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NACA RM A55L14
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
PRELIMINARY REPORT ON A STUDY OF SEPARATED FLOWS
IN SUPERSONIC AND SUBSONIC STREAMS
By Dean R. Chapman, Donald M. Kuenn,
and Howard K. Larson
This paper is a preliminary and brief account of some research con-
ducted during the last two years on the general problem of flow separation.
The research is fundamental in nature, being partly theoretical and partly
experimental. Measurements have been made at subsonic as well as super-
sonic speeds for a variety of two-dimensional model shapes, each involving
separation. Study is made of the over-all pressure rise for incipient
separation, as well as the pressure rise to the separation point and to
the first peak (or plateau) pressure in flows where sizable separated
regions exist. Detailed cognizance is taken throughout of the location
of transition relative to the reattachment and the separation positions,
as this relative location was found to be the most important variable
Flow separation is an unusually common and important phenomenon in
aerodynamics. It can occur, for example, on compressor blades, near
control surfaces, in rocket nozzles, on airfoils, or near regions of a
surface from which a shock wave has been reflected. Separation often
limits the effectiveness of various devices which depend on the dynamics
of fluid flow for their successful operation.
The purpose of the present research was to obtain fundamental or
general information about separated flows. It was hoped that such research
would lead to a better understanding of separation phenomena. This
approach was taken with the philosophy that, to a designer, one general-
ization or one understanding can sometimes be worth many data points.
Inasmuch as an understanding was a prime objective, the various model
shapes selected for study were relatively simple. All were two-dimensional
NACA RM A55L14
configurations. They included forward facing steps (which would simulate
the flow, for example, upstream of a spoiler control), rearward facing
steps (which would simulate the flow behind a base or a spoiler), com-
pression corners (which would simulate the flow over an inlet ramp or a
deflected flap), curved surfaces (which would simulate the flow over one
side of a compressor blade), special models producing leading-edge separa-
tion, and configurations producing separation by reflecting a shock wave
from a boundary layer.
The experiments were conducted in the Ames 1- by 3-foot supersonic
wind tunnel no. 1 at Mach numbers between 0.4 and 3.3. The over-all
Reynolds number range investigated (based on characteristic model length)
was between 4,000 and 4,000,000. Wall static pressure distributions,
surface oil-film observations, and high-speed motion picture studies were
made, In the present publication, development of theory and description
of experimental details are not included.
ef local skin-friction coefficient at beginning of interaction
L characteristic model length
M Mach number
p static pressure
Ap P Po
q dynamic pressure, u-
Re Reynolds number
x longitudinal distance along model chord
p mass density
o beginning of interaction at outer edge of boundary layer
* just downstream of reattachment zone
d dead air
NACA RM A551J4
The most general result arising from the research is that a single
variable appeared dominant throughout in controlling pressure distribu-
tion, irrespective of the particular Mach number, Reynolds number, or
model shape investigated. This signal variable is the location of transi-
tion relative to the reattachment and separation positions. Because
transition is so important, classification of the separated flows is made
at the outset, as illustrated in figure 1, into three essentially differ-
ent types, depending on the relative location of transition: a "pure
laminar" type illustrated at the left for which transition is downstream
of reattachment, a "transitional" type illustrated in the center for which
transition is between separation and reattachment, and a "turbulent" type
at the right for which transition is upstream of separation. The pressure
distributions represent wall static pressures. As is indicated, the par-
ticular configuration for this figure is a step model tested at a Mach
number of 2.3. The characteristics here exhibited, however, actually are
rather general. For the laminar case the separation point S, (which was
determined by oil-film observations) is associated with a relatively small
pressure rise and is followed by further rise to a plateau pressure which
represents the dead-air pressure of the separated region. High-speed
motion pictures taken of this pure laminar separation at several thousand
frames per second show the flow field to be remarkably steady. These
characteristics are in contrast to those of the transitional-type separa-
tion in the center portion of figure 1. The pressure rise to separation,
and the plateau pressure rise remain small, but an abrupt pressure rise
associated with transition, and occurring at about the same streamwise
location as transition, now makes itself evident and alters the flow
field. High-speed motion pictures showed this transitional type of separa-
tion to be unsteady. Random movements of the shock waves were observed
as were random changes in the angle of flow separation. Perhaps we should
expect this since the transition phenomenon itself, which is of dominant
importance to these flows, is known not to be steady. Same of these
characteristics of transitional separation are in contrast to those of
turbulent separation represented by the example at the right of figure 1.
