Evaluation of Optimum Modes and Conditions of Cavitation and Acoustic Absorption Intensification for Increasing Efficiency of Gas Mixtures Separation

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1 Joa of Aed Fd Mechacs o. o Avaabe oe a ISS EISS DOI:.8869/acadb.afm Evaao of Omm Modes ad Codos of Cavao ad Acosc Absoo Iesfcao fo Iceasg Effcecy of Gas Mxes Seaao R.. Goyh Bys Techoogca Ise (bach) of Aa Sae Techca Uvesy amed afe I.I. Poov Bys Aa Rego 6595 Rssa Ema: omag9@gma.com (Receved May 6; acceed A 8 7) ABSTRACT The ae eses heoeca sdes of absoo gas mxe seaao de asoc vbaos fece whch ovdes cavao ad acosc ocess esfcao. The heoeca sdes based o cosecve cosdeao of hs ocess begg wh sge cavao bbbe dyamc whch geeaes shocwave fo ceasg eface gas-d ad edg wh deemg absoo odcvy ovdg eed coceao of age gas mxe comoe. I es of he sdes s evaaed ha cavao ad acosc esfcao cease eface gas-d o mes wh amde of oscaos of sod sface μm. Fom he daa abo sface ceasg he aayss of he gas absoo ocess he d fm was efomed. Fo hs aayss he mode of gas absoo ag o acco sface ceasg de acosc cavao fece was deveoed. The mode of absoo aows o oba ha he absoo odcvy de asoc vbaos fece s ceased o mes ad moe. The obaed ess ca be sed fo deveome of hgh-effcecy absoo aaas ha s semeed by asoc fece soces. Keywods: Absoo; Cavao; Gas mxe; Uasoc; Iehase sface. OMECLATURE A amde of asoc aco A -h comoe of he max of ea sysem a ads of he cavao bbbe a maxmm esse he ces b saaeos dsace bewee he cee of he cavao bbbe ad he sod sface b dsace (a maxmm bbbe exaso) bewee bbbe cee ad sod sface b -h comoe of veco of gh a of ea eaos sysem C coceao of absobed gaseos comoe d fm Cg coceao of absobed gaseos comoe gas mxe Cg a coceao of absobed gaseos comoe gas mxe Cgo coceao of absobed gaseos comoe a o c oca veocy of sod d hase D coeffce of gaseos comoe mass asfe o d fm d veco of cee e of -h ad -h bbbes coe whch eas d=- E fdamea soo of Laace s eao f feecy of asoc aco h hcess of d fm I I J egas ove o each boday em aveage mbe of cavao bbbe sao befoe s coase mea amo of he ce geeaed a he beaage of he seaae bbbe K mea cvae of he was of he cavao bbbe KP eave absoo odcvy ceasg de asoc fece KS eave ehase aea sae ceasg de asoc fece B cosa of coaescece ae of he bbbes L egh of he mode aea of absoo ocess om of dffeece vecos ad om of veco

2 R.. Goyh / JAFM o. o α α vecos whch ae deeded o α om of veco co of boday ems mbe coceao of cavao bbbes deedg o me veco of oma a ow coceao of cavao bbbes saoay coceao of cavao bbbes saaeos vae of esse of d hase who cavao bbbes sac esse d c() esse he ces of he cavao bbbe esse of saaed vao of d w gas esse ea he was of -h bbbe R saaeos ads of he cavao bbbe R ads of cavao ces R ads of -h bbbe ces R saaeos ads of -h bbbe RMAX maxmm ads of he bbbe vecos of coodaes of he os of he wa of he cavao bbbe coodae veco of he cee of - bbbe S secfc aea of he eface SA wa of he cavao bbbe SB sod sface o whch s ea Seff sae of effecve bbbes coso s coss-seco whch s oooa o RMAX T eod of asoc vbaos momes of me veocy of d fm moo <> aoach veocy of he cavao bbbes g veocy of gaseos mxe moo oma comoe of fd veocy vome of he cavao bbbe oma veocy o -h bbbe wa boday em wh coodaes (; ) ad (+; +) τ agea comoe of fd veocy vl saaeos vbaoa seed of d hase who cavao bbbes λ egh of he caay wave defed fom he codo α amh age γ adabac dex of saaed d vao µ dyamc vscosy