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III IlIlIllIllIllIll
111 111
BREAK
SEPARATED-FLOW TRANSITION
PART 1 - EXPERIMENTAL METHODOLOGY AND MODE CLASSIFICATION
Ansa Hatman and Ting Wang
Department of Mechanical Engineering
Clemson University
Clemson, SC 29634-0921, USA
ABSTRACT
This first part of the paper presents techniques implemented for
the experimental investigation of the transition mechanism in 2-D
pressure driven separated boundary layer flows over a flat plate at
inlet free-stream turbulence intensities ranging from 0.3 to 0.6%
and imposed adverse pressure gradients ranging from K = - 0.68
x10 6 to - 6.25 x10-6 . The structure and behavior of the separation
bubble were investigated for various flow conditions. The
separated•flow transition modes were identified and classified. The
distribution and strength of the adverse pressure gradient were
obtained by varying the test section outer wall divergence angle.
Specific methods identifying the main parameters that
characterize separated-flow transition are introduced and issues
regarding measurements of reverse flow are discussed. The methods
implemented in determining the separation point, maximum
displacement location, the unsteady reattachment region, the start
and end of transition, etc. are described.
NOMENCLATURE
Cp
En(f)
H12
= 1 - ( 1J.../1J...0)2; pressure coefficient
I-D power spectrum of u
frequency
shear layer thickness
= 81/82 ;shape factor
.(WU.,2 )(dUeddx): pressure gradient parameter
1-8
geometrical pressure gradient parameter, eqn. (2)
local pressure gradient parameter, eqn. (3)
= (41. - ts); separation bubble length
Rex
.U.,x/v ; local Reynolds number
Rea
.U...,LTN; transition length Reynolds number
Reg,
.U.,81/v ; displacement thickness Reynolds number
Re81
Re g2
.U.,82/v ; momentum thickness Reynolds number
KO
Kim&
Regax =Re82T Re82r
integral time scale
lii
free-stream turbulence intensity, u71.1.„
mean velocity in streamwise direction
u'
r.m.s. streamwise velocity fluctuation
V
mean cross-stream (normal) velocity
v'
r.m.s. cross-stream velocity fluctuation
-uv
Reynolds shear stress
YD
Yo
coordinate in streamwise direction
dividing streamline
zero velocity line
Clack
8
81
62
O
•
•
X
▪
•
boundary layer thickness
displacement thickness
momentum thickness
divergence angle
separation angle
turbulent intermittency
integral length scale
dissipation time scale
kinematic viscosity
Utica=
LT
max
MD
•
RI
u'ron
- Real t
0
= (xi - ic,); transition length
peak value
maximum displacement location
reattachment
first reattachment (long bubbles)
separation
onset of transition
end of transition
mid-transition point, where us reaches maximum
local free stream conditions
inlet conditions
INTRODUCTION
Presented at the International Gas Turbine & Aeroengine Congress & Exhibition
Stockholm, Sweden — June 2—June 5,1998
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To predict the aerodynamic and heat transfer characteristics of a
body immersed into a flow stream, the boundary layer development
along its surface must be accurately determined; this development is
influenced by the laminar-to-turbulent transition, which causes a
drastic increase in both skin friction and convective heat transfer.
In engineering applications, extended transitional boundary
layers can be encountered. For example, it is common that 20 80% of the boundary layer developed on the gas turbine blades or
vanes are in transitional regime. Especially in the low pressure
turbine of an aircraft engine crusing at high altitudes, when the air
density is reduced and the Reynolds numbers become very low,
extended transitional boundary layer is a norm, and boundary layer
separation may occur. Accurate predictions of both aerodynamic
and heat transfer performance are important for turbine design.
Transition can be affected by different parameters such as
pressure gradients, free-stream turbulence intensity, acoustic
waves, flow unsteadiness, surface vibration, surface curvature,
surface roughness, wall temperature, etc. Each of these parameters
can influence the start and length of the transition and the structure
of the transitional boundary layer. A generally accepted
classification (Mayle, 1991) shows that there are four important
modes of transition in a boundary layer: natural transition, bypass
transition, separated-flow transition, and reverse transition. The
natural transition begins with weak instabilities (infinitesimal
disturbances). Through the amplification of the TollmienSchlichting waves and nonlinear vorticity breakdowns, it becomes
a fully turbulent flow. The bypass transition is caused by large
(finite) disturbances in the external flow (e.g. high free-stream
turbulence intensity) or on the surface (e.g. roughness)• and
completely bypasses the Tollmien-Schlichting mode of
instability.
For large streamwise adverse pressure gradients, the formation of
a transitional separation bubble is likely to occur. The detached
laminar shear layer is inherently unstable and promotes the growth
of disturbances leading to an earlier laminar-to-turbulent transition.
Then, turbulent mixing due to the increased entrainment in the
rapidly growing turbulent part of the separated shear layer causes
the shear layer to reattach. The separated-flow transition may or
may not involve linear instability of the Tollmien-Schlichting
type. At high Reynolds numbers, the extent of such a separation
bubble is small, on the order of 1% of the chord (Tani, 1964), and
the slight change in the pressure distribution produced by the dead
air region has a negligible effect on the forces acting on the
surface. With an increase of incidence angle or a reduction in speed
or Reynolds number, the shear layer may fail to reattach, and the
short bubble may burst to form either a long bubble, or an
unattached free shear layer. The pressure distribution associated
with a "long" bubble is different from that of the inviscid flow, and
the forces acting on the airfoil are therefore changed. Bubble
bursting creates a significant increase in drag and an undesirable
change in pitching moment.
