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Zdcs onhteht d`s beeh jnwhan`jej lrnm CNWsocehoe. Wae`se sornaa jnwh tn see tde luaa text.

Jnwhan`j jet`cas6

CW @jjress6 032.0;:.?;.57

Zdcs onhteht w`s jnwhan`jej nh 03/70/2705 `t 2760:

Wae`se hnte td`t terms `hj onhjctcnhs `ppay.

@h ev`au`tcnh nl sever`a metdnjs nl jetermchchk tde ano`a `hkae nl `tt`oi nh wchj turbche

ba`jes

\cew tde t`bae nl onhtehts lnr tdcs cssue, nr kn tn tdefnurh`a dnmep`kelnr mnre

270: F. Wdys.6 Onhl. _er. 555 7027:5

(dttp6//cnpsocehoe.cnp.nrk/0;:2-

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@h ev`au`tcnh nl sever`a metdnjs nl jetermchchk tde

ano`a `hkae nl `tt`oi nh wchj turbche ba`jes

_ Kuhtur, H H _rehseh

[chj Eherky Jcvcscnh, Zeodhco`a Uhcverscty nl Jehm`ri (JZU), Rcs o`mpus, Rnsicaje, JI

E-m`ca6 srkuGjtu.ji

@bstr`ot. _ever`a metdnjs nl jetermchchk tde hkaes nl `tt`oi (@N@s) nh wchj turbche ba`jes`re jcsoussej ch tdcs p`per. @ brcel survey nl tde metdnjs td`t d`ve beeh usej ch tde p`st `represehtej, `hj tde `jv`ht`kes nl e`od metdnj `re jcsoussej rea`tcve tn tdecr `ppaco`tcnh ch tdeBEM tdenry. J`t` lrnm excstchk `s weaa `s hew luaa rntnr OLJ onmput tcnhs nl tde METCONrntnr `re usej ch tdcs `h`ayscs. @ mnre `oour`te estcm`tcnh nl tde @N@ cs pnsscbae lrnm ?J luaarntnr OLJ onmput`tcnhs, but wdeh wnrichk wctd expercmeht`a j`t`, pressure me`suremehts`hj seotcnh a lnroes `re nlteh tde nhay j`t` `v ca`bae. Zde `cm nl tdcs wnri cs tn `h`ayse tdereac`bcacty nl snme nl tde scmpaer metdnjs nl estcm`tchk tde ?J eeotcve @N@ onmp`rej snme

nl tde mnre rcknrnus OLJ b`sej metdnjs.

0. Chtrnjuotcnh

Zde `hkae nl `tt`oi (@N@) nl `h `crlnca cs ` 2J onhoept jeffhej `s tde `hkae betweeh cts odnrj`hj tde uhjcsturbej stre`maches l`r upstre`m. @ re`a, ffhcte, `crlnca tr`cas vnrtcoes wdcod `atertde eeotcve `hkae nl `tt`oi. Lurtdermnre, cl tde `crlnca cs ` p`rt nl ` rntnr td`t `jjs nrextr`ots eherky tn/lrnm tde flnw, `jjctcnh`a `ernjyh`mco eeots `rcse m`ichk ct ` od`aaehketn onhoeptu`aay jeffhe tde ano`a @N@. Zde oa`ssco`a BEM tdenry `ssumes ` 2J bed`vcnur `t `aa

sp`h wcse pnsctcnhs nh tde rntnr. @atdnukd tdcs `ssumptcnh wnris qucte weaa ch tde mcj bn`rjrekcnhs, ct bre`is jnwh `t tde tcp `hj tde rnnt rekcnhs. Ch l`ot, dere ct cs `asn lnuhj td`t tde2J `ssumptcnhs bre`i jnwh `asn ch mcj-bn`rj rekcnhs, cl tde sp`h wcse an`j jcstrcbutcnh cs hntuhclnrm. Ct cs heoess`ry tn jeffhe `h eeotcve @N@ lnr tde wchj turbche ba`jes espeoc aay chtde rnnt `hj tde tcp rekcnhs beo`use mnst `ernea`stco onjes tnj`y use 2J pna`rs tn estcm`tetde lnroes nh tde rntnr ba`jes. Onjes b`sej nh tde oa`ssco`a BEM tdenry `re onrreotej lnrtde ?J eeots he`r tde rnnt rekcnh uschk onrreotcnh mnjeas lnr rnt`tcnh`a aclt `ukmeht`tcnh,see e.k. Y0, 2, ?, :, 5,

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2. Metdnjs nl jetermchchk `h `hkae nl `tt`oi

_ever`a teodhcques excst by wdcod tde eeotcve @N@ o`h be estcm`tej lnr ` kcveh rntnr. Nl

ntders, tde lnaanwchk lnur teodhcques `re usej ch tde ourreht wnri.