of d ξ( ) vae of dsaceme of he eface d-gas aog he axs ρ desy of d ρl desy of d hase ρg ebm desy of gas sde he bbbe σ d sface eso φ fd veocy oea o he wa of he cavao bbbe o sod sface ω cca vbao feecy of sod sface. ITRODUCTIO The obem of afca seaao of gas mxes cased by he ad deveome of eches ad echooges s fo ove yeas (Mde 996). U oday coeco wh he deveome of odco echoogy asoao ad medce demad fo he seaao of gas mxes fo seaao of fshed odcs ad o emove desabe mes s cosay gowg. Oe good exame s he ceasg demad fo chemcay e hydoge. Today de o avaache cease he mbe of exhas gases emed o he amoshee fac s ecessay o ogae a ewo of hydoge fg saos o cay o a wde sead of evomeay fedy ds of aos. Obvosy hs w ee a mafod cease he hydoge odco vomes o vaes whch ae comaabe wh oday's vomes of odced foss fes based o cde o ad aa gas. I hs case s ecessay o ovde a ow cos of he odc. I aay foows he eed o ceae hgh-efomace ad ow-cos gas seaao as becase as he may mehod of hydoge odco s seam efomg of aa gas/mehae (Ros-ese ad Sehesed ). The seam efomg ess a gaseos mxe of H CO CH4 HO ad CO fom whch s ecessay o seaae he H oy. Aohe exame s he gowg eed fo oxyge egeeao fom CO o ogae dewae exedos ad og maed sace fgh o sdy exaeesa obecs. The fe so sysems fo sch fghs ad exedos eed hgh efomace cos-effecve ad comac devce fo he O. I oe way o aohe he ocess w be edced o he seaao of oxyge fom a mxe of cabo comods (Kooff 96). Hgh demad o he efomace ad effcecy of hese sysems s de o he eed fo he geaes ossbe mbe of cew ad sevee escos o he amo of eegy odced o boad he sacecaf o sbmae vesses. Yo ca ead a o of ohe exames ha show he eed o cease odcvy ad edce eegy gas seaao mxe. Howeve dese he beadh of acao of he seaao of gas mxes a vaey of shees of hma acvy ad a he same me hgh eegy effce gas seaao ocesses o dae does o exs. Exsg devces fo gas seaao based o 6

3 R.. Goyh / JAFM o. o cyogec membae ad soo mehods (Mde 996; Mce e a. ; Ho e a. 8; Schoes ; Am e a. 4) have med caacy ad ae ow wog vay a maxmm caacy. The oea effecveess of he cyogec ad membae seaao echoogy gases oday ca be cosdeed as exhased. Fo cyogec echooges s e becase of a og sa- eod ad he eed o coo he gas mxe o he bog o of he owes bog o comoe fo he membae echooges s e de o he hgh comessed gas fow essace of he membae. Ths oday s he mos omsg dvso soo mehods (Ho e a. 8; Lage e a. 8; Schoes e a. ). Amog soo mehods he gaseos absoo by seca absobg d has he geaes acca ees. The absoo efomace ca be o m /h de o he fac ha he absoo of he gas comoe occs by he a vome of he absobg d. Howeve de o ceasg demads he gas mxe seaao oday hs efomace s sffce. Aems o move he efomace of absoo by ceasg he absobe fow ae s a d eads o a dsoooae ceasg he cos of he ocess de o he hgh cos of he egeeao of he absobe. Iceasg of he fow of he gas mxe obvosy eads o decease he y of he gases de o med dffso ae. Theefoe oe of he ossbe ways o cease he absoo caacy s he se of exea fece eadg o cease he eface d-gas ha eads o cease gas absoo ae. Kow absobes s base o ceag of he age eface aea sg say absobg d (aomg absobes) eg ae RU 84 by Zyadova e a. (). Howeve hs case gases ha ae e sobe he absobe s accay o absobed de o occece of be mcosaos. Ths he effecveess of aomg absobes fo hese gases s edced o ohg. Theefoe o sove hs obem s ecoaged by ayg of acosc (asoc) cavao he mac of whch ceases he efaca sface of he d-gas (Lage e a. 8). The