Separation is the generic name given to a broad class of flow
phenomena. The most important feature characterizing this class is
that the flow becomes detached from the body surface allowing a
region of reverse flow to develop between the body and the
separated shear layer. Fig. 1 presents a conventional view of a
pressure driven separated boundary layer development. A dividing
streamline between the shear layer and the recirculating region
starts at the separation point x s and makes an angle y with the
surface. The height of the separation region, yD, increases almost
linearly downstream of the separation point, reaches a maximum
Transition Turbulent
.1.11 0.1 4
separated boundary layer
free-stream velocity distribution
Laminar
, unseparated bo ndary layer
free-stream velocity
distribution
XR
dividing
streamline
ge of separated
separated
boundary layer
shear
.,,,a11141111110111111
lay
w
ge of unseparated
bound la er
ano
reverse
flow vortex
zero velocity line
turbulent
reattachment
dividing streamline
Fig. 1 Conventional view of a 2-D laminar boundary
layer separation: (a) streamwise free-stream
velocity distribution; (b) boundary layer
development; and (c) velocity profiles along
the separation bubble.
above the center of the reverse flow vortex and collapses with the
reattachment process. Due to this actual displacement of the shear
layer, the rate of growth of the separated boundary layer thickness
8(x) is considerably higher than that of an attached boundary layer,
and the free-stream velocity distribution is locally modified.
In a decelerated boundary layer, the retarded flow in the boundary
layer does not posses sufficient momentum and energy along the
body surface to overcome the pressure rise downstream, and finally,
the fluid particles near the wall are brought to rest. The main
stream, itself decelerating, is unable to energize the fluid in the
boundary layer, and an almost stagnant fluid region develops near
the wall. The abrupt thickening of the near-wall reverse flow region
accompanied by significant values of the velocity component
normal to the wall leads to the reverse-flow-vortex breakaway and
subsequently to a strong interaction with the free-stream flow.
Separation provides a mechanism whereby vorticity can be
transported into the inviscid flow field; whereas, in attached flows
the vorticity is confined within the boundary layer.
There are too many published studies related to boundary layer
separation to be cited here. Empirical data on the formation of the
transitional separation bubbles, under different experimental
2
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F.>
conditions, have been obtained by many authors, such as: Gault
(1955), Caster (1967), Horton (1968), Malkiel and Mayle (1995)
or Hazarika and Hirsch (1995), etc. The influence of the free-stream
turbulence intensity on separated flow behavior was studied by
Roberts (1980). Significant computational work on separated flow
transition was undertaken by Smith (1987), Brown et al. (1988),
and Pauley et al. (1990), to name a few. However, not many studies
specifically investigated the interaction between separated flow and
laminar-turbulent transition.
Therefore, to improve the physical understanding of the
separated-flow transition process, detailed measurements were
performed in two-dimensional boundary layers over a flat plate at
zero incidence. The main work focuses on investigating the
complex interaction between laminar-turbulent transition and flow
separation. The results of this study will serve as a reference for
future studies under more realistic gas turbine conditions, such as on
airfoil surfaces under elevated free-stream turbulence.
x
Flat Plate Test Surface
Outer Wall
Fig. 2 Test section geometry
Table 1 Synopsis of experimental flow conditions
U.,0
IK671 xpl iml 1 xD2 im)
_ _a
r iisj_ 1
BASELINE 20.55
EXPERIMENTAL PROGRAM
To investigate the effects of the streamwise pressure gradients on
transition, the nondimensional pressure gradient parameter:
(1)
K= (v/U2)(dUadx)
was used to characterize the experimental flow conditions. The
desired K distribution was obtained by adjusting the geometry of
the test section in the wind tunnel. Theoretically, by assuming onedimensional inviscid flow and ignoring the effect of the boundary
layer growth, the free-stream velocity distribution can be derived
from mass conservation.
A constant value of K parameter can be kept simply by setting
the flexible outer wall of the test section into a wedge shape. When
the boundary layer separation occurs, the resulting pressure
distribution is very different from the theoretical one. For constantK favorable pressure gradient and low adverse pressure gradient
cases without separation, the fine adjustment of the outer wall for
eliminating the effect of the boundary layer growth can be applied.
For separated boundary layers, the adjustment for a constant-K flow
is no longer feasible. Consequently, the configuration with the
outer wall straight in a wedge-shape was adopted for all the
experimental cases.
The pressure gradient parameter K evaluated from the test section
geometry is designated as the geometrical pressure gradient
parameter KG and it is determined by the value of the inlet freestream velocity, the test section outer wall divergence angle 0, and
the inlet test section width L:
(2)
KG = tan / UL.
CASE 1.1
CASE 1.2
CASE 1.3
CASE 1.4
CASE 1.5
CASE 1.6
CASE 1.7
CASE 1.8
CASE 1.9
16.25
15.90
8.25
5.30
8.85
9.50
4.90
4.06
4.39
CASE 11.1
CASE 11.2
CASE 11.3
CASE 11.4
CASE 11.5
16.20
11.60
7.05
3.55
2.38
1
Series 1
-0.91
0.7
-0.69
0.48
-1.26
0.23
-2.07
0.48
-1.24
0.48
-1.16
0.70
-2.13
0.23
-2.57
0.23
-3.38
0.70
Series 11
-0.92
0.70
-1.28
0.70
-2.10
0.70
-4.17
0.70
-6.22
0.70
0 [o]
0
0
8.1
6
5.7
6
6
8.1
5.7
5.7
8.1
1.60
1.60
1.60
1.60
1.60
8.1
8.1
8.1
8.1
8.1
The parameters were selected based on the results obtained in the
preliminary studies, so that transitional separated boundary layers
could be produced for various types of bubbles.