0. Zde chverse BEM metdnj Y0?, 0:], wdcod uses tde pre-jetermchej ano`a lnroes tn o`aoua`tetde ano`a chjuotcnh.

2. Uschk OLJ j`t` tn nbt`ch tde `hhua`r `ver`ke nl tde `xc`a veanocty (`hj tdereby tdechjuotcnh `) `t ` kcveh r`jc`a pnsctcnh ch tde rntnr pa`he Y05, 0

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(cv) O`aoua`te hew v`aues nl` `hj `,

`hew= 0

4rLsch2 oBOH

+ 0 , (2)

`hj,

`hew= 0

4rLsch onsoBOZ

0. (?)

(v) Cl tde jcerehoe betweeh tde hew v`aes nl Y`, `] `hj Y`hew, `hew] cs mnre td`h ` oert`ch

tnaer`hoe, kn tn step 2. Ease, onhtchue.

(vc) Onmpute OA `hj OJ `s,

OA,?J =OHons +OZsch ,

OJ,?J = OHsch OZons . (:)

Zdese v`aues `re tde hew, ?J, aclt `hj jr`k oneocehts.

Lckure 2. _odem`tco sdnwchk `hhuac `t v`rcnus stre`m wcse pnsctcnhs nver wdcod tde `xc`aveanoctces were extr`hoej `hj usej ch metdnjs (2.) `hj (?.).

2.2. Metdnj (2). Onmputchk tde ano`a chjuoej `ver`ke veanoctces uschk OLJ

@hntder metdnj nl estcm`tchk tde ano`a @N@ cs tdrnukd tde `h`ayscs nl tde veanocty ffeaj lrnm` luaa rntnr ?J OLJ onmput`tcnh. Zde `cm cs tn nbt`ch tde chjuoej `xc`a veanoctces `t tde rntnr

?

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pa`he, uschk tde `v`ca`bae j`t` `t sever`a upstre`m `hj jnwhstre`m ano`tcnhs Y05, 0

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Lckure ?. Ex`mpae - tde `hhua`r `ver`kenl `xc`a veanocty `t sp`h wcse pnsctcnh r/R =7.25. Zde veanoctces `t jcereht stre`m wcseano`tcnhs nbt`chej jcreotay lrnm tde OLJ j`t` csjehntej by\0. \2 jehntes td`t nbt`chej lrnmchterpna`tcnh uschk equ`tcnh (5), wdcod cs usejlnr estcm`tchk tde eeotcve @N@. Dere, z/R= 7onrrespnhjs tn tde rntnr pa`he `hj tde `cr flnwslrnm aelt tn rckdt.

Lckure :. @xc`a chjuotcnh l`otnr `s ` luhotcnhnl tde `zcmutd `t r/R = 7.35. Zde ba`jes `reano`tej `t = 37, 207, `hj ??7, dckdackdtejby tde jnttej vertco`a aches.

ourve w`s csna`tej `hj onmp`rej wctd tde 2J pressures. Zde oansest 2J m`tod tn tdcs ?J OWjcstrcbutcnh w`s jetermchej, jnhe dere uschk tde ae`st squ`res metdnj, `hj tdcs `hkae w`s t`ieh`s tde ?J eeotcve @N@. Lckure (

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Lckure ;. Estcm`tej OA v`aues uschk tdeeeotcve @N@s lrnm ffkure (5).

Lckure 4. Estcm`tej OJ v`aues uschk tdeeeotcve @N@s lrnm ffkure (5).

?. Zde METCON expercmeht

Zde METCON (Mnjea Expercmehts ch Onhtrnaaej Onhjctcnhs) expercmeht w`s ` prnfeot td`t w`sp`rtc`aay luhjej by tde Eurnpe`h onmmcsscnh `hj w`s onhjuotej ch 277< ch tde a`rke so`ae l`ocactynl tde JH[ (Kerm`h-Jutod) wchj tuhhea ch tde Hetdera`hjs Y27]. Zdcs expercmeht keher`tej,`mnhk ntder sckh`as, surl`oe pressure j`t` nh tde ba`jes nl ` wchj turbche rntnr nl :.5 m jc`metertd`t o`h be usej tn extr`ot tde lnroes nh tde ba`jes. Ch tde expercmeht, pressure jcstrcbutcnhs `tffve sp`h wcse pnsctcnhs were me`surej, `t sever`a pctod settchks `hj lnr tdree tcp speej r`tcns.

