Boundary Lyer Theory

252 XI. .\xi:rlly ~yrnrnctriral and t,llrce-ditncnsiot~al bonntlnry layer3
Approxi~~lntr ~rtrtl~ntl. 1,. l'r:~.t~rlt.l 1721 laic1 tlowtr a. progr:~~r~tnc: for ot)t,airlillg
so111lio11s wilh I,IIc nifl of IIIV tnonrct~tum I~I~wr(~rn, i. r. ill a wajr which
:I.II~II,~X~III:I~(*
is siniihr 1.0 I hat. r~scvl ill Sro. X'1 11. In l)art,icular, t-hc set of rqunt,ions (1 1 .45) to (1 1.48)
tr:~nsli)rtns illto lh;~,, Iiw :L y:~wcttl cylintlcr when it. is assurnccl formally that - const
:111tl when t,llc a.zitnr~ll~:ll IIIOI~~II~~IIIII thiclctlcss rj~?.~ is rrprrscntcd 11.v t)l~c formula.
=7
A siti1il:tr :tpl)roxil~lat~(~ rncthod was usrtl by J. M. Wild 11241 for the solution of
thc prol)l(trn of the ynwocl cylirdcr. Figure 11 .I4 reprcscnt.~ the pn.t.tern of st.rcamlines
for :I y:~wctl rllij)t.ic cylirdrr of slrndcrnrss ratio 6 : 1, placed at, an angle of incitlcnce
to the sI.mnm. 'i'hc lift corfficirnt has a valuc of 0.47. The arrows shown ill the sketch,
intlic:at.c~ the ~lirrct~io~i of flow of thn vclocity conlponent pan.llcl to the wall in its
immctlint~c ~lcighl~or~rllootl, i. e. thc value
A
Il'ig. 11.14. Ihnd:~~y-l:~yrr flow abor~L a
y:rwrd rlliptical ryli~drr with hfL, altar
.I. M. Wild ( 1241
Vig. ,I 1.15. JSxplnnation of origin of crous-
flow, on a yawcd wing at an angle of inci-
dcnce. Curves of constant pressure (isobars)
on the ~nction side of the wing. Near the
leading edge on the uppcr snrface of the wing
there is a harp pressure gradient at right
angles to the main stream and towards the
receding end causing cross-flow
d. Three-dimensional boundary laycrs 253
The respective streamline is shown as a broken line, and the potential streamline
is seen plotted for comparison It is noticeable that thc flow dircction in the boundary
layer is turned by a large angle towards the rrrecling end of tho cylinder. This rirrum-
stanre is very important when flow patterns on yawed wings are obscrvcd with the
aid of tufts
Swept wings. The cxistencc of cross-flow which occurs in the boundary laycr of
a yawed cylinder is important for the aerodynamic properties of swept wings. When
yawed or swept-back wings operate at higher lift values the pressure on the suctiot~
side near theleading edge shows a considerable gradient towards the receding tip,
the effect being due to the rearward shift of the acrofoil sections of the wing. This
phenomenon can be inferrcd from Fig. 11.15 which shows the isobars on the suctibn side
of a yawcd wing. The fluid particles which become dc~clcrat~cd in the boundary layer
have a tendency to travel in the direction of this gradient, and s cross-flow in khe
dircction of the rccctling tip results. As dc~nonsLr~~.tod by in011~11romotit.s p~rror~no(l
by R. T. Jones [58] and W. Jacobs [55], thc boundary layer on t h receding portion
thickens, the effect leading to prcmaturc scpnration. In aircraft cq~~ippcd with sweptback
wings separation begins at the receding portion, i.e. ncar the ailerons, nntl causes
the dreaded one-winged staU to occur. It is possible to avoid this kind of sepamt.ion,
and hence to prevent one-winged stalling, by equipping the wing with a 'boundarylaycr
fence' which consists of a sheet-metal wall placed on the suction sidc in the
forward portion of the wing, thus prevent,ing cross-flow. An aircraft with swept-back
wing.? and x boundary-layer fence on each half of the wing is shown in Fig. 11.16.
W. Liebe [66] reported on the improvement in wing charactmistics which can be
attained by these means. A paper by M. J. Queijo, B. M. Jaquet and W. 1). Wolhart
[90] t1cscril)cs extensive mcnsurcment,s on models providctl with 'houridnry-layer
fences'. The papers by ,J. Black [8] and I). ICucchemann (641 contain morc details
Fig. 11.16. Jet fighter De ITavilland D. 11. 110 wil.ll rrwcpt-back wings and a I~wndnry-layer
fence at cdge of each ailcron; from W. J,icl)c [66]