs θ hg 1 sin b R cs φ {( 1 c) sin θ} (19) The leakage fl rate thrgh the seal ring takes lace frm the high ressre side t the l ressre side in the aial directin. Q θ h Rddθ Q Q blk 1 R sin 1 L Rb π π h ddθ 3 h dθ () The frictin frce n the shaft is btained b integrating the shear stress τ er the shaft srface L π F R dθd τ f b Ff F RL f μ 1 π h 1 sin dθ d h (1) here F f is the dimensinless frictin frce. RESULTS AND DISCUSSION Fig.5 shs the dimensinless leakage fl rate as a fnctin f the dimensinless ressre dr fr different ales f stri angle. The reslts sh that the relatinshi beteen the dimensinless leakage fl rate and the dimensinless ressre dr is linear irresectie f the ale f the stri angle. It is clear that the larger the stri angle the lesser the leakage rate. The timm ale is the 9 angle bt the stri angle shld alas be less than 9 fr mechanical stabilit reasns. On ther hand Fig.6 shs the ariatin f the dimensinless frictin frce ith the dimensinless ressre dr fr the same stri angles selected reisl. It is seen that fr small ressre dr ales the rate at hich the frictin frce increases ith the increase f ressre dr is er mch larger than that fr larger dimensinless ressre dr ales sa larger than arimatel 1.5. This behair is er mch rnnced fr larger ales f the stri angle. The effect f the stri angle n the leakage rate can be shn mre clearl frm Fig.7. A tentatiel selected ale f dimensinless ressre dr sa Δ 1 is sed t rdce the relatinshi fr different ales f the dimensinless sacing arameter t g /t s. It is bis that the sacing arameter has in general minr effect n the leakage rate fr small ales f the stri angle bt fr larger ales sa fr 7 angle dble t g /t s leads t an increase in the leakage rate b arimatel ercent. A rerdctin f this figre is in Fig.8 hich the effect f sacing arameter n the erfrmance ο 5 ο 7 ο DIMENSIONLESS PRESSURE DROP Fig.5 The ariatin f the dimensinless leakage rate erss the dimensinless ressre dr fr different ales f the stri angle ο 5 ο 7 ο DIMENSIONLESS PRESSURE DROP Fig.6 The ariatin f the dimensinless frictin frce erss the dimensinless ressre dr fr different ales f the stri angle. 63

7 Am. J. Sci. Ind. Res. 11 (1): tg / ts 1 tg / ts 1.5 tg / ts Fig.7 The ariatin f the dimensinless leakage rate erss the stri angle fr different ales f the sacing arameter t g /t s tg / ts 1 tg / ts 1.5 tg / ts Fig.9 The ariatin f the dimensinless frictin frce erss the stri angle fr different ales f the sacing arameter t g /t s. dimensinless leakage rate ο 5 ο 7 ο Sacing arameter (tg/ts) Fig.8 The ariatin f the dimensinless leakage rate erss the sacing arameter t g /t s fr different ales f the stri angle. The effect f the sacing arameter n the dimensinless frictin frce is gien in Fig.9. Increasing the ale f the sacing arameter t g /t s leads t a cnsiderable decrease in the frictin frce and this is er mch rnnced at smaller ales f the stri angle. Fig.1 shs the ariatin f the dimensinless leakage rate ith the stri angle fr different ales f stri thickness t shaft radis rati. It seen that this rati ( t s /R ) has a minr effect n the erfrmance irresectie f the ale f stri angle. The site hlds in Fig.11 fr the frictin frce here the rati t s /R has a srrisingl cnsiderable effect n it. An increase f the rati t s /R frm sa. t.5 redces the dimensinless frictinal frce arimatel fr time er the hle range f stri angle. DIMENSIONLESS AXIAL LEAKAGE ts / R. ts / R.3 ts / R.4 ts / R Fig.1 The ariatin f the dimensinless leakage rate erss the stri angle fr different ales f dimensinless stri thickness. 64