Zde onmbch`tcnh nl tdese p`r`meters kcves rcse tn v`rcnus eeotcve @N@s `t jcereht pnsctcnhsnh tde ba`je. Luaa rntnr OLJ scmua`tcnhs nl tde METCON rntnr d`ve beeh o`rrcej nut lnr tdes`me nper`tchk onhjctcnhs prevcnusay Y02]. Zde ourreht wnri choaujes tde j`t` lrnm Y02] `s weaa`s snme hew onmput`tcnhs, wdcod `re jesorcbej ch tde a`ter seotcnhs. Zde nrckch`a METCONj`t`b`se onhscsts nl m`hy jcereht o`ses, acie y`w, jcereht pctod `hkaes, jyh`mco tests, eto.,but dere tde lnous cs nh tdnse o`ses wctd ste`jy chflnw, zern y`w, ffxej pctod `hkae (2.?7),rntnr speej = :25 rpm, `hj lree stre`m wchj speejs \7= {07, 02, 05, 0;, 20, 2:, 24} m/s.

Lckure 3. Mnjcffej twcst jcstrcbutcnhs nl tderntnr, Z0 `hj Z2.Lckure 07.

@hkae nl `tt`oi `s ` luhotcnh nlr/R, lnr twcstej o`ses Z0 `hj Z2.

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:. OLJ onmput`tcnhs

Zde OLJ onmput`tcnhs nl tde METCON rntnr were perlnrmej wctd tde Eaacpsys?J OLJ snaver,

`s jesorcbej ch tde wnri nl Beodm`hh et `a., see Y02]. Ch `jjctcnh, ch nrjer tn chvestck`te tdepnsscbae eeots nl ` tr`cachk vnrtex ch tde mcj-bn`rj rekcnhs, hew onmput`tcnhs nl ` re-twcstejMETCON rntnr d`ve beeh o`rrcej nut. Zde nhay jcerehoe betweeh tde rntnr onhffkur`tcnh chY02] `hj tde hew onmput`tcnhs cs tde hew ba`je twcst jcstrcbutcnh, wdcod cs sdnwh ch ffkure (3)`s Z0 `hj Z2. Zdese hew onmput`tcnhs were o`rrcej nut `t \7= {07, 02, 05, 0;, 27, 25} m/s.

Lckure 00. @ onmp`rcsnh betweeh tde aclt `hj jr`k pna`rs `s prejcotej by tde ?J onrreotcnhmnjeas `hj OLJ j`t` `t r/R 7.22 `hj 7.:;. Zde 2J j`t` cs t`ieh lrnm wchj tuhheaexpercmeht`a j`t` `t Re = 7.5 07

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Lckure 02. @ onmp`rcsnh betweeh tde aclt `hj jr`k pna`rs `s prejcotej by tde ?J onrreotcnhmnjeas `hj OLJ j`t` `t r/R 7.35. Zde 2J j`t` cs t`ieh lrnm wchj tuhhea expercmeht aj`t` `t Re = 7.5 07

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Lrnm ffkure (00), ct o`h be seeh td`t tde metdnjs (0.), (2.) `hj (?.) `re ch re`snh`bae `kreemehtlnr sm`aa @N@s. Metdnj (0.) bekchs tn jevc`te wctd respeot tn tde ntder twn metdnjs `s tde

@N@ chore`ses, `hj metdnjs (2.) `hj (?.) rem`ch ch very knnj `kreemeht lnr rea`tcveay dckder@N@s. Dehoe, uhaess tde `crlnca nper`tes ch jeep st`aa, tde perlnrm`hoe nl metdnjs (2.) `hj (?.)seems tn be he`ray tde s`me.

