Contributions on the Mechanics of Boundary-Layer Transition Page: 4 of 12
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REPORT 1289-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
region contains a mixture of the two distinct mean-velocity
profiles, one pertaining to the laminar flow and the other
pertaining to the turbulent flow. The steps from the one
to the other register on the hot-wire as fluctuations and
account largely for the high fluctuation level in the vicinity
of the maximum. Referring to figure 3, it is seen that the
step between laminar and turbulent profiles disappears
around 0.1 inch and is small percentagewise at greater dis-
tances. This is about the location of the foot of the peak in
figure 4. It is seen also that the peak subsides as the down-
stream end of the transition region is approached. The
fluctuation profile at 8 feet is similar to that observed for
fully developed turbulent flow.
It is clear that turbulent characteristics are fully developed
at the end of the transition region. This is perhaps not
surprising since this is already far from many points of initial
transition. An interesting question is, how close to the point
of actual breakdown are the steady-state characteristics of
turbulent profiles to be found ? At this stage of the investi-
gation it appeared that the real obstacle to obtaining the
answer to this question, as well as to studying the mechanism
of transition itself, was the fluctuating character of transi-
tion which made measurements at a transition point prac-
tically impossible. Since the well-known wedge of turbu-
lence behind a single roughness element appeared to offer
the possibility of a sharp line of transition well away from
the disturbing element, attention was turned to this case.
TURBULENCE WEDGE
If a particle of sufficient size is placed on the surface in a
region of laminar flow, transition occurs at the particle, and
a wedge-shaped region of turbulent flow extends down-
stream. Such wedges have frequently been observed on
airfoils starting from particles of dirt or similar surface
irregularities. It has also been observed that when the
particle size or the velocity is reduced, the wedge may begin
some distance downstream from the particle. In any case
the particle introduces disturbances which cause breakdown
of the laminar flow.
It appears that various observers agree on nearly the same
value for the half-angle of the wedge and report values in
the neighborhood of 100. Thus, the width of the turbulent
region increases more rapidly and is always much wider than
the wake of the object initiating the wedge. Charters (ref.
5) appears to have been the first to call attention to this
more rapid spreading and termed the effect "transverse
contamination."
The wedge was introduced into the present investigation
mainly in the hope that it would provide a reasonably sharp,
stationary line of demarcation between laminar and turbu-
lent flow at which phenomena at the position of changeover
could be studied. However, it was soon discovered that the
previously reported sharp outline was only an average con-
dition and that the wedge was in reality bounded by an
intermittent region as shown in figure 5. It was further
found that only when the particle was sufficiently large orthe velocity was sufficiently high did the sides become
straight and the angle attain a constant value. When these
conditions were not met, even though transition occurred at---Time-
_ - r / .. IS1/8 in sphere
2ft from L E
FIGrraE 5.-Turbulence wedge produced by three-dimensional rough-
ness element (A-inch sphere) on surface. Time interval between
dots, 1/60 second; U1==80 feet per second.
the particle, the sides initially curved outward, approaching
the proper angle asymptotically.
Figure 5 shows a fully established wedge produced at a
free-stream velocity of 80 feet per second by a g-inch sphere
cemented on the surface of the plate 2 feet from the leading
edge. This case was investigated in some detail with a hot-
wire probe and a total-head tube. Beyond a fully turbulent
core, subtending a half-angle of 6.40, was a region in wllichl
the turbulence was intermittent, as illustrated by the oscillo-
grams in the figure. The outer limit of the intermittent
region subtended a half-angle of 10.60. It is interesting to
note that this value agrees reasonably well with the value of
9%3 found by Charters to be the angle of transverse con-
tamination.
Since one purpose in using the wedge was to learn how soon
after abrupt transition the fully developed, steady-state
condition would be found, mean-velocity profiles were
determined with a total-head tube. Within the turbulent
core the profiles were those characteristic of a fully developed
turbulent boundary layer. While the so-called transition
in this case was not sharp, the intermittent region was short.
compared with that found in free transition on a flat plate:
Thus it appears that the only requirement for the existence
of the fully developed character is that the flow be turbulent
all of the time.
The oscillograms in figure 5 show typical conditions at
several points. Here, as in figure 1, the time scale runs from
right to left, and the interval between timing dots is eo
second. The top record shows the sudden velocity step-up
at the beginning of a turbulent region and the ending followed
by a slow fall in velocity which was always characteristic
of a record obtained with a hot-wire close to the surface.
A possible explanation of the regular repetition of turbulent
bursts is given in the section "Artificially Initiated Turbulent
Spot." The second record shows a very short pulse near
the outer limit having a suggestion of the characteristic
shape. The third record obtained near the apex of the
wedge, although giving the appearance of being composed
largely of spikes jutting upward, has traces of the character-
istic shape. The fourth record shows disturbances in the
laminar layer caused by the presence of the wedges. With-856
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Schubauer, G. B. & Klebanoff, P. S. Contributions on the Mechanics of Boundary-Layer Transition, report, February 28, 1955; (https://digital.library.unt.edu/ark:/67531/metadc60685/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.