The pressure rise to the turbulent separation point is about five times
greater than that to a laminar separation point. There is no plateau
pressure, although there is a peak pressure in the separated region.
Downstream of this region the pressure rises to a terminal value higher
than the peak pressure. It was somewhat surprising to observe in high-
speed motion pictures that this turbulent-type separation is relatively
steady not rock-like steady as the pure laminar separations but, never-
theless, quite steady compared to the transitional separations. In pass-
ing, it is to be observed that plateaus in pressure are associated with
laminar separations and may be thought of as approximating the idealized
"dead-air" region; but in turbulent separations an eddying motion keeps
the air very much alive so that the term "dead-air" is only a figurative
NACA RM A55L14
It does not seem necessary to exemplify further the three types of
flow separation, although each type has been found and studied for the
various other models investigated. They exhibit the same qualitative
phenomena, that is, they show the relative transition location to be domi-
nant in controlling pressure distribution throughout the investigation.
Although the dominating role played by transition previously does not
appear to have been generally appreciated, the recognition of transition
as significant to separated flow is by no means new. In studying the flow
over a cylinder, for example, Schiller and Linke (ref. 1) noticed the
strong influence of transition location within a separated layer relative
to the location of separation. Other examples can be cited from experi-
ments, such as the recent ones of Gadd, Holder, and Regan (ref. 2), wherein
the importance of transition relative to the location of reattachment also
was clearly recognized. It should be noted, further, that Crocco and Lees
(ref. 3) attempt directly to include the relative location of transition
as an essential variable in their analysis of separated flows. They
consider the importance of transition relative to a "critical" station
in the wake (this station being determined from mathematical character-
istics of their equations), rather than relative to the reattachment
location (this being determinable from experiments with oil film or surface
shear stress), but these two ways of describing relative transition loca-
tion may represent essentially the same thing.
By keeping close account of the relative location of transition
throughout the investigation, several experimental trends were observed
which appeared to be general. These trends can be illustrated from a plot
of the dead-air pressure in various separated regions as a function of
Reynolds number. Figure 2 represents such a plot: once again, pure lami-
nar separations are on the left, transitional separations in the center,
and turbulent separations on the right. The Reynolds number is based on
body length. Individual data curves are not identified, as this is unnec-
essary for the general purpose at hand. Suffice it to say that these
curves represent various combinations of Mach number and model shape. They
also include one set of data obtained by Love (ref. 4). The ordinate is
the absolute value of the pressure change across the reattachment region
p' p divided by the pressure p' just downstream of reattachment; p is
measured at an arbitrary fixed point in the separated region. By focussing
attention on the pure laminar separations at the left, it is seen that some
of these are affected to a negligible extent by variation in Reynolds
number. This agrees with a theory described later which indicates no
effect of Reynolds number on those pure laminar separations for which the
boundary-layer thickness at separation is zero. Other curves show a
Reynolds number effect which amounts, at the most, to only about a 1/4
power variation. In these cases the boundary-layer thickness at separa-
tion is not negligible. Generally speaking, pure laminar separations are
affected only to a small extent by Reynolds number. If focus now is
shifted to the transitional separations in the center portion of figure 2,
it is seen in contradistinction, that these flows can be affected markedly
by variation in Reynolds number. Such effects are particularly pronounced
NACA RM A55L14
when transition is near reattachment, as is the case for the left portion
of each curve. Movement of transition upstream of reattachment (brought
about by an increase in Reynolds number) increases the pressure change
through the reattachment region. Turning now to the turbulent separations
on the right portion of the slide, it is seen that for this type of separa-
tion there is no significant effect of Reynolds number discernible from
An explanation can be given as to why transition location is so
important to a separated flow. This explanation is based on a theoretical
mechanism postulated as fundamental to all separated flows. Very briefly,
the mechanism requires that a balance exist between the mass flow scav-
enged out of the dead-air region by the separated mixing layer and the
mass flow reversed back into this region by the pressure rise through the
reattachment zone. Inasmuch as the mechanism helps in understanding vari-
ous results, a digression temporarily is undertaken to present some results
of experiments especially designed to test quantitatively this mechanism.