A systematic method of generating various types of transitional
separated boundary layers was applied by varying the free-stream
velocity and the outer wall divergence angle. The flow rate was
adjusted through a variable frequency motor controller. To avoid the
wind tunnel unsteadiness in the low-speed cases, an additional inlet
fan damper was used to control the flow rate. Table 1 shows the
geometrical parameters for the baseline case (zero pressure
gradient) and the fourteen separated boundary layer experimental
cases. The tests in Series I were conducted in a flow configuration
with constant divergence angle from xrn to the end of the test
section. For the tests in the Series II, the adverse pressure gradient
was reduced downstream of x02.
For each experimental case, boundary layer single hot-wire
measurements were taken on a test surface that was instrumented
with pressure taps for pressure distribution measurements. Among
the many tested conditions, three representative cases. CASE 1.9,
11.1, and 11.3, were selected to be repeated using the cross-wire of a
three-wire probe for detailed turbulent shear stress measurement.
The behavior of separated flows is sufficiently different from
unseparated flows to warrant special attention to experimental
techniques and the data reduction procedure used. Flow qualification
studies must be carefully done to assure that the time averaged
properties of the flow field are satisfactorily two-dimensional in
KG is a convenient parameter to be used for indicating the global
pressure gradient strength, however the actual K deviates locally,
more or less, from the geometrical determined constant value.
To control the relative locations of the separation point and the
onset of transition, the laminar boundary/ layer was allowed to
develop in zero pressure gradient conditions from the leading edge
to some location, xDI, as shown in Fig. 2. The adverse pressure
gradient was applied downstream of this location. For several sets
of data, the effect of the flow conditions at reattachment on the
separation bubble's structure was also investigated by suppressing
the wedge angle downstream of xD2 location to reduce the adverse
pressure gradients.
The experimental flow conditions for each case were obtained by
combining different overall streamwise pressure gradients 1CG
(different Qand U.„0) and different locations for the start and the end
of the adverse pressure gradient region, xDi and xD2.
3
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the test section. The two-dimensionality was checked by evaluating
spanwise agreement of wall pressure measured at several streamwise
locations. The experiments were conducted at low free-stream
turbulence intensity, with the inlet value varying from Tu = 0.3 at
high velocity cases to 0.6 % at lowest velocity case. Ambient
conditions that included temperature, barometric pressure and
humidity were also measured for corrections of air properties.
Heating and Cooling
Circulating System
Honeycomb
thid
Test Facilities
A 2-D, open circuit, blowing type wind tunnel shown in Fig. 3
was used. Before entering the test section, the air was drawn
through a filter box, forced through two grids, a honeycomb, a heat
exchanger, a screen pack and a contraction nozzle.
The flow rate was adjusted by a variable frequency motor controller
and inlet damper to obtain wind tunnel speeds from 1 m/s to 25 m/s.
The vertical test wall is a rectangular surface 2.4 m long and 0.92 m
high. The test section had a width of 0.15 in and a large aspect
ratio of 6 that helped reduce edge effects and achieved twodimensionality for the boundary layer flow in the center-span of the
test wall. The boundary layer suction was applied through a double
slot bleeding at the ellipsoidal shaped leading edge of the test wall,
so a near zero thickness boundary layer could be achieved at the
theoretical x = 0 streamwise location. A longitudinal slot was cut
along the centerline of the test section's outer wall that allowed the
velocity measurements to be obtained by traversing the hot-wire
probe along the test wall centerline through the slot at any
streamwise location. Other than the measuring location, the
remaining slot was covered with rubber bands. The test surface was
instrumented with 48 pressure taps, 1 mm in diameter and flush with
the surface. The pressure taps arrangement is shown in Fig. 4.
Flow Rate Heat
Control Exchanger
Valve
Fig. 3 Plane view of the low-speed 2-0 boundary
layer wind tunnel facility
Flow direction
Equal spacing: 50
Equal spacing: 30
fc&gicpacing: 25
Equal spacing: 30
Equal cpacirtg' 50
ual spacin :150
,20011'
Instrumentation
The boundary layer measurements were obtained using hot-wire
anemometry. First, a single hot-wire was used to measure the mean
streamwise velocity and ruts values for all 15 cases investigated. A
single TM hot wire, model 12185-TI.5, operating in constant
temperature mode at an overheat ratio of around 1.8 was used. The
single hot-wire measurements served as a guidance for the multiplewire measurements because the single wire could better approach
the wall, to within 0.1 nun. The cross-stream Reynolds stresses and
the cross-stream velocity component were determined for three
cases using the 2.5 gm tungsten cross-wire arrangement of a
custom-designed three-wire probe, which is smaller than a
commercial one (the spacing between the 'X' array is 0.3 mm). The
third wire of this probe is a 1.2 gm platinum wire, which will be
used for future temperature measurements in similar separated flow
conditions. The details regarding the development and qualification
of the three-wire sensor were presented by Shome (1991) and Wang
et al. (1996). Attention was paid to the calibration procedure,
especially in the low-velocity range below 1 m/s, where the
calibration equation shows large deviation from King's Law. A
polynomial calibration equation was used to reduce the uncertainty
of low velocity measurements in the near-wall region and at the
interface between the shear layer and the separation bubble.