acosc ad cavao fece s effecve fo he esfcao of he ocesses of absoo ha s exemeay ove by domesc ad foeg eseaches. Acosc cavao fece has he foowg advaages:. The ossby of esfcao of absoo egadess of chemca comoso of he seaaed gas ad d absobes de o he ossby of choose of he oma asoc fece mode ad exose codos (feecy esy ocao ad deco of he of asoc vbaos adag aea) deemed by he hysca oees of gaseos mxe ad absobg d.. Isaao of asod soces does o ee chages he desg ad fcoay of he absobes.. Low owe cosmo. Accodg o he ess of aboaoy ess he esfcao of gas absoo occs eve a ow esy exose f yo seec a cea esoace feecy of he oscao. 4. The ossby of smaeos esfcao of chemsoo becase cavao cobe o beaage of chemca bods ad he fomao of ew oes. 5. Comac soces of asoc vbaos ad eecoc geeaos fo he owe. Howeve dese a mbe of advaages acce oday he acosc cavao effecs s o bee memeed de o ac of owedge of he hysca mechasms of he ocess ad he ac of scefc daa of he bes modes of asoc aco ovdg maxmm effcecy of he ocess as coseece. De o me cosmg ad exesve exemea sdes s ecessay o deveo a mahemaca mode of he effec of asoc fece o he efaca sface aea of he d-gas ad he ecs of absoo aowg evaag oma modes of acosc cavao esfcao of hs ocess.. PROBLEM STATEMET Accodg o he mehod of acosc cavao esfcao of absoo (Fg. ) o he h d fm (absobe) owef acosc o asoc (US) oscaos (feecy of...5 H) s odced by sod-sae asme (Khmeev e a. ; Lage e a. 8). Fg.. Scheme of he acosc cavao esfcao of absoo. Uasoc vbaos fd ceae acosc cavao fed (Roebeg 968; Khmeev ). I s he cavao bbbes whch eodcay exad ad coase o o-sheca ce (osheca shae s cased by sod sface) fomg mcoscoc shocwaves wh esse ses o amoshees (Fg. ) (Roebeg 968; Kedsy ; Bee 995; Rcese ad owaows 99; Maage e a. 5a). Shoc waves ead o he fomao of sabe caay waves o he eface d-gas (Khmeev e a. ) whch aows o cease he aea of he 7

4 R.. Goyh / JAFM o. o eface ad hece seed of seaao of gas mxes. (Roebeg 968): R R R R R 4 R R R 4 f Ahs f () Fg.. Scheme of he caay wave fomao de fece of cavao bbbe. Ths he mode o defy oma modes of acosc absoo esfcao shod cde he foowg sages of he ocess evew (Khmeev e a. 4b):. exaso of cavao bbbe o maxmm ads whch s shecay symmec de o he ow seed of s was (o moe ha 5 m/s);. asymmec coase (Maage e a. 5b 6) of he cavao bbbe fom maxmm ads o mmm se;. geeao ad oagao of aow decoa shoc wave he h d fm a he coase of he cavao bbbe; 4. fomao of caay waves o eface d-gas. I hs sage caay waves ofe s deemed ad sae of he eface d-gas s cacaed; 5. absoo of gaseos mxe fow comoe by d fm. I hs sage he absoo odcvy ovdg he ecessay y of age comoe s deemed. Fhe oosed mode s descbed.. THE MODEL OF ACOUSTIC CAITATIO ITESIFICATIO OF ABSORPTIO. Exaso of Cavao Bbbe A he sage of cavao bbbe exaso s maxmm ads RMAX ad cee ocao eave o he sod sface ae deemed. A hs sage s assmed ha:. exaso of he bbbe s shecay symmec whch s cased by ow seed of was moo howeve he bbbe cee vecay moves eave o he sod sface he cose of me;. a me he cee of he cavao bbbe s ocaed ea he sod sface as sch bbbes mosy fece o he fomao of caay wave. Maxmm ads of he bbbe RMAX s defed o he base of og-eas eao whee R s he saaeos ads of he cavao bbbe m; R s he ads of cavao ces m; σ s he d sface eso /m; ρ s he desy of d g/m ; s he sac esse d Pa; f s he feecy of asoc aco H; h s he hcess of d fm m; A s he amde of asoc aco m; s he esse of saaed vao of d Pa; s he me s; µ s he