There are certain special conditions for which both the mass flow
scavenged from a separated region and the mass flow reversed back into
the region can be calculated without empirical information. These condi-
tions are for pure laminar separations with zero boundary-layer thickness
at separation. All calculation details will be bypassed and only end
results shown. The theory provides an equation in closed form for the
dead-air pressure as a function of the Mach number M' and the pressure
p' which exist just downstream of the reattachment zone. The equation
is not very complicated, as is evident from figure 3. It involves the
ratio of specific heats 7, the Mach number, and a number 0.655 which
arises from the solution of a nonlinear differential equation with definite
boundary conditions. This number involves no empirical information; it
cannot be adjusted to take up any slack between experiment and theory.
The data points represent both supersonic separations from the present
experiments, and low subsonic-speed separations from some experiments of
Roshko at the California Institute of Technology (ref. 5). Three different
models are represented: A model producing leading-edge separation, a
flat plate normal to the stream, and a circular cylinder. It is evident
that the strictly theoretical calculation, which indicates the dead-air
pressure to be independent of both Reynolds number and model shape, agrees
well with the experiments.
With the knowledge that the mechanism postulated has satisfactorily
been put to quantitative test, an explanation can be given as to why the
location of transition relative to reattachment is so important to a
separated flow. Suppose transition were to move suddenly from a position
just downstream of reattachment to a position just upstream of reattach-
ment. The introduction of eddies just upstream of reattachment would not
affect the scavenged mass flow (since this depends on conditions along
the length over which mixing takes place) but would have a pronounced
effect of reducing the reversed mass flow (since the eddies would energize
NACA RM A55L1-4
the low velocity portions of the mixing layer just before reattachment
and thereby would enable more air to excape downstream). Consequently,
balance of the two mass flows would occur at considerably different pres-
sure when transition moves upstream of reattachment. Whether the flow
upstream of reattachment is laminar or turbulent is just as fundamental
to a separated flow as whether the flow upstream of separation is laminai
In regard to the quantitative test of the theoretical mechanism,
reference is made to the recent researches of Korst, et al. (ref. 6).
Korst considered the case of fully turbulent (rather than fully laminar)
separation with zero boundary-layer thickness at separation. Comparison
of his calculation method with the one used above for fully laminar separa-
tion reveals some differences in detail, but essentially the same physical
idea as to the mechanism which determines the pressure of the separated
region. Good agreement is obtained by Korst between his calculations and
measurements of base pressure for thin turbulent boundary layers at separa-
tion. The results of the two independent researches appear complementary
in substantiating the common physical idea employed.
While distinction need not be made between subsonic and supersonic
separations when considering qualitatively the importance of transition,
it is necessary to make such distinction when considering most other
aspects of flow separation. There is a basic difference between subsonic
and supersonic separation which should be recognized before discussing
such questions as "What pressure rise will separate a given boundary
layer?" Figure 4 illustrates the pressure distribution upstream of a
compression corner in subsonic flow at various Reynolds numbers. The
dotted line represents the calculated distribution that would exist in
inviscid flow. Variation in Reynolds number is seen to bring about only
small departures from this distribution. Moreover, the separation point
(indicated by the filled symbols) and the pressure rise to separation are
essentially independent of Reynolds number. These results indicate, as
is well known, only a minor interaction of boundary layer with an external
subsonic flow. The situation is quite different in supersonic flow, as
first anticipated by Oswatitsch and Wieghardt (ref. 7), and as illustrated
in figure 5. These data are for the same model as that in figure 4, tested
in the same wind tunnel, and investigated over the same Reynolds number
range, only at a supersonic Mach number of 2. In this case the dotted
line representing pressure distribution in inviscid flow bears little
resemblance to the experimental distributions; moreover, both the location
of separation and the pressure rise to separation depend considerably on
the Reynolds number. Such results indicate a dominant interaction of
boundary layer with an external supersonic flow. Local interaction of
this type near supersonic separation can dominate the picture to the exclu-
sion, for example, of effects of downstream object shape. Such supersonic
separations can be termed "free interactions."