The hot-wire probes were positioned by a traversing equipment
that consisted of a stepper motor mounted on a slide and was
controlled by the data acquisition program. For all the probes, a TSI
Model IFA 100 system was used as a constant temperature
anemometer. A sampling frequency of 2 kHz for 20 seconds
acquiring time was used. In the preliminary studies, it was
determined that the mean and fluctuating velocity components
maailwiwww)66
6' „ tow 0350
500
650
All holes- 4) Ini
R011
1100
All dimensions are in mm
F g.4 Layout of static pressure taps on the test
surface
converged to within I% for sampling durations of about 10 seconds
even for very low flow speeds.
The wall static pressure measurements were performed using the
pressure taps on the test surface, which were connected to a pressure
transducer through a 48-channel Scanivalve system.
Pressure Measurements
Time averaged static pressure distribution provided a way of
determining the mean free-stream velocity distribution in the test
section. Surface pressure measurements were used to roughly
determine the bubbles location and its extent.
The static pressure measurements were used to evaluate the
pressure coefficient: C p=2(p-p.,)/(pU.,02) and the pressure gradient
parameter K = (v/I.J... 2)(dUn/dx). The difficulty in determining the
pressure gradient parameter K resides in the proper evaluation of the
velocity gradient (d1.1 0„/dx) from discrete data points. Besides the
geometrical pressure gradient parameter, KG, given by equation (2),
a local pressure gradient parameter. Kieed, given by equation (3),
was defined. The local value of the pressure gradient parameter at
any location situated between two consecutive measured locations
x(i-l) and x(i) was determined as:
Kic,cat = v (U(i) - U(i-1)1 / [x(i) - x(i-1)) / U(i) / U0-0
(3)
4
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K w"! follows the local rapid pressure variations associated with
the separation and reattachment processes, while the K G
g eometrical parameter serves as a reference for the comparison
between different cases.
Velocity Measurements
For all fifteen cases investigated, the mean velocity (U) and the
streamwise velocity fluctuation (u') were acquired using a single
hot-wire probe. Some specific problems arose for the hot-wire
measurements in the recirculatin g region of the separated flow
because the hot-wire sensor is not directionally sensitive. Since in
the reverse flow and reattachment re gions of the separated flows
instantaneous flow direction is changing, the hot-wire sensor is
not an accurate velocity measuring tool. The hot-wire sensor's
insensitivity to the flow direction would result in distorted velocity
profiles, as shown in Fig. 5.
The actual magnitude of the reverse-flow velocity could not be
accomplished by simply inspectin g the profiles obtained with a
single hot wire. The region containing reverse flow is unstead y in
both streamwise and cross-stream directions; this results in a finite
minimum value at the location (y = yo) of the theoretical zero
velocity value. Therefore, even if the hot wires are not sensitive to
the flow direction, the near-wall local minimum could be treated as
the average zero velocity location yo. Due to the unsteadiness of
the reverse-flow region, and the possible rectifyin g effect of the
hot-wire measurements in the low speed flow, the velocity values
below yc, are subject to large uncertainty. Since in this study the
recirculation region was very thin, a more accurate measurement,
such as using the flying-wire technique was difficult and was not
employed.
The uncertainty in the mean velocity profiles near the wall makes
any indirect method unreliable. As a result, the boundary layer
integral parameters could not be accurately determined, and the
classical Causer procedure for determinin g the skin friction
coefficient of an attached turbulent boundary layer can not be
satisfactorily used in the separated flow re gion.
Furthermore, it is likely that such a probe disturbs the flow to
some degree. Mandel (1994) observed that a single wire probe
noticeably chan ged the velocity distribution only when it was
positioned very close to the separation location. In this case, the
free stream was observed to accelerate about 5%, and the size of the
bubble decreased about 2%. At no other location was the flow
significantly sensitive to the sensor intrusion. It must be
mentioned that in Malkiel's experiment, the separation bubble
dimension was one order of magnitude smaller than the bubble's
dimension analyzed in the present study. Therefore, it was
reasonable to expect that the present results were less affected by
the separated-flow sensitivity to the sensor intrusion than those of
Malkiel and Mayle (1995).
8
a)
(b)
Separated boundary layer mean velocity
profile: (a) typical velocity profile for
separated boundary layer flow; (b) velocity
profile measured using hot-wires.
YD
UN. dy 0
the resulting displacement thickness can be derived in the
following manner:
8 1 =58 (1 — UM.) dy =IY° (1 — UN.) dy 8(1
0
= y D — IYD
(U/U.,) dy + (1 — U/U.) dy = yp + f8 (I — U/U.) dy
YD
The Csplacement thickness is therefore at least as large as the
recirculation region, which may be greater than the thickness of the
separated shear layer: h = (5 - y o). The momentum thickness of the
entire velocity profile, including the zone of recirculatin g flow,
results primarily from the separated shear layer. Since (U/U.) is on
the order of 10-2 in the zone of recirculating flow, it can be
neglected, and the momentum thickness can be estimated as:
, 62
d
WUJ I — UN.) dy
=.
1YD
WU.,01 — UN) dy +
+ ja UN.(1 — U/U.) dy a lb UN(1 — UN.) dy
As a resul , accurate information of the velocity profile in the
reverse flow region is not necessary for calculating the boundary
layer integral parameters; 81 and 82 can be evaluated by considering
only the portion of the velocity profile outside the recirculation
region. This topic was extensively discussed by Schmidt and
Mueller (1989).
integral Parameters
INTRODUCTION TO A NEW APPROACH IN
ANALYZING SEPARATED-FLOW TRANSITION
The effect of the separation bubble on velocity distribution
downstream of laminar separation results in the development of a
recirculation region that causes a significant chan ge in the
displacement thickness.