dyamc vscosy of d Pa s. The dsace bewee he cee of he cavao bbbe (a he mome of maxmm exaso) ad he sod sface s defed fom he eao gve Rohdesvesy s boo (977): b R b R 6b b R R () whee b s he dsace bewee he cee of he cavao bbbe ad he sod sface m. Obaed vaes of maxmm bbbe ads ad he dsace bewee s cee ad he sod sface ae sed fo heoeca sdes of fhe sages of he caay wave fomao.. Coase of Cavao Bbbe Dg he sdy of he sage of cavao bbbe coase s fom he mome of he mmm se s deemed. The fom of he cavao bbbe s defed fom he ega eao () wh boday codos (4 5) o he wa of he cavao bbbe fo d veocy oea ad ey codos (6 7) o cavao bbbe wa: E E S () S A S B K τ 4 γ R MAX (4) (5) (6) R (7) MAX whee ae he vecos of he coodaes of he os of he wa of he cavao bbbe o sod sface m; φ s he fd veocy oea o he 8

5 R.. Goyh / JAFM o. o wa of he cavao bbbe o sod sface m /s; ad τ ae he oma ad agea comoes of fd veocy m/s; E s he fdamea soo of Laace s eao; s he vome of he cavao bbbe m ; s he esse of saaed vao of fd Pa; ρ ad σ ae he desy (g/m ) ad sface eso (/m) of fd esecvey; K s he mea cvae of he was of he cavao bbbe m - ; SA s he wa of he cavao bbbe; SB s he sod sface o whch s ea (See Fg. ). Wh he he of sysem of eaos (-7) we cacae defomao of he was of he cavao bbbe he cose of me. Ey codos (5-7) beg a a of he sysem (-7) s deemed by he bbbe ads ad he oso of s cee a he mome of maxmm exaso whch wee fod a he evos sage of he mode sdy. Iega eao () amed a he deemao of dsbo of fd veocy oea o he was of he cavao bbbe s soved by he boday eeme mehod. Fo hs ose he dsceao of he cavao bbbe wa o g eemes s caed o as s show Fg.. Fg.. Dsceao of he cavao bbbe wa o g boday eemes. I s assmed ha he famewos of each g eeme he veocy oea s cosa. I aows sovg boday ega eao () as a sysem of ea eaos (8). Ths sysem s obaed by sg mehod of mages (eacg sod sface by symmecay aced cavao bbbe). b A (8) whee {A} s he max of ea sysem; s oma veocy o -h bbbe wa boday em wh coodaes (; ) ad (+; +); {b} s gh a of sysem; s co of boday ems; The coeffces of he sysem of ea eaos (A ad b) ae defed by he foowg obaed exessos: ) m( ;) max( b b b J b ) m( ;) max( b b b J (9) b b b I b b I A () whee I J I ae egas ove o each boday em; b s dsace bewee bbbe cee ad sod sface a maxmm bbbe exaso m. I exessos (9-) s meoed ha foowg eaes ae e:

6 R.. Goyh / JAFM o. o ;. Iegas I J I ae defed as foows (-): 4 4 cos J () I 4 () I m () 4 whee ae vecos of coodaes ; ; ; s veco of oma ; cos ; cos ; ; ;. Obaed sysem of ea eaos (8) s soved by eave Sede mehod. Obaed foms of cavao bbbe was (by eaos (-7) a he coase dffee momes of me ae show Fg. 4. The a mome of me ( µs) s he mome of he maxmm bbbe exaso. Fg. 4. Shaes of cavao bbbe a dffee mes. As s show Fg. 4 cavao bbbe es a hemsheca adao of shoc wave. The shae ad se of cavao bbbe obaed a he coase ae daa fo sdy of geeao ad oagao of shoc wave.. Geeao ad Poagao of Shoc Wave A he sdy of he sages of geeao ad oagao of shoc wave aows aoxmag s esse ofe a dffee dsaces fom he

