Boundary Lyer Theory

XVT. Origin of turbulcncc I n. Some rxprrirnrntd reuulte on t,rn~~sitiott iron^ lnmir~nr to turb~~lcnl flow
Fig. 16.4. Vcloc:it,y profilcs in n
boundary lnycr or1 n flat plate in
the trar~sit~ion rcgion, ns nic:buurrd
by Srhuba~~cr nnd Klcbunoff
[83]
(1) laminar, I$la~iua pronle; (2) lerba~lcnl.
I/,-lh pwcr law, d = 17 lnln
(= 1.30 in), ext.orna1 vclocil,p ti, =
27nl/scc (89 ltfscc); t~~rln~lcnce inlensily
T = 0.03%
tlistril,~~tion curve. 'l'l~c changes in the velocity profiles in the transit.ion region have
becn plottctl in Fig. 16.4. They arc based on ~noasurcmcnts pcrformctl by C. R. Schubauer
and 1'. S. Klcbanoff [$3] in a stream of very low turbulence intensity and
it is seen that in this case the transition rcgion extends over a range of Reynolds
numlwrs from about R, = 3 x 10Vto 4 x 10" In this mngc, the boundary-layer
profile cl~angcs from that of fully tlcvclopccl laminar flow, as calculatecl by Rlnsius,
to fully tlcvclopctl turl)uloit flow (see Chap. XXI). The process of transition involves
a large tlccrcnsc in the shape factor lIlz .-.. d,/d,, as seen from Fig. 16.5; here dl clenotcs
tlie clisplnmmont thickness anti cSz is the momentum thickness. In the case of a
flat plxta, the shape factor tlecrcxscs from IIlz w 2.6 in the laminar regime to Illz w 1.4
in t,lio f.~trl~~~lt?rit, rcgirnc.
'I'his change in the velocit,y di~tribut~ion in tho transition region can be utilized
for the convcnierit tlctcrminntion of the point of transition, or, rather, of the tmnsition
region. The principle is explained with the aid of Fig. 16.6. A tmtal-hen11
t,ul,c or a I'itot tube is moved parallel to the wall at a distance which correspontls
t,o the maximurn tlifirc~noe bctwccn tho velocities in the laminar and turl~ulcnt
rrgirncs. On I,cit;g rnovctl clownstrca~n across the t,ransition region, the tubo sl~ows
a fairly sudtlcn it~c:rcasc in the total or tlynamic pressure.
'I'mnsitiorl on n flat plate also involves n large change in tile rcsistanrc to flow,
in this rnsr in t.11~ skin friction. In laminar llow the skin friction is proportiorid
to I 111. I .5 pnwt~ of vrlocity. cyn. (7.33), wlir~-as in t ~~rl~~lrnt, llow the powrr inrrrnsrs
to :~l)oul, 1.85, as shown a long time ago by W. I'rordc (2!)1 who prrforrnc~l towing
~xprrimenta wit11 platcs at very high Itrynolds rininbers In this conncxion the
I
reader may also wish to consult Fig. 21.2.
Morcrcrcnt cxpcrimrnb performed by 11. W. Etnmons [25], and G. 73. Scl~~tbaucr
and 1;. 8. Itlrbanoff [83] have ~hown that in the case of a flat phlc tfhe process
of tr:~nsit,ion is also intrr~nitt~ent and ronsists of an irrrgular scqncriro of Inminar
ant1 t,11rI1111rnt. rrgions. As cxplnin~cl in Fig. 16.7, at. n given point in the boundary
laycr there occurs sudtlcnly a small t.~~rhnlcnt area ('turbulent spot'), irregular
Fig. 16.5. CIIRIIR~ in L11c s11nj)c inctor
Illz = 0116~ of t,l~e hol~ndnry Inycr for n
flat plnte in the t,rnnnition rcgion nu men-
28
L6
uttrctl by Schuba~~cr nnd Klcbnnofi [R3]
qltot.otl from [ti51
14
1. / 1. 1 I
Fig. 16.6. Erplnnntion ofthe rnrtl~ocl oiclclrrrnining the
poiition nf thr point of trnrmit.ion with tho nid oin totd-
I--l--
'F JW rW 600 1
hend tube or n Pitot tube I- bminar A- trawhbn 4- turbulent --
in shape, whicl~ then travels downstream in a wedge-shaped region, as shown. Such
turbulent spots appear at irregular intervals of time and at different, mntlomly
distribulad points on tho plntc. In the inlmior of the wodgc-like tlo~nain tho llow
is prctlo~ninantly ttnrl)ulentt, wht?rcns in the adjoining regions if, nltcrnirt,os co~~t,it~r~oirsly
het,wecn being laminar and turbulent.. In this conncxior~ sco also rcf. I I:)]. A 1)a.pr.r
by M.E. McCormick [57n] deals with l.hc problem of thc origin of sr1c:11 tturl,r~lt3~~t
spots. St turns out tht an artificially created turbulent spot docs not persist w11r11
the Rcynolds number has a value lower than Ril = GOO; Ibis is consist.ct~l~ wil.11 t,ltc:
value of the criticnl Itcynolds nu~nl~cr cnlc~~lntctl with 1hc nid of I.hc li~~tsnr #I.nl~ilit,y
t,heory, cqn. (16.22). Vcrg dctnilcd cxpcrimcnt,ml invrstigntions t,t~rl,ril~trt, sl,ot.s,
and in particular of the velocity distril~t~t.in~~ in them, havc been cnrricd out by
J. Wygnanski et al. [lo$].