Downstream of the reattachment point, the rate of change in
displacement thickness is much smaller. As shown in Fig. 5 (a), the
height of the dividing streamline (ye), which determines the
normal extent of the recirculating flow, is defined as the line of zero
massflux.
By assuming that on an average basis the net mass flow of the
recirculating region is zero:
The main objective of this research was to provide significant
physical insight about laminar-to-turbulent transition in separated
flows. At present, a reliable method for predictin g the characteristics of separation bubbles or a fully satisfac tory theory to explain
the bubble bursting process is yet to be developed. Furthermore,
the difference between the transition process in boundary layers
which are laminar at separation and those which are already
transitional at separation has not been addressed. The present
approach to analyzing the separate-flow transition is to identify
key parameters for describin g the phenomena of mutual
interactions involved in the transition process ' in the separated
shear layer.
5
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PRIMARY SEPARATED
FLOW TRANSMON MODES
Separated-Flow Transition Modes
The experimental results of Hatman (1997), presented in part in
this paper, led to a positive identification of three primary modes
of separated-flow transition. A detailed discussion of these modes
will be presented in part 3 of this paper, and the supporting data are
presented in part 2. However, a brief summary is presented here, to
make the data discussion easy to follow.
It was observed that the separated boundary layers which separate
in a laminar state behave differently from those which are already
transitional or highly unstable (pre-transitional) at separation. In
this study, the separation bubble types are defined by the flow
regime at the separation location.
A laminar separation bubble is defined as a separation that occurs
in the laminar or pre-transitional flow, x s <xt. A transitional
separation bubble is defined as a separation that occurs downstream
of the onset of transition, x s>xt.
At least three primary separated-flow transition modes were
positively distinguished. In this study they are defined as
transitional separation mode, laminar separation - short bubble
mode, and laminar separation - long bubble mode. The location of
the separation point relative to the onset of transition is used to
distinguish between transitional separation and laminar separation
modes. The differentiation between the separated-flow transition
modes also relies on the relative locations of the maximum
displacement and mid-transition points, as shown in Fig. 6.
The transitional separation mode occurs when the boundary layer
separation takes place at relatively high Reynolds numbers and low
adverse pressure gradient strength. The onset of transition takes
place prior to boundary layer separation and develops mostly as
natural transition. The transitional separation bubble can be
accompanied by vortex shedding.
The laminar separation - short bubble mode occurs at moderate
Reynolds numbers and mild adverse pressure gradients with the
onset of transition induced downstream of the separation point by
inflexional instability at the location coincidental with that of the
maximum displacement of the shear layer. It is characterized by a
quick transition completion due to a complex interaction between
the separated shear layer and the reverse flow vortex. The laminar
separation - short bubble mode is characterized by distinctive
vortex shedding.
When the laminar boundary layer separation takes place at low
Reynolds numbers and strong adverse pressure gradients, the shear
layer may fail to remain reattached and the laminar separation long bubble mode is likely to occur. Similar to the bubbles in the
short mode, the onset of transition in the long bubble mode is also
induced downstream of the separation point by inflexional
instability. The high fluctuations associated with the midtransition point lead to a local reattachment-like behavior. The
transition is forced to occur at low Reynolds numbers by the
ejection process, but due to a deficit of turbulence production, the
transition completion is considerably delayed. The laminar
separation long bubble is not accompanied by vortex shedding.
The passage from the transitional separation mode to the laminar
separation modes take place gradually through a succession of
intermediate stages dominated by one mode of transition or
another. The mode of transition is mainly determined by the
conditions at separation; however, the conditions at reattachment
may influence the length of the separated shear layer. A shear layer
in laminar separation - long bubble mode can be "forced" short
when the external flow configuration is such that the adverse
pressure gradient downstream of first reattachment is suppressed.
transitional separation mode
xt < Xs Xternax = XMD
Xt
INTERMEDIA1E
STAGES
laminar separation - dominant
transitional separation mode behavio
xs < xt < XMD Xu'max = XMD
Xs XMD XR
xthilas XT
Xs
dominant laminar separation mode
xs < xt < MAD Xtimax = XR
laminar separation
short bubble mode
xt = XmD
XmD XR
Xt Xdmax XT
Xdmax = XR
U
I
xs
Xs
XIND XR
XlifILIX
XmD XR
Xt
laminar separation
"forced" short bubble
xt - xmD
laminar separation long bubble mode
xt = XMD
Xl1.1113X =
XR1
XT
= XR1
-
xR
/OA
Xs
XMD XR1 XR
Xt Ulnas XT
XMD XR1 XR
Xt &in= XT
Fig.6 Separated-flow transition modes
Table 2 presents a classification and the main characteristics of
the primary separated-flow transition modes and of the intermediate
stages observed in the present study. In literature, the laminar
short bubble mode represents the most studied case, and it is
considered to be representative for the separate-flow transition.
The transitional mode has been ignored or unrecognized.
Mayle (1991) and Walker (1992) emphasized the limitations in
predicting separated-flow transition and the necessity of more work
of a fundamental nature in this area. Many existing separated-flow
transition models assume "instantaneous" transition at an
empirically determined "transition location" within the shear layer,
which gives good results for a laminar bubble in the short mode,
but completely fails to predict the transition onset of the
transitional mode and the length of transition of a laminar bubble
in the long mode. The present work intends to address these issues
with the support of experimental results.