7 R.. Goyh / JAFM o. o bbbe by he foowg obaed exesso (4). Re s c a a c cos c c ce s cos s с a ; ; (4) whee (; ) ae he coodaes of he os m; ω s he cca vbao feecy of sod sface s - ; ad ae he momes of me s; μ s he vscosy of d Pa s; ρ ad c s he veocy of sod d m/s; c s he esse he ces of he cavao bbbe Pa; a s he ads of he cavao bbbe a maxmm esse he ces m. The fco of shoc wave esse he ces of he cavao bbbe c beg a a of he exesso (4) s defed as: c 4R MAX ; whee s esse of saaed d vao; RMAX s bbbe ads a maxmm exaso; s bbbe vome a me ; γ s a adabac dex of saaed d vao. Gve ofe of shoc wave esse s sed fhe fo he defo of caay wave fom ad fay ehase boday aea..4 Fomao of Caay Waves o Sface Ld-Gas The fom of he sge caay wave s defed fom he exesso (5): whee (5) s he vae of dsaceme of he eface d-gas aog he axs. Howeve a he eaao of he echoogca ocess s mossbe o oba seaae bbbe ha s why s ecessay o cosde he eaco bewee he aggegae of cavao bbbes ad he eface geeag se of caay waves. The secfc aea of he eface d-gas e vome of d hase a he geeao of he se of caay waves s defed by he exesso (6): 5 S (6) h whee S s he secfc aea of he eface m /m ; λ s he egh of he caay wave (m) defed fom he codo ; s he coceao of cavao bbbes m - ; < > s sg of aveagg by d fm hcess; h s hcess of d fm m. 5 The em chaacees a shoc wave eegy beg geeaed a bbbe coase. Fo he coceao of cavao bbbes ec eao (7) obaed fom Smohovsy s eao (Sheg ad She 6) fo he ocesses of coaescece ad beaage of dsese aces (d dos gas ad sod aces) s e (Mags 7): B (7) T whee s he cacag coceao of cavao bbbes deedg o me m - ; s he aveage mbe of cavao bbbe sao befoe s coase; B s he cosa of coaescece ae of he bbbes m /s; T s he eod of asoc vbaos s; s he mea amo of he ce geeaed a he beaage of he seaae bbbe. By sovg he eao (7) foowg aayc exesso s obaed: ; (8) B e whee s he a ow coceao of cavao bbbes m - ; s he saoay coceao of cavao bbbes m -. Accodg o he exesso (8) he coceao of he bbbes me whch eas es eods of asoc vbaos acheves sabe vae ad eas o whch s defed by he exesso (9): ; (9) T B aabe beg exesso fo sabe coceao (9) s cacaed fom exemea daa gve Roebeg s boo (Roebeg 968). The cosa of coaescece s defed as foows: Seff B ; () whee Seff s sae of effecve bbbes coso s coss-seco whch s oooa o RMAX m ; <> s aoach veocy of he cavao bbbes m/s. To defe aoach veocy of he cavao bbbes <> he mode of bbbe eaco cased by he foces of he secod ode s sed. The eaco mode s based o he d ewo s Law fo he seaae cavao bbbe 4

8 R.. Goyh / JAFM o. o ag o cosdeao Bees foce acg fom he eghbo bbbes ad cased by ada vbaos of he as oes. Accodg o hs mode he oso of he cee of each cavao bbbe mag he esembe ca be descbed by he foowg eao (Mags 7): 4R 4R v L G L R R 4R L d d 4R 4R v L L v L () whee s he oda mbe of he bbbe oe of d hase; R s he saaeos ads of -h bbbe m; c s he oca veocy of sod d hase m/s; w s he gas esse ea he was of -h bbbe Pa; s he saaeos vae of esse of d hase who cavao bbbes Pa; ρl s he desy of d hase g/m ; vl s he saaeos vbaoa seed of d hase who cavao bbbes m/s; R s he ads of -h bbbe ces m; ρg s he ebm desy of gas sde he bbbe g/m ; s he me s; μ s he vscosy of d hase Pa s; s he coodae veco of he cee of -h bbbe m; d = - s he veco of cee e of -h ad -h bbbes coe m. O he base of he ess of eao soo (8) aoach veocy of cavao bbbes s defed by he foowg exesso: T d d T. () Fhe he aoach veocy s sbsed he exesso (9) ha aows fay o deeme he aea of he eface d-gas. Ths hs sage of mode cosdeao (caay wave fomao) he deedece of sface aea of ehase boday o he modes of asoc aco (feecy ad vbao amde of sod sface coveed wh d fm whch bodes o gas hase) ad d oees ca be defed. I s foows hs sage aows o defe eave sae ceasg (KS) de asoc fece: K S S S US who US h 5 5 h h. () Fhe he eave sae ceasg s sed fo cacao of absoo