Free interactions are subject only to the boundary-layer equations
and the external-flow equations; it turns out that they are amenable to
NACA RM A5514 7
a simple dimensional analysis, the details of which will not be presented
here. The end result of such analysis, for both laminar and turbulent
separation, is that any distinguished pressure rise in a free-interaction
flow is proportional to the square root of the local skin-friction coef-
ficient existing at the beginning of interaction. Comparison of this
theoretical result with experiment is made in two figures: figure 6 for
laminar separation, and figure 7 for turbulent separation. In figure 6
both the plateau pressure rise and the pressure rise to the separation
point are plotted as functions of Reynolds number for various model shapes.
Both are seen to be independent of object geometry inasmuch as four dif-
ferent shapes are represented a compression corner, a step, a shock
reflection, and a curved surface. Such independence would be required
of a free interaction. Also, the variation in both cases follows closely
the theoretical variation as the square root of skin friction, which, for
laminar flow, is a variation as Re' 14. Mention is made that for the
special case of pressure rise to a laminar separation point, a Re-J/4
variation was first calculated by Lees (ref. 8), although various sub-
sequent analyses, most of which neglect the interaction phenomenon, have
obtained different variations. The present experiments cover a wide enough
range in Reynolds number (a factor of 50 to 1) under sufficiently con.
trolled conditions to settle finally this question of Reynolds number
dependence in two-dimensional, supersonic, laminar separation.
Turning now to free-interactions in turbulent flow, it is clear that
the square root of turbulent skin-friction coefficient will vary little
with Reynolds number, so the pressure rise to turbulent separation also
should vary little with Reynolds number. Experimental data confirm this,
as shown in figure 7 which includes same data of Gadd obtained at the
NPL in England (ref. 2). The trend of data is consistent with the dotted
line representing a variation as the square root of turbulent skin fric-
tion, although it could be said with equal correctness that there is no
significant effect of Reynolds number evident from the data.
In order to simulate in a wind tunnel any flow separation phenomenon
of flight, it is necessary that the location of transition relative to
reattachment be duplicated. This requirement is especially pertinent to
hypersonic wind-tunnel investigations as a consequence of two results:
(1) If a separated laminar mixing layer is relatively stable, transition
will occur near reattachment, a condition under which Reynolds number
effects are most pronounced, and (2) the stability of a separated mixing
layer increases markedly with increasing Mach number. The first of these
results can be deduced from the center portion of figure 2. The various
curves are steepest at their left, where transition is near reattachment,
rather than at their right, where transition is near separation. The
second of these results is illustrated in figure 8. Plotted against Mach
number in this figure are data points representing the maximum Reynolds
number up to which pure laminar type separations were found under the
present wind-tunnel conditions. The reference length for this Reynolds
number is the distance Ax along the separated layer between the reattach-
ment point and the separation point. Consequently, such Reynolds number
NACA RM A55LL4
measures the stability of a separated laminar mixing layer. According
to figure 8, the separated laminar layer at subsonic Mach numbers is
stable only to about 30,000 Reynolds number, whereas at Mach numbers near
5, it is stable to several million Reynolds number. Thus, an increase
in Mach number has a pronounced stabilizing effect on the mixing layer.
This trend is consistent with that calculated by Lin (ref. 9) for neutral
stability to certain restricted types of disturbances.