Methodology for Establishing the Separated-Flow
Transition Parameters
In the present study, the separation location, the separation
bubble extent and elevation were primarily judged by analyzing the
mean velocity profiles, the rms velocity fluctuations and the isovelocity contours. The extent of separation was also cross-checked
with a tuft mounted on a thin pin and moved along the surface.
6
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1.7
1.8
1.9
11.1
11.2
11.3
11.4
11.5
665
2.71
0.69
-101
313
12
10
8
2.43
0.18
-2186
92
3.69
0.38
-2009
291
4.84
1.17
-91
954
1.74
0.47
-4108
-215
1.56
0.36
-1737
75
2.66
0.28
-2826
104
E S
2.78
734
835
4.98
1.88
181
710
3.67
0.97
-629
546
2.28
0.14
-1985
160
1.59
0.42
-2079
-135
E
E
So
$
o
o
x
a
x
al
0
li
x
li
x
ivID
R
02 4 60 24 6 0 24 6
U [m/s
e
E
o
a
x
E
o
u
x
6
u
x
E
E
6
II
x
at
o
n
x
R
S
0 01 02 0 01 02 0 OA 02 0 CO 02 0 01 02 0 OA 02 0 01 02
(b)
12
10
E
,
8
8 6
II
E 6 x
E
S
6
II
x
4
.
6.42
0246024
(a)
x = 0.66M
646
11
1.45
0.001S01
h‘.
5.11
2
0
CT
1318
m
1405
E
CO
cii
o
i
2
0
12
10
8
1
E6
;4
2
0
NOTE: The negative Resin. and Reams will be discussed in Part 2.
5
E
6
II
x
E
Zii
a
il
x
MD
1---'-'s
0204T02 0.4 0024
(c)
E
1g
c; o
II a
x Ic-
E
0
Ill
00
II a
x L.
0 0.5 1 0 0.5 1
(d)
S
d
u
x
R
S
0 02t4
E
CO
CR
6°
a II
x t-
0 02 0.4 J 02 0.4
E
•- ea? au
06
a u
x L.
R
0 0.5 1 0 0.5 1
0 0.5 1
F (ky
-
For bubbles generated at low Reynolds numbers, which were
characterized by large displacement and relatively strong reverse
flow vortex, the tuft method proved to be effective in determining
the separation bubble extent. However, this method gave
ambiguous results for the transitional separation bubbles, which
were relatively thin. Complementary information that supported
the decision-making was drawn from the pressure gradient and
integral parameters distributions. Fig. 7 shows the near-wall region
of the mean and normalized rms velocity profiles of a separated
boundary layer in laminar separation - short bubble mode of
transition (CASE 1.4). The separation parameters (xs, itmD, xR) can
be directly determined from the mean velocity profiles by
determining the elevation of the interface between the shear layer
and the recirculation region, yD, at each station. By plotting y0(x)
versus x, as in Fig. 8 (a), despite the uncertainty in determining the
wall-position in the separated region, a monotonic increase of yD
can be obtained for the laminar part of the bubble. This plot
presents a good outline of the separation bubble geometry and
provides a close estimation for the separation point, xs, maximum
displacement location, amp, and the reattachment point, xR.
At y = yo, the velocity fluctuations u values are relatively high,
and the mean streamwise velocity 13 reaches a local minimum.
Consequently, the interface y o between the separated region and the
shear layer is clearly indicated by a local maximum in the rms
streamwise velocity normalized by the local velocity, u'/U profiles.
E t E
..4.
r.:
o
o
x
x =0.96 m
r = 098
1.6
4.55
0
It
x
ei
II
I-:
o
u
x
r= o.o4
1.5
6.94
E 64
E
Nr
z x = 0.74 m
1.4
871
x10-5
E
o
wl
x= 0.66 m
1.3
885
Sear
• x= 0.58m
1.2
10.73
Rem.
RestLT
r= o
1. 1
Rex t
x1 05
5.05
to
Base
Separated-Flow
Transition Mode
natural transition
transitional
separation mode
transitional
separation mode
dominant
transitional mode
laminar separation
short bubble mode
laminar separation
short bubble mode
dominant
laminar mode
laminar separation
long bubble mode
laminar separation
long bubble mode
laminar separation
long bubble mode
transitional
separation mode
transitional
separation mode
laminar separation
short bubble mode
laminar separation
forced short bubble
laminar separation
forced short bubble
o ,
CASE
12
10 E
8
0
Table 2 Separated-flow transition parameters
zero velocity line, yo
Fig.? Separated-flow transition parameters for the
short bubble mode (Case 14)
The location of maximum displacement, xm D, is easy to
determine from the mean velocity profiles, as the location where
the near-wall low velocity region is the thickest (see Fig. 7 (a)).
The extent of the near-wall low velocity region is obvious even for
the thinnest separation bubbles.
The separation point is indicated by the occurrence of the first
sign of near-zero velocity gradient in the near-wall region (e.g.
Fig. 7 (a), at x = 0.5 m). If the actual separation point is situated
between two measuring locations, the point of the boundary layer
detachment, x s, can be determined by extrapolating the line that
connects the yD values of the first two stations in the separation
region until it crosses the y = 0 line, as shown in Fig. 8 (a). The
contour plot of U/Uoi, can also provide a visual aid for identifying
the separation location. The contour plots of U/1.1. and u'/U. are
presented in Part 2 of this paper. For a boundary layer measurement
very close to the separation point, the (u7U) profiles may also
show a local near-wall peak. The final decision regarding xs was
made by cross-checking all the above features.