odcvy ex sage of mode cosdeao..5 Absoo of Gaseos Mxe Fow Comoe by Ld Fm I he sage of mode cosdeao he ocess s cosdeed accodg o scheme eseed Fg.. The absoo odcvy s defed as maxmm odcvy ovdg absobg comoe coceao a gaseos mxe o whch does o exceed defed vae. Fo defg of he odcvy he eaos of gaseos comoe dffso o d (4) ad mass cosevao (5) ae sed: C D C x g C ; (4) C g C g ; (5) x x s veocy of d fm moo m/s; g s veocy of gaseos mxe moo m/s; C s coceao of absobed gaseos comoe d fm; Cg s coceao of absobed gaseos comoe gas mxe; D s coeffce of gaseos comoe mass asfe s -. If asod acs o d fm he coeffce D s med by KS ad he eao (4) s edced o (6) C DK x S C g C. (6) The aayca soo of eao sysems (4-5) gves he exesso (6) fo he absobg gaseos comoe coceao a o: C go DK L S g g C g e ; (7) g g whee s egh of he mode aea of absoo ocess m. I aows o cacae eave ceasg KP of he absoo odcvy ovdg Cgo=εCg de asoc vbaos fece (8) K P G G g g g g ; (8) whee Gg Gg ae he eed absobed gaseos mass fows ovdg coceao Cgo=εCg hogh o who ad wh US esecvey g/s; g g ae he eed absobed gaseos veoces ovdg coceao Cgo=εCg a o who ad wh US esecvey m/s. The veoces g g exesso (8) ae deemed by he foowg eao Dg L g g g e g g g g DK L S g g e. Ths he sage of mode cosdeao aows o 4

9 R.. Goyh / JAFM o. o deeme eave absoo odcvy ceasg de asoc vbaos fece. I he ex seco he ess obaed by he mode aayss s eseed. 4. OBTAIED RESULTS The obaed ess coa eave ehase aea sae ad odcvy deedg o sae ceasg deedeces o asoc fece modes ad d hase oees. Fsy he eave sae ceasg de asoc fece deedeces wee obaed. The deedeces ae eseed ex sbseco. 4. Reave Iceasg of Sae The eave ceasg of sae s deemed by fomao of caay waves o sface dgas sage of mode cosdeao. Obaed deedeces of eave cease of he eface aea KS (see exesso ()) o he modes of asoc aco ae show Fg. 5. Fg. 5 shows he beaage of he gah coesods o he fac ha caay wave oses s saby ad beas o dos (Khmeev e a. ). The deedece of feecy (Fg. 5b) s b a heshod amdes whe caay wave emas sabe. wh he feecy of 6 H he gowh of he aea esseay becomes sowe ad eegy oss of he asoc adao ceases adacay. Tha s why; he acao of feeces of moe ha 6 H s acca. Fg. 6 shows he deedece of heshod vbao amde a whch caay wave emas sabe o he feecy of aco. Fg. 6. Deedece of heshod amde a whch caay wave emas sabe o he feecy of aco. Accodg o eseed deedece he asymoc amde edces wh he se of feecy. I aca a he feecy of 8 H he heshod amde exceeds μm ad a he feecy of 6 H s. μm. Fg. 7 shows he deedeces of secfc eface aea o amde a he chage of hysca oees of d vscosy (a) ad sface eso (b) whch fece o he ofe of coac sface ogehe wh he modes of asoc aco. a) a) b) Fg. 5. Deedeces of secfc aea of he eface o he modes of asoc aco: (a) o amde a dffee feeces; (b) feecy a maxmm amde. Fom eseed deedeces s evde ha wh he cease of amde eface aea gows. If feecy ses sface aea gows ( o moe ha mes) de o he cease of cavao bbbe coceao (Roebeg 968). Howeve sag b) Fg. 7. Deedece of secfc aea of ehase boday o amde a dffee oees of d (feecy of 6 H): vscosy (a) ad sface eso (b). 4