8 Am. J. Sci. Ind. Res. 11 (1): ts / R. ts / R.3 ts / R.4 ts / R C / b.5 C / b.1 C / b Fig.11 The ariatin f the dimensinless frictin frce erss the stri angle fr different ales f dimensinless stri thickness. The clearance beteen the stri and the shaft is seen frm Fig.1 t hae a little effect n the leakage rate. Althgh the ale f the dimensinless clearance c/b des nt affect the leakage it des affect the frictin frce t a great etent as can be seen in Fig.13. Increasing the ale f c/b frm.5 t.15 reslts in a decrease frm abt 5 % at 9 t less than 1 % f the riginal ale at. Fig.14 shs the ariatin f the dimensinless leakage rate ith the stri angle fr aris stri idth t shaft diameter rati. It is clear that the ider stri the lesser the leakage rate fr all the ales f. The site effect is tre fr the dimensinless frictin frce fr all ales f as seen as in Fig.15. Rerdctins f Fig.14 and 15 are gien in Fig.16 and 13 resectiel. It is qite clear that fr relatiel ide stri the leakage rate is er fr all ales f. The relatinshi beteen the frictin frce and the stri idth is fnd t linear fr all ales f C / b.5 C / b.1 C / b Fig.1 The ariatin f the dimensinless leakage rate erss the stri angle fr different ales f the dimensinless clearance Fig.13 The ariatin f the dimensinless frictin frce erss the stri angle fr different ales f the dimensinless clearance L / D. L / D.3 L / D.4 L / D Fig.14 The ariatin f the dimensinless leakage rate erss the stri angle fr different dimensinless stri idth L / D. L / D.3 L / D.4 L / D Fig.15 The ariatin f the dimensinless frictin frce erss the stri angle fr different dimensinless stri idth. 65

9 Am. J. Sci. Ind. Res. 11 (1): ο 5 ο 7 ο L / D Fig.16 The ariatin f the dimensinless leakage rate erss the dimensinless stri idth fr different ales f the stri angle L / D Fig.17 The ariatin f the dimensinless frictin frce erss the dimensinless stri idth fr different ales f the stri angle. Fr all the reslts cnsidered s far the shaft and stris ack inner diameters are cncentric. Fig.18 shs the ariatin f the leakage rate ith eccentricit rati fr aris stri angles. It can easil be arged that the eccentricit rati has n sensible effect n the leakage rate fr all ales f bt in Fig.19 has a nticeable effect n the frictin fr eccentricit rati greater than arimatel.4 fr the ales f cnsidered here ο 5 ο 7 ο ECCENTRICITY RATIO ( e / c ) Fig.18 The ariatin f the dimensinless leakage rate erss the eccentricit rati fr different ales f the stri angle ο 5 ο 7 ο ECCENTRICITY RATIO ( e / c ) Fig.19 The ariatin f the dimensinless frictin frce erss the eccentricit rati fr different ales f the stri angle. CONCLUSIONS In this rk the flling cnclsins are dran: 1- The stri angle has a majr effect n the erfrmance f the seal as ell as n the frictin frce. Since the larger the stri angle the lesser the leakage rate and the larger the frictin frce. The timm ale fr minimm leakage rate is 9 bt fr mechanical stabilit and drabilit reasns it shld be less than that. - The sacing beteen the stris has a minr effect n the leakage rate fr small ales f the stri angle bt fr larger ales sa fr 7 angle the increase in leakage rate 66

