Boundary Lyer Theory

218 X. Approximntn met,hods for shndy equntions d. Further oxnrnplea 219
-4 f~~rther example is shown in Fig. 10.12 which contains results for a symmetrical
Zhukovskii nerofoil at zero incidence. The point of minimum pressure is at x/l' =
= 0.141 which is very far forward on the aerofoil. The pressure rise at the rear is
very gradual so that the point of srpamt,ion lies very far downstream of the point
of minimum pressure, i. e. zll' = 0.470. Since the Zhukovskii aerofoil has a cusped
trailing edge t,hc potential velocity at tho trailing edge is djffcrent from zero. For
details of additional systcmntic boundary-layer calculations concerning nn extensive
serics of Zhukovskii aerofoils with different thickness and camber ratios and at
cliffrrcnt angles of incitlcnre, refcrcnce may he made to a piper by K. nussmnnn
and A. Ulrich [2].
Pig. 10.0. Potcntinl velocity
distribution function on ellip-
tical cylinders of slenderness
o/h = 1, 2, 4, 8, tlic direction
of the stream being parallel to
tho major axis
R ;-; position or point of srpnrrtion
Fig. 10.10. Ilrsulls of Lhc? cnIculnt,ion of hor~ndnry In.yers on ollipt,icd cylinders of ~lcndorncss
n/b t 1, 2, 4, 8, Jcig. 10.9. n) displnrernnnt~ t,liickrirsa of the boundary layer, h) shape factor
r) chraring st.rrw nt the? ~d. 2 1' -- rircllllifcrr~~~~c of blic rllipsc; n/b -. 1 rirct~lnr cylintlcr; n/b = m
flnt plate
A review of the very numerous approxi~nate methods which have been proposed
so far is contained in the collective book entil.lod "Laminar Boundary Layers"
1181 - . nnd edited by 1,. Rosenhcad.
In an effort to improve t,he accuracy of the calculation of laminar boundary
layers, many authors replaced the preceding single-pnrameter methods by oric employing
tim pramelers. This is acl~icvcd whon t,hc encrgy intcgrnl cquntion is sntisfed
in addition to the momentum intcgrnl equation (ace e. g. I