TRANSIENT PROCESES FOR VENT-EJECTORS ASSISTED BY COANDA EFFECT

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1 Scieific Buei of he Poiehica Uiversiy of Timisoara Trasacios o Mechaics Specia issue The 6 h Ieraioa Coferece o Hyrauic Machiery a Hyroyamics Timisoara, Romaia, Ocober -, TRANSIENT PROCESES FOR VENT-EJECTORS ASSISTED BY COANDA EFFECT Vicor BENCHE, Prof. Deparme of Thermoyamics a Fui Mechaics Trasivaia Uiversiy of Brasov Age HUMINIC, Assis. Prof. Deparme of Thermoyamics a Fui Mechaics Trasivaia Uiversiy of Brasov ABSTRACT I his paper are efie he rasiory processes for some origia Coaă ve-ejecors - exhausers. I his way, i is suie he kickig of he ejecio for a apparaus wih epressive baes or ierior auar wig wha is fucioig i saioary omia regime. I is examie he possibiiy a avaages of he iscoiuous suppie wih primary fui, he ejecor havig i his way a iermie fucioa regime. There are efie he paricuariies of he ejecors wih iscoiuous, pusaory iucio, regarig he ejecor wih epressive ambour (pae RO 88769) a he roaive wih siig baes, boh wih Coaă overappe effecs, je-faps, Magus. The ejecors yamics is approache from he ecoomic poi of view, he aayic reaios a he umerica exampes eaig o cosrucive a fucioa opimizaios, a raisig heir performace (improve epressio iesiy, icrease fuiic iucio, a a more uiform ejecio a.o.). KEYWORDS Trasie processes, ve-ejecors, Coaã effec ABBREVIATIONS carryig fui ep epressive rivig fui rv rivig w epressive wave ka kickig of he aspiraio mf mixure fui s so eivery uc ED exhaus uc ie uc. INTRODUCTION I previous pubishe papers of he auhors, [5], [6], here were presee some probems a resus cocerig he opima esig, from eergeicay poi of view, of a few isaaios use i raspor of he fuis uer pressure, as he ve-ejecors, cassica or assise by Coaa s effec a hyrauic rives. Aso, he way of usig of he evices use for he coro of fow raes, as vaes, aps a oher, was approache from he same cosieraios. I his paper are emphasise a efie he rasie processes for some origia ve-ejecors/ exhausers assise by Coaa s effec. I his orer i is suie he kickig of he ejecio for a apparaus wih epressive baes or ierior auar wig wha is fucioig hem i saioary omia regime. I is examie he possibiiy a avaages of iscoiuous suppie wih primary fui, he ejecor havig i his way a iermie fucioa regime. There are efie he paricuariies of he ejecors wih iscoiuous, pusaory iucio, regarig he ejecor wih epressive ambour wih rivig sos [] a he roaive wih siig baes, boh wih Coaa overappe effecs, je-faps, Magus. The ejecors yamics is approache from he ecoomica poi of view, he aayicay reaios a he umerica exampes eaig o cosrucive a fucioa opimizaios, a raisig heir performace (improve epressio iesiy, icrease fuiic iucio, a more uiform ejecio a.o.). Figure shows he scheme, i axia secio, of a cassica ierior ejecor assise by Coaa s effec. The epressive ozze (exhauser) ca be forme by wo ieica epressive baes (faps) i a symmerica posiio reaive a he ogiuia axe (for a recaguar secio of he exhaus uc), or by a auar wig (for a auar secio of he exhaus uc). The foowig oaios were mae: : ie uc, by egh ; N : epressive ozze; ep

2 N ep ED m w s m mix N rv V, m Figure. Scheme of a cassica ierior ejecor assise by Coaa s effec N rv : rivig ozze (coroabe oe); w s : wih of so (submiimerica, ajusabe oe) ;, : characerisic imesios of eivery uc of he rivig fui (iameer a egh); : mass fow rae of he carryig fui (secoary fui); : mass fow rae of he rivig fui (primary fui), coroabe by he vave V ; mf : mass fow rae of he mixure resua fui; i represe he sum bewee a. m & & + & mf m m [kg/sec] (). THEORETICAL APPROACHING The aayse rasie processes i his paper are cocerig he auchig of he rivig fui hrough he rivig ozze, coroe wih he ai of he vave a he sabiizaio of he coiuous suppie process. Aso, are akig io cosieraio he geeraio of a epressive wave ue o he Coaa moveme, propagaio of his o owsream a he kickig of he secoary fui hrough he ie ozze. The foowig Equaio is a pracica oe for he compuaio of he mass fow rae of he rivig fui, reae as a icompressibe oe wih he esiy c, wha is auche hrough he so: p µ As [kg/sec] () µ represe he coefficie of fow rae; ca be compue wih he Equaio (); is he area of he so; p is he gauge pressure of he rivig fui. A s α f µ α + f [-] + ζ is he Coriois coefficie is he pipe fricio facor; () ζ represe he sum of oca coefficies of hea oss; The o-imesioa fucio of variaio of veociy v i he ime of rivig fui, respecivey of fow rae, ca be efie by he foowig Equaio: e ϕ ( ) [-] () e + represe he omia ime, compue wih he Equaio (5): [s] (5) v v [m/s] π (6) Usig he fucio ϕ ( ), he foowig rasie quaiy are efie: Mass fow rae of rivig fui: m & ( ) ϕ ( ) & (7) m Pressure of rivig fui: p ( ) ϕ ( ) (8) p

