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ITig. 10.2. Variation of flow vclority in a pipc in thc tranuition range at dihrent distances r<br />
from pilw axis, as 111cas11rrt1<br />
by .J. I n d ~ k nurn0~r A = ii.d/v = 2550; axial tlistnn~e z/d = 322; E x 4.27 m/scc (P 14.0 ltlsec); vclocitien given<br />
in nrlsrr. .rhr.rr vclorily plols, oblninnl with tho mid ol n Iwt-wire nncmomatrr, rle~nonstrate the i~~termitlont naluro<br />
vf llm Ilow in fltxl pcrindr nl Inrninnr nnd lurhu~lrnl flow aurcerrl crch othrr In time<br />
d<br />
Fig. 16.3. Intermittct~cy factor<br />
y for pipe flow in the transition<br />
range in ternls of the<br />
axial distance z for different<br />
Itrylrolds nurnbers R, as rneasr~rpd<br />
by J. Rotta [75]<br />
Ilrrc y = i dcnotcs rnnlinllnll~ly tllr-<br />
IHIIPIIL, IIII~ y = 0 1-onti1iunil5~y larnlrlnr<br />
Bnw<br />
rango frorn R 1 2300 t,o 2600 ovcr which transitpion is completctl. At Rcynolds<br />
rtllrnhtw rlcar l,l~c lowcr limit, the process of tmnsit,ion to f~lly dcvclopcd turbulent<br />
Hr)li(:J1 1,l1(, (lo,,r pS~,t:tl(lS ~ V ( T very I ~gc tIist,anccs mcasurctl in thousa~ids of tlialnctcrs.<br />
Mc~asrlrc:tnt~nt.s ol. i,llis kind have been reccntly amplified by J. Meseth [GO].<br />
a. Some exprrinicnlnl results on transition from laminar 1.0 L~~rl~ulrnt<br />
flow 453<br />
important ones being the prcssure distribution in tllr rxternal flow, tthr rl:lfurc- or<br />
tlir wall (ronghr~rss) and the nature of thr disturbanrrs in t,hc frro flow (ir~irtisiIj~<br />
of turbulcncc).<br />
Blimt Ilodies: A pnrticularly rcvn:wkal)lo phenomrnorl c:onrlrnt,rtl wit,l~ i,rt~nsil it111<br />
in thc hour~tlary laycr occurs with blunt bodies, for cxnl~~plc spl~cros or (:irc:~tl:ir<br />
cyIintl(:rs. It is seen frorn Figs. 1.4 :~nd 1.5 that thc r1r:i.g c:ocflicic~rlt or a sj)l~c:rr: or<br />
cylindcr tlccrcascs :~l)r~~pi,Iy at Itcyr~oltls rn~mbcrs R :-: IrI)/v of al)orlt :1 x lo5.<br />
, .I I his almpt drop in thc tlr:~~ corfficicnt, noticctl lid 11y 0. 12ifli.l [231 in rcsl;rt ion<br />
to sphc:rc?s, is a conscc~~~cnc:c of Lr:lrlsiUor~ it1 the I ~ I I I I ~ 1:iyc:r. I : ~ ~ '1'r:l.tlsil.iotl t.;tttsi*x<br />
tltc jminl. of scp:lr:lt.ion to move clowt~st.rcar~~ wllicll consitlrr:~l)ly tlt:crc~:~sos i,l~(:<br />
width of the walrc. 'l'hc truth of this cxpl:in:~tion was tlc1nonsi.r:il,nt1 i)y I,. I'r:r11111.1<br />
1411 wl~o nlor~ntctl n thin wire hoop sotncwl~:~t .-llrntl of tht: cquator of a si~llorc:. 'l'liis<br />
causes artificinlly the b0undar.y layer to 1)ccomc turbrllcnt at a lowcr Ilcynol~ls<br />
numhrr antl protluccs the same drop in drag as occurs w11t:n I,lic Itoyt~oltls IIIIIIIIIW<br />
is nmtla to incrrasc. 'l'hc stnolrc photogrii~)l~s in l'ig. 2.2.1- nntl 2.26 S I I ~ ) +:~rIj~<br />
~ ~ ~<br />
thr cxtcnt of t,hc waltc on a sphcrc: it1 thc sub-critic:~l Ilow rcgirnc t,llc \v:~ltc is uitlt.<br />
arid the drag is large, antl in t-bc supcr-crit,icnl regime it is narrow nntl thc clrag is stnall.<br />
The lattrr flow rcgimc was here crcatctl witll-the a.itl of L'rantltl's 't,ripping wire'.<br />
These experiments show coriclusively that the jump in the drag curve of a sphrrc<br />
is due to n boundary-layer cKect and is caused by tmr~sitio~~.<br />
Flat plate: Thc procrss of transition on a flat plate at zrro incitloncc is sonrrwhat.<br />
simplcr to understand than that on a blunt hotly. Thc prorcss of t.r:rnsit.ion in t.11~<br />
bountlary layer on a flat plate was first stntlictl by ,J. nl. nrwgrrs 161. 13. (:. van<br />
der IIcggc Zijncn 1411 antl Iat.er by M. ITanscn antl, it1 grca1.c.r clrt,ail. I1.y 11. I,.<br />
1)ryclrn 116: 17, 181. According t,o Cl~:lp. VlT, t,llc bo~~ntlnt~y-layer t.l~ivlztlrss on :i flat<br />
plntc incrcases in proportion to j/z, whcrc s tlcrmtlcs tl~c tlistancc from thc Ic:atling<br />
edge. Near the lending edge the bountlary Iaycr is always Iamit~art, l~cnorning i,urbulent<br />
further downstream. On a pl;~tc with a sharp lratling edge ant1 in a. tlormal<br />
air stream (i. c. of int,crisit,y of turbulcncc T = 0.6 %) t,mnsit.ior~ t.:il~s p l ; at, ~ ~ :I<br />
distance z from it, as detcrminecl hy<br />
On a Axt plaLe, in thc same way as in a pip, the c:rit,ic:il Itcyt~oltls n11~11)c.r ran 1)r<br />
incrcasctl by provitlitig for a dist,urbancc-frcc cxt.orna1 flow (vc.rp low ir~t.c*~lsil,y or<br />
tllrl)ulcncr), c/. Scc. XI1 tl 2.<br />
'I'r:~rtsit,ion is casirst to pcrrrivo Oy a s111tly of t.lw vrloc~i1.y tlisl.t~il~i~iiot~ ill (11t-<br />
1)oun~Iary la,ycr. As SCCII from Fig. 2.23, t~r:insit,io~~ is shown ~)rnt~ti~~(-~~I,l~y<br />
1j.y :I, sit~ltlt:~~<br />
incrrase In the boundary-layer tliick~lcss. 111 a lalninar l)ou~iclarv Iavor tlrc tli~ncq~ion-<br />
. .<br />
-. . .. ..<br />
less I~ountlary-1;~ycr trhickricss, d /i v :,;/Urn , rcrnnins rorlst,:~nt ant1 rtl11;11, :I l)pro,yimatcly,<br />
to 5. 'I'he dimcnsiortlcss boutidary-layrr t01icknrss is scct~ plot,t.c~tl :~z:~ir~st.<br />
thc length Rcynolds numbcr R, =-: U, z/v in l'ig. 2.2:) nlrmtly mc!~lt~iot~rtl: :I(,<br />
R, >. 3.2 x 105 n sutltlcn incrcaso ill 1.llo I)o~~t~tl:~~r~-l:~~~~r<br />
I.l~i(.l
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