Boundary Lyer Theory

360
XIII. Laminar bonndory Inyers in compressible flow
l'tg. 1:1.1!). Srl~licren photogrnpl~ of shock wave; direction of flow front left to right, aftcr
Adtrrrt, Ifrldtnnnn nnd Ilott [I]: rr) 1:lrninnr bonntlery layer; tnult.iplo I-sliock, M = 1.92.
R,r, - :!!)(I; I)) turl)ulrnt 1)011ndwy lnyrr; normal ul~ork, M - 128, Rn, - 1159
I'ig. 18.20. lsohars in a shock re-
gion in Intninnr flow (I-sl~ock),
i~flrr Arkc-rrt. Iprldrnnn~~ and
I(ot,t I I ]
au& t)econie of the same order of magnitude, and tmnsvrrsc prrssurc grntlirrlts ciLn
also occur tllcrc. Both conditions rcntler tho well-known nss~~mptions of hnrttltl:uylayer
theory invalid.
The a,ppenrancc of tho shock wave is funtlamcrltnlly tliFfcrctlt tlrl)c.t~tlillg 011
whrthcr the boutttlary lnycr is laminar or t,url)rtlcnt,, Fig. 133.19. A sllor(, tlist:~iic-p
allcntl of tltc point wltcrc the csscnt,ially pcrpctdicrtl:~r sltovlc wave itnpit~gcs "11 :I
laminar boundary layer, there nppea.rs a short Icg forming a so-cnllcct I-s~Io&.
Fig. 13.19n.. Tn gcncml, wllcn the boundary lnyer is turbulcnt,, the rtor~nnl sltoc:li tloc.~
not split and no I-shocks a.rc formed, Fig. 13.19b. An obliv~ce shock wlticlt ilnpit~gek
on a laminar boundary laycr from the outside becomcs rcllectcd from it in t,llc for111
of n fan of expansion waves, Fig. 13.30a. Ilowever, whcn t.he bountlary lnyrr is
trurbnlcnt, the rcflcxion nppmrs in the form of n mow concc?ntmt,cd cspnt~aiotl wn.vcx
(Fig. 13.30b).
The plot of isobaric curves in Fig. 13.20 ant1 the prrssrtrc curvcs in lcig. 1:j.21
how t,hat t.lw rat,c of prcssnrc incrcnsc along a Iaminnr or :I tnrl)~rlcnL Im~titl:~r~.
lnycr is more gratlnal than in tltc cxtcrnal strcam. 'l'his llrtttcnirlg ol' Lltc prcssltrc
gradient in the boundary layer is described by stating t,llat the prcssurc dist.ribrrtion
"diffuses" near the wall. It is observed that diflusion is much lnorc prono~tncctl
for a laminar tphan for a turbulent boundary Iaycr. The tlifkrcncc bcLwccn 1nniinn.r
and turbulent shock diffusions can also be recognized from Fig. 13.22 which roprcscr~t,~
tho pressure variation along n flat platc placed parallcl to n supersonic st.rmtn. 'L'hc
mcasnrcmcnts were pcrforrnctl by 11. MT. Ilicpmnnn, A. lto~ltl~o attd S. I)h:r\viw
[64]. The pressurc plob llavc been tnlren mar thc point on tllc platc whcrc t,hc
oblique shock produced by a wedge interacts with thc boundary laycr. Tltc prcssurc
gradient is co~;sitlcrnbly stccper for the turbulcnt t,hnn for the 1:rrninnr I)oltntlary
Iaycr. The witltl~ of diffusion is cqunl to about 100 d in t,hc case of int.nr:wfiotl with
Fig. 18.22. Prrsqnro tlistrihution along n
flat plate at supersonic velocity in the
016
ncigl~bonrl~ood of the region of reflcxion
of n shock wave from laminar and tur-
8 7
hrllcrtt borrntlnry layers, xftrr Lirpmann,
008