3 Hyrauic power of rivig fui: N ( ) ϕ ( ) (9) N The omia hyrauic power is evauae wih Equaio (): p N [W] () Figure epics he variaio of he fucio ϕ ( ) versus he reaive ime. ω() Figure. Variaio of ϕ ( ) versus The maximum vaue of his fucio is.6. From echica (pracica) poi of view he rasie process ca be cosiere fiishe whe m & ( ).96. The ime of rasiio, ecessary for he kickig of he fow hrough eivery uc, rivig ozze, ierior faps, fiishe whe he Coaa moveme appears a is a sabiize oe, ca be compue usig he Equaio: 9 v.89 v.89 [s] () A ecoomica suy of he eivery evice of he ejecor ivoves he miimisaio of he omia eergy, ecessary for he carryig uer pressure of rivig fui hrough he force pipe (,, f ) o he rivig ozze. This ecoomica cacuus is eaig a a opima ier iameer of eivery uc, op. The omia hyrauic eergy, E, wha is ecessary for he ouchig of he seay work regime has hree compoes, as foowig: The eergy ecessary for he carryig of rivig fui hrough eivery uc a he work chamber of he rivig ozze, havig he voume V N rv ; his compoe is square fucio i erm of mass fow rae: E + π V π N rv [Nm] () The eergy ecessary for hea oss: E f ζ π + [Nm] () The eergy ecessary for icreasig of he pressure of rivig fui from eivery uc a he work chamber of rivig ozze a he omia work pressure p : E π + 8 π V N rv p [Nm] () The oa eergy E E + E + E is a compex fucio i erm of iameer of eivery uc,. A opima vaue of his ca be compue from coiio ha he oa eergy E E + E + E E is miima, E, or. A origia, simpifie Equaio is he foowig: op. ( + ζ ) p [m] (5) The Equaio use for he compuaio of he oa rasie eergy, i erm of he variaio fucio, ca be wrie as: ϕ + E ( ) E ( ) + ( E E ) ϕ ( ) (6) The uraio of he rasie process represes he ecessary ime for he accumuaio of he oa eergy E a he omia hyrauic parameers, p a N. The Equaio use o compue he veociy a w of propagaio of epressive wave wha characerise he Coaa moveme o fap hrough he ie uc is (Jukovski): E δ a w [m/s] (7) + E δ is he buk mouus of easiciy; is he esiy; represe he sum of oca coefficies of hea oss; is he hyrauic equivae iameer; is he hickess of he ie uc. 5

4 The Equaio (7) has a arge appicabiiy i he cases of icompressibe fuis (iquis). For he compressibe fuis (air, mixure of gases, vapours ec.) i a aiabaic sae, Equaio (7) ca be wrie i a simpifie form: a w R T [m/s] (8) is he aiabaic cosa; R is he gas cosa; T is absoue emperaure; Kowig he vaue of veociy a w, he ime ka ecessary for he kickig of he aspiraio ca be compue wih he Equaio: ka [s] (9) a w. NUMERICAL APPLICATION NO. As primary (rivig) fui is cosierig waer wih he foowig characerisics: kg/m, 9.7 N/m 5, p 7 N/m, 5 kg/hr, v s 7. m/s (veociy of rivig fui hrough so). The mai geomerica a fucioa N () [W] 5 p () [N/m ] characerisics of he rivig ozze are: A s mm, 5 µ.6, ζ. 5,. 7 m, VN rv m. Usig Equaio (5) is obaie he foowig vaues of opima iameer of eivery uc, veociy of rivig fui hrough eivery uc a Reyos umber: op 7 m, v. 7 m/s, R e 5. For a smooh uc, he pipe fricio facor is (Basius) f. 7. Wih Equaio (), () a () are eermie he compoe of he oa eergy: E 8.5 N m, E.8 Nm, E. 7 Nm a E. Nm. The oa rasie eergy is: E ( ).7 ϕ ( ) +.5 ϕ ( ) The o-imesioa fucio is cosiere:. () e ϕ ( ) [,] (). e + Usig Eq. (5) a () are obaie:. 8 sec. a 9. sec. Figure show he variaios of ( ), p ( ) a N versus he reaive ime. m () [kg H O / h] N () p () m () Figure. Variaio of ϕ ( ) versus As he secoary (carryig) fui is cosiere he amospheric air, havig he foowig characerisics: p N/m,. kg/m a.. 5 Usig Eq. (8) a (9) are obaie a w m/s, respecivey ka s for a egh of ie uc m. The vaue of he ime ecessary for he kickig of he aspiraio is pracicay isigifica. A opimisaio of eivery ca be obaie if he vave V is pace eares is possibe o he ejecor. A cosequece of his is he shoreig egh of eivery uc. For. 5 m he ime is reuce wih 5%:. 55 s.. NUMERICAL APPLICATION NO. Is cosiere he same rivig ozze as i firs exampe. As primary (rivig) fui is cosierig he compresse air wih he foowig characerisics: 6. kg/m 5, p.7 N/m, kg/hr, v s m/s (veociy of rivig fui hrough so). 6