10 R.. Goyh / JAFM o. o Peseed deedeces (Fg. 7) ca be sed fo he deemao of he aea chage cased by chage of he d ye ad chage of s oees. I aca s saed ha gowh of vscosy eads o he decease secfc aea of he eface. I s cased by he absoo of eegy of shoc waves d hase de o foces of vscos fco. A ha decease of sface eso eads o he gowh of he aea as sface eegy of a d decy deeds o s sface eso. Fhe he deedeces ae sed fo cacao of absoo odcvy. 4. Reave Iceasg of Absoo Podcvy The deedeces of absoo odcvy ceasg KP (See exesso (8)) o asoc fece modes (Fg. 8) ad d oees (Fg. 9) ae obaed by absoo of gaseos mxe fow comoe by d fm sage of mode cosdeao. The deedeces e he deedeces of sface aea ceasg. The beaage of gahs meas a oss of caay waves saby as we as fo eave sae ceasg deedeces. becomes sowe ad eegy oss of he asoc adao ceases adacay. Tha s why; he acao of feeces of moe ha 6 H s acca. Peseed deedeces o amde a dffee d oees (Fg. 9) ca be sed fo he deemao of he absoo odcvy de asoc fece cased by chage of he d ye ad chage of s oees. I aca s saed ha gowh of vscosy eads o he deceasg odcvy o he ceasg amdes whch ae ecessay o defed odcvy acheveme as we as fo eface aea. A ha decease of sface eso eads o he deceasg amdes whch ae ecessay o defed odcvy acheveme ad he deceasg maxmm amde ovdg caay waves saby (o bea o dos). a) a) b) Fg. 9. Deedece of secfc aea of ehase boday o amde a dffee oees of d (feecy of 6 H): vscosy (a) ad sface eso (b). b) Fg. 8. Deedeces of secfc aea of he eface o he modes of asoc aco: (a) o amde a dffee feeces; (b) o feecy a maxmm amde. Fom eseed deedeces s evde ha wh he cease of amde absoo odcvy gows o moe ha mes. As we as fo he eave sae ceasg deedeces sag wh he feecy of 6 H he gowh of he maxmm odcvy esseay 4. The Powe of US Oscaos Reed fo Absoo Iesfcao Fhe esmao of owe of US oscaos se fo caay waves fomao ad absoo esfcao was efomed. Fo h aye of absobg d (h << s wave mbe m ; h s d aye hcess m) aho obaed he exesso fo secfc owe of US oscaos (owe e of aye aea Icav W/m ) se fo caay waves fomao (9): 44

11 R.. Goyh / JAFM o. o I cav C f 4 A c 4 A c 5 5 I h h h h. (9) Fo he exesso (9) obag aho assmed ha ma a of owe s asfomed o cavao bbbe coase ad oscaos aeao coeffce (K m ) cased by cavao (Khmeev e a. 4a) ca be aoxmaed by (): f K ~ C I I. () I exesso (9) ad () I s heshod esy whch s ecessay fo cavao aeag W/m ; ρ s desy of d g/m ; A s amde of oscaos m; ω s age feecy s ; f s oscaos feecy H; c s sod seed d m/s; h s aye hcess of d m. The vaabe h (9) s cacaed by h сi. 4 A The oooay coeffce () ca be esmaed as vesey o f : C f ~. () f The oooay ca be exaed he foowg way. The maxmm ads of cavao bbbe a he sma sod esse s vesey o f becase he hghe f he owe me of bbbe exaso. Howeve he wo of gas he bbbe dg exaso s oooa o vome of 4 bbbe whch s deemed as R. Ths he eegy se o cavao s vesey o f. The obaed aoxmae deedeces of US oscaos owe se fo caay waves fomao ae show Fg.. owe a 6 H 6 mes moe ha owe a 8 H. Howeve he ceasg of odcvy a 6 H. mes moe ha ceasg a 8 H (see Fg. 8). Ths shows aoaeess of sg owe feeces fo absoo esfcao whe sma devaos of odcvy ae o cca. 5. COCLUSIO Ths he mode of acosc cavao absoo esfcao was deveoed. Aayss of he mode has show ha acosc cavao fece eads o he geeao of caay wave ad coseey o he gowh of sface of hase coac o mes. I acceeaes of gaseos mxe comoe mass asfe o d hase ad coseey ceases absoo odcvy. Fo maxmm absoo odcvy ceasg he omm modes of asoc aco ae evaaed. I s show ha he mos aoae feecy of asoc vbaos s 6 H a amdes o moe ha. μm a whch moe ha mes cease of coac sface ad moe ha mes cease of absoo odcvy. Heewh he d hase vscosy gowg eads o ceasg amdes whch s ecessay fo acheveme of defed odcvy. Ad deceasg of sface eso eads o he