Zde chfluehoe nl tde tcp vnrtex nh tde ano`a ba`je `ernjyh`mcos ch tde tcp rekcnh `hj tde use nltcp anss l`otnrs tn onrreot lnr tdcs eeot ch BEM onjes cs weaa ihnwh, see e.k. Y4, 3, 07, 00, 03, 20].Zde jeffhctcnh nl tde tcp anss l`otnr ch terms nl tde `xc`a chjuotcnh l`otnr d`s beeh ` m`tter nljeb`te. @oonrjchk tn Y20], cts jeffhctcnh by Ka`uert Y3] w`s

LWR = `

`B,

`B = `

LWR, (;)

wdere ` cs tde `hhua`r `ver`ke nl tde `xc`a chjuotcnh `t ` kcveh r`jc`a pnsctcnh (represehtchkchffhcte ba`jes) `hj `B cs tde ano`a `xc`a chjuotcnh `t tde `zcmutd`a ba`je ano`tcnh lnr ` rntnrwctd ffhcte (ch tdcs o`se, ?) humber nl ba`jes. Lckure (:) sdnws ` onmp`rcsnh betweeh tdev`aues nl ano`a chjuotcnh`B ch tde tcp rekcnh estcm`tej jcreotay lrnm OLJ, `hj o`aoua`tej uschkequ`tcnh (;). Lrnm tdcs ffkure, ct o`h be seeh td`t tdere cs ` bck jcerehoe betweeh tde v`auenl`B nbt`chej by metdnj (?.) `hj td`t nbt`chej uschk equ`tcnh (;). Zdcs sukkests td`t tdeWr`hjtas tcp onrreotcnh l`otnr `s jeffhej by equ`tcnh (;) o`hhnt be usej tn `oour`teay estcm`tetde ano`a veanoctces `t tde ba`je.

Lckure (07) sdnws tde @N@ estcm`tes `anhk tde sp`h wcse jcreotcnh, `hj ffkure (02) sdnws tde

estcm`tej OA ourves oanse tn tde tcp, r/R = 7.35. Lrnm ffkure (02), ct o`h be seeh td`t tde OAourve cs anwerej tdrnukdnut tde r`hke nl, wdcod cs ` resuat nl tde tcp vnrtex. Hntchk td`t tdeeeot nl tde tr`cachk tcp vnrtex cs tnanwertde aclt ourve, ct cs tderelnre re`snh`bae tn expeot td`t` tr`cachk vnrtex ch tde mcj bn`rj seotcnh tnn sdnuaj d`ve tde s`me eeot nh tde ba`je seotcnhsch cts vcochcty.

Zde vnrtcoes tr`caej ch o`se Z0 d`ve tde s`me nrceht tcnh wctd respeot tn tde seotcnh `tr/R = 7.?7 `s jnes ` tcp vnrtex wctd respeot tn tde seotcnhs he`r tde tcp. Zdcs cmpaces td`tcts eeot nh tde onrrespnhjchk `crlnca seotcnh must be td`t tde estcm`tej aclt ourve cs anwerej(onmp`rej wctd tde 2J ourve), `hj tde nppnscte ch o`se Z2. Lrnm ffkure (0?) ct o`h be seehtd`t tdcs cs chjeej tde o`se, `s tde aclt ourve cs anwerej ch o`se Z0 `hj chore`sej ch o`se Z2.

@s mehtcnhej prevcnusay, ` BEM scmua`tcnh chonrpnr`tchk onrreotcnh mnjeas lnr tde rnt`tcnh`a

aclt `ukmeht`tcnh w`s `asn o`rrcej nut. @ hntewnrtdy nbserv`tcnh cs td`t tde `ukmeht`tcnh nlaclt jue tn rnt`tcnh OA (=OA,?J OA,2J) prejcotej by tde ?J onrreotcnh mnjeas cs tnn dckdch tde very chbn`rj seotcnhs (see r/R = 7.22, ffkure (00)) `hj tnn anw ch tde mcj/nut bn`rjseotcnhs (seer/R = 7.:;, ffkure (00)), onmp`rej tn td`t nbt`chej lrnm OLJ. Zdcs me`hs td`ttde eeot nl rnt`tcnh`a `ukmeht`tcnh noours lnr ` rea`tcveay a`rke pnrtcnh nl tde ba`je, `hj tder`te `t wdcod tdcs eeot cs mnjeaaej tn od`hke (jeore`se) `s ` luhotcnh nl tde r`jc`a pnsctcnh csch keher`a tnn dckd.

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Lckure 0?. Zde ?J aclt `hj jr`k pna`rs onmputej `t r/R = 7.?7 lnr tde jcereht ba`je twcstonhffkur`tcnhsZ0,Z2, `hjZ7, wdereZ7 jehntes tde nrckch`a METCON twcst onhffkur`tcnh. Zde2J j`t` cs t`ieh lrnm wchj tuhhea expercmeht`a j`t` `t Re = 7.5 07

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