The location of the reattachment "point" can not be precisely
determined due to the unsteady nature of the reattachment process.
Defining a "reattachment region" seems to be more appropriate
since a relatively extended region (5% to 15% of the separation
7
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bubble length) presents characteristics which can be associated
with the reattachment process.
The reattachment location, xR, can be identified by examining
the experimental data for three distinctive features. First; the
reattachment process is accompanied by a drastic drop in the mean
free- stream velocity; consequently, the local pressure gradient
parameter Ktocai reaches a minimum value at reattachment. Second,
the mean velocity profiles in the reattachment region have a
particular shape that reassembles Horton ' s "universal reattachment
profile " and is characterized by (aU/ay)y, = 0 and linear mean
velocity profile across the boundary layer from zero to the free stream value. To illustrate this feature, the velocity profiles at x =
0.74 m and x = 0.81 m are replotted in Fig. 9 along with Horton 's
reattachment profile. The velocity profile at x = 0.74 in is situated
upstream of reattachment region while the profile at x = 0.81 m
resembles Horton 's reattachment profile and can be considered at
the reattachment location. The analysis of the shape of the velocity
profiles acquired in the reattachment region for all the present
experimental cases has shown that they are similar, although they
deviated from Horton 's theoretical velocity profile in the near -wall
region where the condition: (aU/ay)y-0 = 0 cannot be strictly
satisfied due to the flow unsteadiness. The present study found that
the reattachment location can be better determined from the mean
shear (au/ay) contour plots which clearly show a near-wall
minimum at reattachment location (See Part 2).
Finally, the reattachment location can be also determined from
the distribution of the rms streamwise velocity normalized by the
local mean velocity, (u '/U). The near-wall (u '/U) peak always
reaches the maximum value at xR. For the laminar separation - short
bubble mode, the absolute maximum of u ' also occurred at xR.
The integral parameters streamwise evolution can also give
supplementary indications to confirm the chosen locations for xs,
amp and xR, as shown in Fig. 8 (b). The boundary layer thickness
6, the boundary layer displacement thickness 81 and the shape
factor H12 start increasing immediately downstream of the
separation point. The maximum values of 81 or H12 are clear
indicators for amp.
The decrease in the displacement thickness 81 downstream of
Xp,m, coupled with a steeper reduction in velocity between amp and
xR, lead to displacement thickness Reynolds number values at
reattachment much smaller than the displacement thickness
Reynolds number values at maximum displacement location.
As a rule, the displacement thickness Reynolds number reaches a
peak value at xMD. For laminas boundary layer separation the start
of transition x, coincides with xmD, therefore, for both short and
long modes, the transition length expressed in terms of
displacement thickness Reynolds number (Rents - Reathic, < 0) has
negative values (see Table 2).
The onset and end of transition were primarily judged by
analyzing the velocity traces, the spectral behavior and the
intermittency distribution. The onset of transition, xt, was ascribed
to the first measurement traverse for which the intermittency factor
was unambiguously I" > 0. It was observed that, for the laminar
separation - short bubble mode, the xt location always coincides
with that of the maximum displacement xmp.
The mid-transition point xis imax is, by definition, the x -location
where the ruts streamwise velocity fluctuation reaches a maximum
in the boundary layer, and it can be easily identified in Fig. 7 (b)
with the (u 'max /11...) profile at x = 81 m.
3.2
2.8
2.4
"E" 2
E 1.6
>.? 1.2
0.8
0.4
0
0.3
0.4
0.5
(a)
—0--
—
0.6
0.7
0.8
x Imi
0.9
1
8
82
s H
•
MD R
12
5
„
0.4
(b)
0.6
0.8
x [m]
Fig. 8 Characteristic features of separated - flow
transition: (a) shear layer - recirculation
region interface; (b) streamwise distribution
of integral parameters.
10
8
0.5
1
0
0.5
10
0.5
1
U/U
Fig. 9 Comparison between Horton's mean
reattachment velocity profile and
experimental data
For the laminar separation short bubble mode of transition, the
itu: max location always coincides with that of the reattachment
point xR and (01.10,),sias reaches values of about 0.18. The first
indication for the end of transition is given by the streamwise tins
velocity fluctuation evolution. As x -r is approached, the (u/U.)
profiles converge asymptotically to the characteristic shape of the
turbulent boundary layer profile, with a pointed, near-wall peak,
which preserves a constant value of approximately 0.12
downstream of x.r (see Fig. 7b). The decisive information regarding
the end of transition is provided by the spectral analysis,
especially by the streamwise evolution of the PSD, as shown in
Fig.10 (a).
8
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12
10
—8
E 6
10
7.4
2
a
FIRS
'2 4 In
(a)
02
30
fl 0
talaill
4J
4
4
U (m/s]
-50
(a)
400
600
Frequency (Hz)
800
1000
'.4
2
0 0 0.15 0 0.150 0.15 0 0.150 015 0 015 00,150 0150 0. 5 0 015 IXE
(b)
Taylor 1-D
Spectrum
U E u/(3.(u)2]
12
E
10
I 86
4
2
0
x=0.74m
S
E
d
u
x
o
u
x
E
E
3
co
d,
n
x
Nu
d
u
x
8
0
II
x
2
0
u
x
R1
t;, i " 1..:'i
Trenernmrttimuntryternmr.