For purposes of comparison, in figure 8 an analogous boundary is
shown which represents the maximum Reynolds numbers of transition reported
to date from wind tunnels under comparable conditions. The area under
this top curve represents the domain of laminar boundary-layer flow under
wind-tunnel conditions of essentially constant pressure and zero heat
transfer. Inasmuch as flight conditions differ from these, and yield
different Reynolds numbers of transition (as do experiments in different
wind tunnels) the significant result is not the detailed position or shape
of the two boundaries in figure 8. Instead, the important result is that
under comparable conditions the stability of a separated mixing layer
encroaches on that of the boundary layer as the hypersonic regime is
Because of this trend, pure laminar separations which have been
primarily laboratory curiosities in the past might become common prac-
tical phenomena in the future. There are several reasons why this trend
looks significant and warrants much research effort. One reason, already
mentioned, is that it means the Reynolds numbers of hypersonic wind tunnels
must match those of flight more closely than has been done in the past.
Another reason is that separated laminar regions have some unusual charac-
teristics which are intriguing from the viewpoint of opening new possibil-
ities: for example, the skin friction in such regions obviously is a
small thrust due to the reversed flow; this is nice from the viewpoint
of drag. Also, the heat-transfer characteristics would be quite different
from those of a boundary layer. In fact, a recent theoretical calculation,
as yet unpublished and untested by experiment, indicates the heat transfer
in a laminar mixing layer to be roughly 0.6 of that in a comparable laminar
boundary layer. Such considerations clearly outline what appears to be
a profitable task for future research.
As a final topic for discussion, distinction is made between various
types of pressure rise associated with separated flow, and an opinion is
given as to their significance for design purposes. Only turbulent sepa-
rations are considered. Three types of pressure rise are distinguished,
as schematically illustrated in figure 9. Here two flow conditions are
depicted for a simple compression corner which can be thought of as a
deflected flap. One pressure distribution, represented by the dotted
line, corresponds to a flap deflection which produces a separated flow.
The other flow condition, represented by the solid line, corresponds to
a somewhat smaller flap deflection for which there is no appreciable
separated region, but for which the flow is just on the verge of separat-
ing. We distinguish between: (1) She pressure rise to the separation
NACA RM A55L14
point S of a flow already separated, (2) the first peak pressure rise in
a flow already separated, and (3) the over-all pressure rise for incipient
separation in a flow for which the boundary layer is just on the verge of
separation. The pressure rise to separation likely would not be of inter-
est to a designer, but would be to a research worker concerned with the
mechanism of turbulent separation. The first peak pressure rise, on the
other hand, would be of interest to a designer concerned with loads, hinge
moments, or flap effectiveness. The over-all pressure rise for incipient
separation would be of interest to a designer who does not want a flow
to separate, yet wants to achieve the maximum pressure rise possible, such
as is the case for inlet design.
All three types of pressure rise are compared in figure 10, the
smallest being the pressure rise to the separation point. This is indi-
cated by a single dotted line inasmuch as it is independent of the mode
of inducing separation. The peak pressure rise always is greater than
the rise to the separation point, and is indicated by a region (shaded in
fig. 10) since it depends on the geometry inducing separation. The over-
all pressure rise for incipient separation of various configurations,
represented by the curves through data points in figure 10, also depends
on the particular configuration. In fact, this dependence is a strong
one. The three sets of data represent shock reflections taken directly
from Bogdonoff's data in reference 10 together with compression corners
and curved surfaces from the present experiments. In the past it some-
times has been assumed, for lack of specific data, that the peak pressure
rise is essentially the same as the over-all pressure rise for incipient
separation. As figure 10 illustrates, and, as was initially pointed out
by Bogdonoff, the over-all pressure rise for incipient separation can be
considerably greater than the peak pressure rise. It is realized that
these available data on over-all pressure rise for incipient separation
are rather meager inasmuch as geometry is so important to incipient separa-
tion. Consequently, additional information along these lines currently
is being obtained.
1. The variable most important to a separated flow is the location
of transition relative to the reattachment and the separation positions.
By classifying the various separated flows studied according to the rela-
tive location of transition, certain qualitative characteristics (Reynolds'
number effects and flow steadiness) were the same for all cases
2. Several predictions of a theoretical mechanism postulated as
fundamental to separated flows have been satisfactorily tested by special
experiments conducted for the case of pure laminar separation with zero
thickness of boundary layer at the separation point.