5 The ecoomica esig sar from a recommee veociy of he rivig fui hrough eivery uc by v m/s. The compue vaue of he iameer of eivery uc is comp.. mm. For a cosiere vaue 5 mm he veociy become v 9. m/s. I his case he ime ecessary for he kickig of he fowig is. 9 s a for a shorer eivery uc by. m, his ime is reuce a. 5 s, sigifica smaer as i firs presee exampe. The omia hyrauic power of he rivig fui is sesiive equa reaive a he vaue compue i he appicaio o. : N 68 wa. From he appicaios previousy presee resu ha he ime ecessary for he kickig of he fowig has more accepabe vaues is he cases of uiisaio of he compresse gases (air, bure gases a.o.). Cocerig he iscoiuous suppie wih he rivig fui, we are proposig a iermie suppies wih rivig fui usig a roaig isribuor wha is esige o reaize a pusaory fucioig wih he ime of shuig-off equa wih of he ime of eivery. I his case here is obaie a impuse per roaio. Cosierig he seco presee appicaio, he ime ecessary for a impuse is ake equa wih. 5 s. I his case he frequecy is ψ ( /.5 ) 8 impuses per seco a he spee of isribuor is 8 roaio per miue. A he same vaue of he 5 pressure of rivig fui, p.7 N/m, here are obaie a ecreasig of he cosumpio of rivig fui a of he hyrauic power wih 5%: kg/hr, N wa. I Figures a 5 are presee wo origia echica souios of ve-ejecors which are suppie usig a roaig isribuor: wih epressive ambour wih rivig sos (pae RO 88769), see Figure a he roaive wih siig baes, see Figure 5. Boh are wih Coaa overappe effecs, je-faps, Magus. m m mix m Figure. Ve-ejecor wih epressive ambour wih rivig sos m m mix m Figure 5. Ve-ejecor wih raaive isribuor wih siig baes 7

6 I he foowig here wi be presee he workig of he firs souio, havig rivig sos. I he firs sage, he rivig fui is auche hrough a so sare wih poi. The je is rasie i o poi umber, where become sabiise, i he ime.5 s, afer a quarer of roaio. I his case he spee of isribuor is T roaio per miue. The je is saioary o he quarer bewee sos a, a is soppe o he haf of roaio bewee pois, a. Sare wih poi here is a overap bewee he saioary je a he rasie je auche i poi. The fui iucio is he resu of his combiaio of he wo jes. Cosierig he exerior iameer of he ambour equa wih T mm a he veociy of he je of rivig fui hrough so v s m/s, he foowig ca be compue: aguar veociy ω T ( π / ) π ra/s, periphera veociy ut ( ω T T / ). 57 m/s, v s ( ) ϕ ( ) v s. The performaces of he ejecors ca be improve if is icreasig he umber of sos, respecivey of he siig baes, or if is icrease he spee of he roaig isribuor, (improve epressio iesiy, icrease fuiic iucio, a more uiform ejecio a.o.). REFERENCES. Beche V., Beche L., Ve-ejecor wi Depressive Faps. Pae RO785. Beche V., Beche L., Ve-ejecor. Pae RO8899. Beche V., Beche L., Ve-ejecor wih Depressive Tambour. Pae RO Beche V., Ugureau V. B., (), Origia Physicomahemaica moe fo he Coaa moveme o a epressive fap. I: The Aas of,,duarea e jos Uiversiy of Gaai, Fascice XIV, Mechaica Egieerig, ISSN -565, pp Beche V., Ugureau V. B., Humiic A., Humiic G., (), A Eergeicay Approachig of he Ve-ejecor assise by Coaa Effec. I: CIB., ISBN ,,,Trasivaia Uiversiy Press, pp Beche V., Humiic A., Humiic G., (), The Eergeicay Opimizaio of Hyrauic Drives. I: MOCM-8, ISSN 78,,,Uiversiy of Bacau Press, pp Beche V., Humiic A., Humiic G., () A Thermoyamicay Approachig of he Veejecor assise by Coaa. I: Proceeig of The XIII h Naioa Coferece of Thermo-Techics, ISSN 5 79, pp