(c)
101
(b)
o
II
x
E
8
x= 0.74M
200
E
42
o
u
x
0
u/U
12
10
1Cf
Normalized Frequency :
8
E6
2
rt10
i
2
0
IL—I
&-SIL Stin-1 1
00.5 00.5 0 0.5 0 OS 00$ 00.5 00.5 00.5 00.5 0 05 0 05
(d)
-
10 4
(c)
zero velocity line, yo
Fig.1. 1 Separated-flow transition parameters for
the long bubble mode (Case 1.7).
10 1
10 0
Normalized Frequency :
Fig. 11 presents the data for CASE 1.7, which represents the
laminar separation - long bubble mode of transition. The behavior
up to the maximum displacement location is similar to that of the
separated boundary layer in the short bubble mode. The onset of
transition xt is coincidental with the location of the maximum
displacement xmD.
Despite the fact that the separated shear layer extends far
downstream, the profiles at x = 0.70 m show the characteristics of
reattachment, i.e., Kt ocat reaches a minimum (not shown here), the
mean velocity profile matches the Horton's universal reattachment
velocity profile, and the near-wall peak in the (u'/U) profiles
reaches a maximum value.
This reattachment-like behavior is identified as the first
reattachment, 'cm. For the laminar separation long bubble mode of
transition, the location always coincides with that of the
first reattaclunent 4(1 where (u'/U...,) reaches a maximum value of
about 0.15. The second reattachment is typically situated in the
turbulent region, and it can be detected mainly from the mean
velocity profiles. The boundary layer data for case 1.7 do not show a
second reattachment location.
Fig.10 Spectral features of separated - flow
transition: (a) streamwise evolution of
power spectral density; (b) Taylor 1-D
normalized power , spectrum at x = 0.74 m (c)
Taylor 1-0 normalized power spectrum at x =
0.96 m.
The end of transition is identified with the location downstream
of which the power spectrum no longer changes. Additionally, for a
turbulent signal, the normalized power spectrum, U.. Ett/IX (t0 2]
vs. ), where A is the integral length scale, shows an
established cascade dissipation at a - 5/3 slope, as shown in Fig. 10
(b) for x = 0.96 m station. The end of transition can be further
verified by examining the turbulent intermittency distribution
which approaches r= I as x -> xi.. as shown in Fig. 7 (d).
The above methodology for determining x s, xmD, AR, yD, xt,
xu.ma, • and xi- applies to all separated-flow transition modes. In
addition to the aforementioned common features, some aspects
specific to each individual mode must be addressed.
9
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•
-
5- 2
E
o
0:1
6
s
x
E
o
r,.
O
s
x
0
10
0 10
a)
E
a
E
o
6
II
X
II
X
a
0
10
Three primary separated-flow transition modes were identified:
the transitional separation mode, for which the transition starts
upstream of the separation point and develops mostly as natural
transition; the laminar separation -short bubble mode, for which
the transition starts downstream of the separation point and rapidly
reaches the turbulent state, and the laminar separation -long bubble
mode, for which the transition also starts downstream of the
separation point, however, for this mode, the transition
completion is delayed. Passing from one fundamental mode to
another takes place continuously through a succession of
intermediate stages.
This paper presented a detailed discussion of the methodology
implemented in determining the separated-flow transition main
parameters (x,, a m p, XR, 3R , x,zu•nu,x , and xT) from experimental
data. Specific aspects for each of the primary separated-flow
transition mode were identified.
u
x
NI
o
a
li
X
0
X
E
E
0
cc?
o
II
X
o
N:
o
II
x
a
X
Ft
0.15
•
0
0.15 0
0.15
a
cc'
o
x
X
ruD
0 0.3 0.6 0 0.3 0.6 0 0.3 0.6 0 0.3 0.6 • 0.3 0.6
E
i e
0.
1 ti
°Ii
t
X
10
u'/U
a
n
X
tk
(c)
6
5
—.4
al
0
NCI
0.15 0
u'/U
1 0
n
x = 0.70 m
C
0
0
a
c0
X
0 0.15 0
0
el
E
0 10
0
6
a
E
O
0 0.15 0 0.15
(b)
o
cl
10
o
3
S
1
0 i-0 0.3 0.6
1
0
0 10 0
U [m/s]
E
o
O
.0
° x = 0.50 m
G.1f)
6
5 'I
4
E 3
•;.: 2
1
0
E 3
o
u
x
IVI)
o
u
x
S
1
0
6
5
4
E3
E
o
ul
o
u
x
E
o
ro
o
u
x
5
4
E3
2
6
MD
xA
MaX
S
0 0.5 1 0 0.5 1 0 0.5 1
(d)
0 0.5 1
0 0.5 1 0 0.5 1
- zero velocity I ne, yo
Fig.12 Separated - flow transition parameters for
transitional separation mode (Case 1.1).
Fig. 12 presents a transitional separation mode case (CASE 1.1).
For this case, the onset of transition, xt, takes place upstream of
the separation point. For the transitional separation mode of
transition, the ke n= location coincides with that of the maximum
displacement xiviD, where (u'/U.),,,a, reaches values of about 0.16.
In this case, the data for the actual reattachment point were not
acquired since xR was situated between two measuring locations.
By analyzing the evolutions of the mean velocity profiles and
ul/U profiles, it can be concluded that the reattachment location
must be situated between x = 0.9 m and x = 1.0 m.
CONCLUSIONS
This paper presented a summary of the most important aspects
associated with the experimental set-up and procedures utilized in
the experimental investigation of the laminar to turbulent
transition in two-dimensional separated boundary layers on a flat
plate at zero incidence. A description of the new approach in
analyzing separated-flow transition was introduced, the key
parameters were specified, and the primary separated-flow
transition modes were briefly discussed.
10
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