Boundary Lyer Theory

Fig.. l3.16. In 13.18. lain~innr honnclary layrr in co~nprrwihlc subsonic flow for the s~~ction
nick? c,T t.llc NACA H4 10 nrrol'oil on I,lm nsnu~npt.ion of :in ncli;r\iat,ic wall. Angle of incirlcnre a - 0".
h1:1~11 11111nlwr M,., -- Il.rr/~,.,; I'r:\ncll.l nl~nilwr P -- 0.725. Chlwliltpion b:wcd on the approxi-
e. Intcractioa between shock wave and bountlary layer
Wlicn a solid hotly is placcrl in a stream whose velocity is high, or when it flies
through air with a high velocity, local rcgions of supersonic velocity can be
forri~ctl in il,s nc~iglil~ourliootl. The transition from snpcrsonic velocity to subsonic
vclocit.y against, the adjoinir~g adverse pr~wn~re gradient will u~nally take place
I hrough :L s110ck WRVC. 011 crossing the very thin shock wave, the pressure, density,
:rntl t.rm~)or:~l.urc of L11c Iluid chnngc at cxt,rcrnely high mt.os. l'lio rates of changc
arc so high t,liat, thc t.ransit,ion can hc rcgdcd as heing discontinuous, except for
the irnmetliat,~ ncighbourhood of the wall. The existence of shock waves is of functarn.cnt,al
itnport,ancc for the drag of the body ,as they often cause the boundary
I:~ycr 1.0 scp:lrnt,e. 'l'ho t,licomtical calcalatio~~ of shock waves and associated flow
lit-lais is wry tlil'lin~rlt,, n.nd wc do not propose to discuss this topic here. Experiments
sliow tl~nt, the processes of shook and boundary-layer formation intteract strongly
Fig. 13.18. n) Velocity distributions and
b) temperature distrib~~tions in tho boundary
lnycr nt dilTcrant Mar11 numlmm
e. Inl~rnolion lwtwccn sl~ock wave and I~OIIII~II~~ lnycr :m
6,
with each othcr. This leads to plienotncna of great cornplcxity I)cca~isc tlhc I)chavio~~r
of the 1)orrndary layer clcpentls mainly on the Reynolds nurnhcr, whereas t,hc conditiorrs
in a wavo arc primarily tlcpendor~t on t,hc I\Iac:Il numI)rr. I'hr c.arIicst. syst(xmatic
investigations in which tlicsc two influences urcrc clcarly scparatrtl Iin.vr been
putt to hand a long t,irnc ago. .I. Acltcwt.. IF. Fcltlnin~it~ alltl N. 1tot.t [I], 11. \,V. Lir11-
mann 16x1, G.R. Qndtl, W. lloltlcr and J. I). Rcg:~.n
l38] varictl ill t.llcir cslwitncnki
t.he Reynolds and Mach numbers inrlcpendcntly of cach other ard so s~tcc:ccdcd in
providing some clarification of this complex interaction. The most import,ant rcs111&q
obtninotl in t.hc ahovc t.tircc invcstignt.ions nrc tlr:xc:ril)c.tl in t.llis wc:t.ion. \Vc IIIIIS~,,
however, add that a cornplctc ~~ntlcrstantling of tthcsc complcx l)hc:nonirn:~ 11:~s 1411tlctl
us to this clay.
The pressure incmasc along the l~ounclary laycr must ultin~:~tcly l)c t,hc same
as that in the cxLcrnal flow because the streamline which sepamt?es tho two rrgions
must, 1)c:oomc pnr:cllol to tho c:oritn)ur of tfho body :~f't,c.r I,llo shoc:k. 111 1,111: I~otrrttl:wy
hycr, by its n:bturc, lhe parliclcs rlcnr the wall rnovc with subsol~ic vc1oc:itics 1)ut.
shock waves can only occur in supersonic stmarns. It is, thcrcforc, clear t,l~at a shock
wavc which origirratcs in thc extcrrlal st,rcarn cannot rcach right 111) to the wall,
and it follows that tho pmssurc gmtlicnt. prnllcl to t.1~: wnll musk On much rnorc:
grwl~rd in the ~lcigIil)ourl~ood of lhc wall thn in tho cxt,crrl:~l sl,ro:~n~. N~ir 1.110 ~toirtt
whcrc the shock wavc reaches t,owards the wall, the rahq of changc of al~laz and