deceasg amdes whch ae ecessay o defed odcvy acheveme ad he deceasg maxmm amde ovdg caay waves saby (o bea o dos). Obaed ew scefc ess have fdamea ees fo he desadg of hysca mechasm of he absoo acosc cavao esfcao ad hey ca be sed fo deveome of hgh-effcecy absoo aaas ha s semeed by asoc fece soces. ACKOWLEDGEMETS The eoed sdy was soed by Ga of Pesde of Rssa Fedeao o. MK REFERECES Fg.. Deedeces of US secfc owe se fo caay waves fomao o oscaos amde a dffee feeces. As foows fom eseed deedeces he ceasg of oscaos amde ad ceasg of feecy cases o avaache ceasg of eed US owe ad coseey US owe cosmed by US adao. Fo exame eed Am R. A. Isam R. Isam ad S. Isam (4). Smao of Gas Seaao Pocess fom A IOSR Joa of Aed Chemsy 6(5) 9-. Bee C. E. (995). Cavao ad bbbe dyamcs. Oxfod Uvesy Pess Ued Kgdom. Ho M. T. G. W. Aso ad D. E. Wey (8). Redcg he cos of CO cae fom fe gases sg esse swg adsoo Id. Eg. Chem. Res. 47(4) Kedsy. K. (). Hydodyamcs of exoso. Exeme ad modes Pbshe 45

12 R.. Goyh / JAFM o. o of SB RAS ovosbs Rssa. I Rssa. Khmeev.. R.. Goyh A.. Shaov A.. Shaova ad D.. Gee (). Reveao of omm modes of asoc fece fo aomao of vscos ds by mahemaca modeg Poc. h Ieaoa Cofeece ad Sema o Mco / aoechooges ad Eeco Devces EDM ovosbs Rssa 4-. Khmeev.. R.. Goyh A.. Shaov S. S. Khmeev ad K. A. Kaaova (4a). Deemao of asoc effec mode ovdg fomao of cavao aea hghvscos ad o-ewoa ds Ieaoa Cofeece of Yog Secass o Mco / aoechooges ad Eeco Devces EDM'4 ovosbs Rssa - 7. Khmeev.. R.. Goyh A.. Shaov. A. eseov A.. Shaova ad E.. Icheo (4b). The sdy of ocess of cavao bbbes eaco wh eface boday d-gas fo evaao of omm modes ovdg maxmm ceasg of hases coac sface Scece ad echca be of oga ego Khmeev.. R.. Goyh S. S. Khmeev ad R.. Basov (). Mehod fo Cacao of Omm Iesy of Cavao Ifece o scos ad Fedsesed Ld Meda Poc. h Ieaoa Cofeece ad Sema o Mco / aoechooges ad Eeco Devces EDM' ovosbs Rssa Kooff J. J. (96). Oxyge ecovey sysems fo maed sace fgh Aeosace Medce 7-7. Lage F. C. Adasfeaa A. M. Whem ad H. Demas (8). Uasod gasd sysems: Effecs o soby ad mass asfe Uasocs Soochemsy 5(6) Magae F. L. Mao ad C. M. Cascoa (5a). Dffse eface modeg of a ada vao bbbe coase Joa of Physcs Cofeece Sees 656() 8. Magae F. M. Gao L. Mao ad C. M. Cascoa (5b). Dyamcs of a vao aobbbe coasg ea a sod boday Joa of Physcs Cofeece Sees 656(). Magae F. M. Gao L. Mao ad C. M. Cascoa (6). Shoc-dced coase of a vao aobbbe ea sod bodaes Ieaoa Joa of Mhase Fow Mags M. A. ad I. M. Mags (7). Dyamcs of bbbes esembe cavag d Physca chemsy oa 8() Mce B. A. E. W. Schaf ad D. G. We (). Iegaed cyogec ad ocyogec gas mxe seaao Pae US 6(6) 97 A. Mde J. (996). Basc ces of membae echoogy d edo Sge eheads. Ros-ese J.R. ad J. Sehesed (). Seam efomg fo hydoge. The ocess ad he mechasm Fe Chemsy Dvso Pes 48() 8-9. Roebeg L. D. (968). Powef asoc feds Scece Moscow Rssa. Rohdesvesy.. (977). Cavao Shbdg Legad Rssa. Rcese E. ad B. owaows (99). A Kec Theoy of ceao Lds Joa of Cood ad Ieface Scece 7() Schoes C. A. C. J. Adeso G. W. Seves ad S. E. Kesh (). Membae Gas Seaao Physca Sove Absoo Combed Pa Smaos fo Pecombso Cae GHGT- Poceedgs of he h Ieaoa Cofeece o Geehose Gas Coo Techooges Kyoo Jaa. Sheg C. ad X. She (6). Modeg of acosc aggomeao ocesses sg he dec smao Moe Cao mehod Joa of Aeoso Scece (7) 6-6. Zyadova L. R. Y. F. Kooov. A. oaev A. A. Ovchov I. S. Dochaeva ad A.. oaev (). ocy aomg absobe Pae RU 84 C 46