10 Am. J. Sci. Ind. Res. 11 (1): reaches arimatel ercent hen the sacing is dbled. 3- The stri thickness has a minr effect n the erfrmance irresectie f the ale f the stri angle. 4- The clearance beteen the stri and the shaft has a little effect n the leakage rate bt increasing the clearance reslts in a cnsiderable decrease in the frictin frce hich arimatel reaches 5 ercent fr 9 stri angle. 5- The ider the stri the lesser the leakage rate fr all ales f stri angle site hlds fr the frictin frce. NOMENCLATURE b the seal ga length m. c radial clearance m. c dimensinless clearance c c/b e eccentricit m. F frictin frce N. f F dimensinless frictin frce f Ff Ff /( μ RL/b) h ga idth m. g h bliqe ga idth h h /sin m. g g g h g dimensinless bliqe ga idth h g h g /b. h film thickness m. h dimensinless film thickness h h/b k Velcit rati k ωr/. L stri idth m. ressre Pa. dimensinless ressre ( μ R / b ) Characteristic dimensinless ressre / k. R shaft radis m. R e Renlds nmber R e ρ b/μ. Q Leakage fl rate thrgh the seal m 3 / s. Q Dimensinless leakage fl rate thrgh the seal Q Q/ b L k. t g The ga beteen the stris m. t s Stri thickness m. Velcit cmnent in '-directin m/s. Velcit cmnent in -directin m/s. Dimensinless fl elcit cmnent in - directin /. Reference elcit m/s Velcit cmnent in -directin m/s. Velcit cmnent in -directin m/s. Dimensinless elcit cmnent in - directin / Velcit cmnent in -directin m/s. Velcit cmnent in -directin m/s. Dimensinless elcit cmnent in - directin /. ( ) Cartesian c-rdinate sstem. ( ) Obliqe c-rdinate sstem. ( θ ) dimensinless bliqe c-rdinate sstem θ /R /b /L Greek Smbls Stri angle. ε Eccentricit rati ε e / c. Stri shae factr. φ μ iscsit Pa s. ν Kinematic iscsit m /s θ ρ τ ω Angle crdinate in circmferential 3 θ R Densit kg/ m. Shear stress er the shaft srface N/ m. Anglar elcit rad/s. REFERENCES [1] R. Mllen M. Bran and R. Hendricks Nmerical Mdeling f Fl in Simlated Brsh Seal Cnfigratins AIAA Paer N [] M. J. Bran R. C. Hendricks and V. A. Canacci Nn- Intrsie Qalitatie and Qantitatie Fl Characteriatin and Blk Fl Mdel fr Brsh Seal Prceedings f the Jaan Inter. Triblg Cnf. Naga 199. [3] J. A. Schlmberger M. P. Prctr and R. C. Hendricks Eccentricit Effects n Leakage f Brsh Seal at L Seed NASA TM [4] R.C. Hendricks S. Schlmberger M.J. Bran F. Ch and R.L. A Blk Fl Mdel Of A Brsh Seal Sstem ASME Paer N. 91-GT [5] J. A. Carlile R. C. Hendricks and D. A. Yder Brsh Seal Leakage Perfrmance With Gases Wrking Flids at Static and L Rtr Seed Cnditins J. f Gas Trbine and Per l [6] C. A. Dler R. E. Ch and G. F. Hlle ''Simle Effectie Thickness Mdel fr Circlar Brsh Seals AIAA Paer [7] R. E. Ch and C. A. Dler Perfrmance Characteristics f Brsh Seal fr Limited- Life Engines Trans. ASME Vl [8] F. J. Bale and C. A. Lng A Cmbined Eerimental and Theretical Std f Fl and ressre Distribtins in a Brsh Seal Trans. ASME Vl

11 Am. J. Sci. Ind. Res. 11 (1): [9] R. C. Handericks T. A. Griffin and T. R. Kline Relatie Perfrmance Cmarisn Beteen Baseline Labrinth and Dal-Brsh Cmressr Discharge Seals in a T- 7 Engine Test NASA TM [1] J. W. Che B. L. Larth and P. J. Millener Mathematical Mdeling f Brsh Seals Int.J. Heat and Flid Fl Vl [11] M. C. Sharatchandra and D. L. Rhde Cmted Effects f Rtr Indced Sirl n Brsh Seal Perfrmance Part 1 : Leakage Analsis Trans. ASME Vl [1] M. C. Sharatchandra and D. L. Rhde Cmted Effects f Rtr Indced Sirl n Brsh Seal Perfrmance Part : Bristle Frce Analsis Trans. ASME l [13] J. Shrt P. Bas A. Datta R. Leenthal and R. Prir Adanced Brsh Seal Deelment AIAA Paer N [14] R. C. Hendricks J. Wilsn T. W and R. Fler ''Bidirectinal Brsh Seal" NASA TM [15] J. W. Che and S. I. hgg Prsit Mdeling f Brsh Seals Jrnal f Triblg Vl [16] A. T. O'NeillP. A. Withers S.I. Hgg and T. V. Jnes Mltile Brsh Seals in Series ASME Paer N. 97- GT [17] M. Demirgl M. F. Aksit and J. A. Tich A Nmerical Std f Brsh Seal Leakage Fl AIAA Paer N [18] M. T. Trner J. W. Che and C. A. Lng Eerimental Inestigatin and Mathematical Mdeling f clearance Brsh Seals ASME Jrnal f Engineering fr Gas Trbines and Per Vl [19] H. E. Las J. M. Vance and S. E. Bchanan Hbrid Brsh Pcket Damer Seal fr Trbmachiner Trans. ASME Vl