Boundary Lyer Theory

3 8
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Y?\
If. 011tli11e of boundary-layer throry
Fig. 2.20. Overall view of
flow pat,tmn (schematic)
around a rcctnngular st.ructure
[MI. a) Side view with
foreward hound vortex in
the stagnation zonr and a
~cperatod roof lmtntlnry
layer; h) ~tpwitd fme and
vortex ~hcdding from the
t hn windward rornrr of thr
roof
Fig. 2.21. Acrofoil and cir-
cular cylinder drawn in
such relation to each other
as to produce the same drag
in parallel flows (parallel to
axis of svrnmetry of awofoil)
circuhr cr/linder: Drag
To conclude this section, we wish t,o tlisc~iss n particr~ln.rly telling example of
enectively it is possible to reduce the drag of a body in n st,rearn wl~et~ the srl)nrntioll
of the boundary layer is completely elirninatrtl antl when, in ntltlit,iol~, the I~otl~ itsrlf
is given a shape which is contlucivc to low rcsist.nncr. Pig 2.21 ill~lstrnt.cs tllr c.i~(:ct,
R fnvvrnble sllnpe (strenndine body) on drag: it syintrteLrlc ncrofoil n~~tl a rirc-lllar
c:ylintlcr (thin wire) have brrn drnwr~ hrrc to n relative scdo wllicl~ rtssr1rc:s c:clrlnl tIrng
in slwnms of cqnnl velocit,~. The cylinder has a tlrag corfficicnt (:I, % 1 wit,l~ rc?spct,
to it,s frontd arcn (scr also Fig. 1.4). 011 t.hc otllcr hnnrl, l .1~ (Irag cocfficic:t~t.oft II(, ;I(.I.ofoil,
rcferrctl to iLs cross-seclionnl arm, has the very low vnl~lc* of f:, - 0.00(;. 'I'll!:
cxt.romrly low tllxg of thc ncrofoil is ncl~icvetl ns n rcsctlt, of n cnrt$r~ll~ cltosc.~~ ,)l.olilc~
which assures llmt the boundnry Inycr rernnins laminar ovcr nlmost t,l~c \vl~olc of its
wett.ed Irngth (Inminnr ncrofoil). Tfit,l~is conncxion, Chap. XVf l nt~tl, c!s~)rc.i:tll~, Icig.
17.14, sl~o~~ltl Ije consult.cd.
c. Turhulertt llnw in n pipe and in n bot~ntlnry layer
hlensnren~cnt,s show t11n.t the t.ypc of mol,iorl tl~ro~~glr n rirwlnr pipr which was
calculal.cd in Section ld, and in wl~ich 1.11~ vclocily tlislril)trt.ion w:~s p:wnbolic,
exists only at low and n~odcrnte Reynolds numbers. The fact that in thc laminar
motion tinder disoussion fluid Inminno slide over each other, and ll~i~t tllcrc: aro no
rndial vclocit.y romponrnt.s, so t.hnt t.he prcsslrre clrop is proportiot~:~l t,o the firs1
power of t.he lncnn flow vrlocit.y, const.itmtrs nn esscnt.in1 c:l~arnrt.rristic: of this t.ypc
of flow. This cI~arnrt.rrist,ic of the motion can bc mntlc rlrnrly visil,lo 1,s inlrotl~lcit~g
a dye into the st.rmm and by tliscl~nrging it tl~rougl~ a t,llin t~~l)c, Fig. 2.22. At, t,l~c
motlernt,~ Rrynolds nunlhers associntcd wit,l~ Intnit~nr flow tl~e tlyc is visit)lr in
lhr form oi a clearly tlefinetl t,l~read ext,cnding ovcr thr. wllolc Irngtl~ of t,hc pip.,
Fig. 2.22a. 13y increr~sing tlte flow velocity it, is pnssil~lc 1.0 rmch a stngr. .vheii t.hc
Ruid pnrtic!les cease to move alor~g st,m.igl~t linrs antl t .1~ rcgrllnrity oC the mot.ior~
brrnks down. l'l~c colourcd Lltrencl bcc:o~nc~ mixed wit,\) the flltitl, its sharp out.li~tc?
becomrs blurred ant1 nvcmt.11a.ll.y thc whole cross-srrtioll Iwrotnrs colortrrtl, Pig. 2.221).
On t.lw n,xinl n~otion t,hcrc are now s~~pr~.i~njmotl irrc~gr1l:tr rntlial Il~~ct.rt:~t.iot~s wl~irlt
clli.c.t the mixing. Such a flow pnttern is cnllccl l~~fiule~r!. 'l'l~r tljw cxl~crilnrnt was
first carried out by 0. Reynolds 1291, who nscertninctl tl~nt, the taansitsic.n honl
the laminar to Llle t~~rh!cnt t,ypc of motion ttaltcs pl:rcc at a tlcfinit.~ v:t.lnr of IIIV
I