BOUNDARY LAYER SEPARATION IN TWO DIMENSIONAL EXPANSIONS

Abstract

' bon tho rolctivo notion of fluid nor tho curfroo of a body rc 3uoon duo to .friction or o, 1 or can u. *c-ontrcotinC r. on .' s thoro moon a problon of rintaininC floc in ro .onn rho"o tho prorru.o in incrorninC In ~rho floe di otion. Thocol? ?:moc a phonorona of oxcor-oivo bounder; ? c yor thtoizon' n , nn O floc? coprra Lion pro tho rooul.to of roduoot' ability or inability of tho f1o' to procoort to rOCIono of hi or procc rce `ho fib T rt o'd In boundary Icyor c-xi bo C'iviGca Into two roCi on o. hi "irrior ro . o&~ s nc:c hz vi1 in E."? o1 ho friction orfocto co preLlo . ^it nn-q to t i cam" n : .rt ioi' thu friction offocto tiro not r orZ-mt mt! t1tc onn bo nc1coto t. The fluid In t hi c o3cn acs 'bo o.tod a. can idocl fluid.. Thin thin ic-.ycr ..hich oo to t'.:) by caion r tho rottod lon ;h to ifoa!y b10 of ru tcin.ifC tho Cooc1& rated fi,aid peiticiCQ. In co^3 Ot] Oo the boundory 1 ryy'or t ii of Horn ino 'oitcoc oonoit1orc~blj in tho dotn'troon diroction cnd tho f1o~Y iii tho bouncltcry layer bccotioc rovorcod a Ohio caur_oc tho 0-000loratod .fluid portiolon to bc forood outoido tho boundary inyor cad2 coparution of tho baun2cry loyor thus tdioo plcoo `»hio phcno' canon in o9.c7aro oocooiatod aith tip for tion of vorticoo and with lur 3o o or r lo:-coo In the rr. o of tho body. 1+ cocuro pritri'1y nonr abrupt chanpjon of bou.idnry in tho floci dirootion. `.ho ctra -lino in tho bo~tndar lc.-or noon uoparation aro oho: di o v tioa11 € in Pia. (1) . Duo to tho G000lcr,-tion of tho 2lot near tho tail thnro in ooncit'orablo t&o toninc of tho boundary lcyor and thoro to a now of boundary 1cyc~r fluid from tho wii into thu otitor roiono At trio point o" ooy rrnt1on one a4~ atroric ho intorcooto tho r11 at a de inito rn ;lcg rnd tho point of ccp(raticn itcoif io Goto inoi by tlio con: it1on th*1t tho volcoity 4,w iont norz1 to tho ccU. vcn shoo thoro v tzEt ice, ^Tyra p ooiro 'location of the point of concrt t on orn bo redo tbrct i intucerct1on or. tho bourinrj lcjor cnit-ntionc. i o fi:? , :; in r A clurill pZin;:; cl art c3.0 ce(wi-a ch' o to OnooI vo 1"OtA- -c C:f:`uro L2iGnt o r C.Ci 'i? if) r,'S rc.-:curo, mar co r cam' I i— `. "_^, .?_ .:? Y? 4'.? t o' `L'2? G" .' l c5 i,ith tho nccar~'cvco in :oO-: , tc r-.lor., tho cn32. ccv.roc the t can :cry otrn. az -Sino to lc.. ivo tho bounc:;,.ry. romotrCc!s1 from t1i., po .nt o ip3'l1 S c..' . r: c '.re -- ori.cci by ro1cr turf"7 ic~it r,CC-,cry ::met rcvor•'o "_c-.-9 c b'.cI . ocucoo n x'oduotion or tho Fier- ccotlo-ii. 2~i u phcne:-,2i.fln cni,a-.00 c coroi'~orrbto eooror.co in the to-; o'ficienncye ¢i o rtcsy of . ropo ^tion p honow^nor In eDr-nno1 o ! ira'k c-ic ic* :two .:gin 4 duo to this i rate A t?oolrablo bcundcr7 Qong'iGur.-tion 'OZ' a C I , rol czpr noion i o tb.^t t hic chow a loon tondonog to c? n cop^r tiQraa - - - we i r .. ~f • .r a_— r _ ho fl.or~ In tho beurt r. r lr•jor silcnj n c-; 11 i:cocr.00 yur lcnt the Iloynol0 c nurbcr of the lcn ?th .o tor.. lvicructrco mwe'Clelontiy0 `7io tronoition Erma 1r r1nt.r to turbulent be riO y laycx In r r1zod by cn in rco In tl'o be tir:zy l(Wcv thio?sno^o cite r oiir.