NACA RM A55LL4
3. The stability of a separated laminar mixing layer increases
markedly as speed increases over the range investigated (from subsonic
Mach numbers to Mach numbers just below the hypersonic regime).
Ames Aeronautical Laboratory
National Advisory Committee for Aeronautics
Moffett Field, Calif., Nov. 3, 1955
1. Schiller, L., and Linke, W.: Pressure and Frictional Resistance of a
Cylinder at Reynolds Numbers 5,000 to 40,000. NACA TM 715, 1933.
2. Gadd, G. E., Holder, D. W., and Regan, J. D.: An Experimental Inves-
tigation of the Interaction Between Shock Waves and Boundary Layers.
Proc. Roy. Soc. of London. Series A, vol. 226, Nov. 9, 1954,
3. Crocco, Luigi, and Lees, Lester: A Mixing Theory for the Interaction
Between Dissipative Flows and Nearly Isentropic Streams. Jour.
Aero. Sci., vol. 19, no. 10, Oct. 1952, pp. 649-676.
4. Love, E. S.: On the Effect of Reynolds Number Upon the Peak Pressure-
Rise Coefficient Associated with the Separation of a Turbulent
Boundary Layer in Supersonic Flow. Jour. Aero. Sci. Readers' Forum,
vol. 22, no. 5, May 1955, P. 345.
5. Roshko, Anatol:
On the Drag and Shedding Frequency of Two-Dimensional
NACA TN 3169, 1954.
6. Korst, H. H., Page, R. H., and Childs, M. E.: A Theory for Base Pres-
sure in Transonic and Supersonic Flow. Univ. of Ill. Engr. Exp.
Sta., Mech. Engr. Tech. Note 392-2, Mar. 1955.
7. Oswatitsch, K., and Wieghardt, K.: Theoretical Analysis of Stationary
Potential Flows and Boundary Layers at High Speed. NACA TM 1189,1948.
8. Lees, Lester: Interaction Between the Laminar Boundary Layer over a
Plane Surface and an Incident Oblique Shock Wave. Princeton Univ.
Aero. Engr. Lab. Rep. 143, Jan. 24, 1949.
9. Lin, C. C.: On the Stability of the Laminar Mixing Region Between
Two Parallel Streams in a Gas. NACA TN 2887, 1953.
10. Bogdonoff, Seymour M.: Some Experimental Studies of the Separation
of Supersonic Turbulent Boundary Layers. Paper presented at the
Heat Transfer and Fluid Mechanics Institute, Univ. of Calif. at
Los Angeles, June 23, 1955. aSection V, pp. 1-10.
NACA RM A55uL4
THREE REGIMES FOR A STEP (M= 2.3)
.5 .7 .9 1.1 .3 .5 .7 .9
LONGITUDINAL DISTANCE, X/L
ON PRESSURE RISE
I 1 1 11. 1 I, I I I I i 1 IIIII I I 1 I 111 11
104 105 105 106 106 107
REYNOLDS NUMBER, U L/U/
NACA RM A55I.4
TEST OF THEORY FOR PURE LAMINAR FLOW
4 8 12 16 x 103
-- 0 -.-O -0 -
0 VO 0 [
o ReL= 115,000
O 2 3
LONGITUDINAL DISTANCE, X, IN
NACA RM A55LL4
(FREE INTERACTION) Mo= 2
o ReL= 184,000
.2 I- SEPARATION
LONGITUDINAL DISTANCE, X, IN
PRESSURE RISE IN LAMINAR SEPARATION
Mo = 2.3
Ac f-(Re) 4
104 2 5 105 2
REYNOLDS NUMBER, 20'
IACA RM A55L14
TURBULENT SEPARATION-POINT PRESSURE
\ (GADD, NPL)
0d OL Q
I I I 1 I I I
4 .6 .8 I 2
REYNOLDS NUMBER, Uox
MAXIMUM REYNOLDS NUMBER
DOMAIN OF LAMINAR K .-
S LAMINAR SEPARATION
N" l l l
I I I XI
4 6 8X106
U0 X trans
NACA RM A55UI4
PRESSURE RATIOS FOR TURBULENT SEPARATION
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