-p incro- co In the rho ctre ct + t -x.bo c;:-11 o The v. ='iuo o,v the or en1 rZoynold c nntbor, flz i'm i y "~~ con('i ~ ~ 2- .,, c 3.2 z 10 Zap the anco of r, f1rt r1rto r t nor© oidc ico. •© aaa res ar_Q r& zruo of € 6 In 2e 0* mçrjr tho^o vr-luoo of oritioai s oynoldo nunbor dopon3 upon tho amount of liotiir b^-nco in tho ortornal flog, cni w1th onooption' 11y Qlotur'brncc-f'rc:o ortorncl. 21oz-*f vcluoo of R:.(cr3ticl) = 1b6 and hlChor lvwo boon ettel»cst'? b r.ho procuuro d: !°trIbution In tho ozctcri n). fio i fiuunco^ tho nooitici of iticn point to a (rcat c.tor.:t. tcundrrr lcijo c, otah1y 1c n r In the rc;, cn of pro rritro t corer%cop least f tic; 1cnG1nr cdco to the point of uinlcrs pro: cza eflfs aa C'? on v nisi : * v oorcc) £mac:., th .t *nof.nt o~3vn., z is tL . [ 3GLF u t!io wo-1 n of t rc~w:o morocco. £sltllc I, { o 1czancr cn? to 'baa:~ ont boma1 cj '! eyorc bot vo in couoz~tla1 .J 4Lo -mar c.t 't:Iio pc:iut of r:~~'#~' ©I~, tho 2 occ tact Of i.i3,o ?.c::.won point on n 4;1vc i o:irvcd cart'^ co :ill be vorg Gl Moron t r,c3^ to *:;a aac^n, In the lrr~2.nr-r 2£ JoE the trcnofor of noco a- i:! t:ao P•ip .a1y coving outor atz ctn throu h the v3. ccouc® craar ;o the inner otratci In clot end inoffcotIvo, Co cr r:;j the 1ciincr boundeavy 1c or In roc1 end cannot n;;:io2- iG mrj to tho call cciinot cn advorco proocuro rtont. '_Ito trnnction to a turbulont boundary lrjor' on tho other hCn8a jc vio7.cnt mi ina of faot—r2ovin„ outer fluid Into tho ~.s;. :ov1n; irror f1i±2 1 a cnd vino—vorca9 `::?ho ccin ro1ooity v? oo to Llr.) b©Un(3r y is ,,*roatl 2ncsroQccG a ::I1in aGcloa cr1orCy oa,~bloo the bound.r±ry l.^ cr bettor to :•.ithctcnd thz: aclvoco 'rode -o i rcic on up t:i'f h the rc:.ul u that the point of ct;u 3rction in Elovod do'. rte"rcen frori tb: point of m-_a::L c prourov Xn thr.o ecrnce tlo-n o it c-R to f;ri.d +.Ii^ t cc j; ivf vti cn c n ou bl be .:voirlc c.' th 'brior. ; bcv. & rcr t1• boon. t J 1CWWor. Concr ally e cc1thiCip tho thic2 ~orao of tho. turbulent boumlcr r lcror to larcor th uhht of a In .nnr bound=r lc.vor ov in to c cator onori loocau :,n tho forror. :Oar a ctooth flat plate at Coro inoir=onco mho turbulent bouJezf layer thiolmoci inc - u-©a dornotroan in c o c a to n0*0 (n += c?icfinoo sfrc,= 1ar_di ociCo) p t ioroan In the Onco of alcn.ncr bcui c y layer It in©ronn- o o in proportion to nO 5 "rho study of turL-!lcsnt bcunC.c•. ? rjc:z' cntl in -OF*v. Lion h d boon rao by the c ►r~x 'i2L:c c~±r3:~ t1 :. r o tetra . Vorr (2) a 0.13. ._Abnuto' r.d 2.'. o z noff c^a s r (i noZ. rational forii1ao h^_.O too ; vcn bj tI ^t. r-'ry r000~ru t of thono t or:zo to 2iron oirc in thin <-lic-wa U-!.v:or rc ~c~.' o lito'n"urov Ploovoro thciw opor:znto.l (iota cro obt4?.nl C'_:t wind tunnel tooto. It to cut ict1 In thie thouio to rhr:i o^tc!tt Chair rorulto are applicablo to boun2arj lvyor ro h In oron ah.nnol ou cnoio ri in iich the floor In chrr^otor1cod by the outntonoo of a free curfaco. Tho proWent paper c3kco no attorpt, to tnvont now otho~lo calculation of turbulent boundary layer or p cC ct o.. of oopnration point. 1Ioc: morQ it to hopc ? that ' the orr tton prorcntod hero my be uccAil in un(?ore Wan Lena the Ix"I'v .vicur of the nov in to incnoioal orpc oiono.