4. ANKARA INTERNATIONAL AEROSPACE CONFERENCE

AIAC-2007-019

10-12 September, 2007 - METU, Ankara

STEADY FLOW STRUCTURE PRODUCED BY SURFACE ROUGHNESSFahrettin Gökhan Ergin, PhD∗
Dantec Dynamics A/S
Skovlunde, Denmark

ABSTRACT
Surface roughness has a direct impact on boundary layer stability and transition. It generates complex threedimensional and unsteady disturbances near the surface. Theoretical efforts aimed to understand how these disturbances are received, and computational studies on disturbance evolution often require a complete planar disturbancefield as initial conditions. The present work aims to provide this information as three components of the steadyvelocity field in a flat plate boundary layer. Experiments are performed in a subsonic wind tunnel and an array ofcylindrical roughness elements is used to disturb the flow over a flat surface. Velocity measurements are obtained
downstream of the array using multiple-sensor, constant temperature hotwire anemometry. The results indicate acounter-rotating horseshoe vortex system which is consistent with previous flow visualization studies in the literature. The results also provide answers to questions regarding disturbance receptivity and its quantification, lift-up
mechanism, transient growth, and optimal disturbances.
INTRODUCTION
Laminar-to-turbulent transition in boundary layers can be caused by environmental disturbance sources such as surface
irregularities, turbulence in the freestream, or certain pressure disturbances. The receptivity of these disturbances canbe explained as the process by which an external disturbance source manifests itself as deviations from the basic state
velocity and pressure fields in the boundary layer [17]. Any two different disturbance inputs are expected to produce
two different deviations in the flow filed, so any initial disturbance input is uniquely connected to an initial disturbancefield by its own receptivity mechanism. For example, transitional initial disturbances produced by supercriticalroughness get amplified by the boundary layer and lead to breakdown and turbulent flow, whereas transient initial
disturbances produced by subcritical roughness experience an initial growth and final decay, producing a disturbed
laminar flow [1]. Therefore, the boundary layer can be viewed as a transfer function operating on and sensitive tothe initial disturbances. In other words, once an initial disturbance is formed, the subsequent evolution (growth,decay, or both) is entirely defined by that particular initial disturbance. However, very little is known on disturbance
receptivity, i.e. how the geometrical irregularities on the surface become velocity and pressure disturbances. This
makes receptivity a critical first stage of the boundary layer transition process and its quantification an extremely
important step in predicting and controlling transition.
Quantification of disturbance receptivity in a boundary layer involves substantial mathematical challenges [6]. Perhaps
the most important challenge is that the eigenmodes associated with the Orr-Sommerfeld and Squire equations are
not orthogonal. In general, for a nonorthogonal equation system, an orthogonality condition among the eigenmodes
cannot be formulated and therefore a conventional orthogonality solution is not possible. However, an orthogonality
condition is possible when the solutions of the adjoint equations are also included in the formulation [6]. This“biorthogonality condition” allows the decomposition of a certain perturbation into modes with known amplitudes;∗ Regional Export Manager, Email: gokhan.ergin@dantecdynamics.com

AIAC-2007-019

Erginand reduces the roughness receptivity problem to computing a finite number of eigenmode constants that represent
a discretization of the continuous spectrum.
This decomposition method presents a serious challenge to the experimentalist, because it requires knowledge ofthe complete disturbance field including the pressure disturbance, all three velocity disturbance components andtheir spatial derivatives. Obtaining the complete disturbance information is trivial in computational studies as thisinformation exists as part of the numerical solution. However, in an experiment it is extremely difficult to measure
the wall-normal velocity disturbances using constant temperature anemometry and perhaps impossible to measurewall-normal pressure disturbance profiles. Fortunately, partial disturbance field information, excluding pressure, canbe used to decompose the flow field into a finite number of discretized eigenmodes if the disturbance consists ofdownstream vorticity eigenmodes only [6]. For stationary transient disturbances in the far wake these are the only
modes that are thought to be important. Providing this partial disturbance information for quantification of roughness
receptivity is the major objective of this work. As this information also provides detailed quantitative information
on roughness-induced disturbances, the measured flow structure is most suitable for comparison with previous flow
visualization studies in the literature.
The effects of low-amplitude surface roughness (k ∼ δ or smaller) on boundary layer flows are summarized in asurvey article[15], which reviews the experimental data for laminar subsonic, turbulent subsonic, laminar supersonicand turbulent supersonic flows. Regardless of the flow type or the detailed shape of the protuberances, three important
observations are made: “1. In the upstream separated flow a system of vortices are formed. 2. These are stretchedaround the protuberance in a horseshoe vortex fashion and persist as streamwise vortices far downstream. 3. Spiralvortices rise up from the surface in the near wake. The details of the downstream disturbance depend on whether or
not transition takes place in a laminar boundary layer.”(Fig. 1) The first two points are especially important; because
both transient disturbances and their numerical counterparts that undergo maximum growth, optimal disturbances,are believed to be generated by a decaying streamwise vortex [5, 9]. Additionally, the lift-up theory that describes
the wall-normal transport of momentum is explained by a streamwise vortex [14]. Although several flow visualization
studies reveal the horseshoe vortices, qualitative data is not sufficient to provide the link to transient disturbancesand lift-up theory.

Figure 1: Flow topology in the vicinity of a cylindrical roughness element. Adapted from Gregory and Walker (1956).
2
Ankara International Aerospace Conference

AIAC-2007-019

Ergin

One systematic study of laminar-to-turbulent transition induced by 3D surface protuberance use smoke and chinaclay flow visualization techniques [21]. A detailed description of the steady flow field around and downstream of thecylindrical roughness element is adapted here in Fig. 1. It was reported that, a static pressure gradient forms along
the front stagnation generator of the cylinder. This leads to a vertical flow towards the surface on the upstream side
and a subsequent horizontal backward flow along the flat surface. (See side view on the left in Fig. 1.) Subsequently,
the flow forms a loop and produces rolls of continuously-generated horseshoe shaped vortices. These then wrap
around the cylinder and trail downstream as multi-ply vortex pairs with axes oriented in the streamwise direction.
The number of plies is reported to increase with increasing tunnel speed to as many as three pairs [21].
Another experiment reveal many signs of the trailing horseshoe vortex system using hotwire anemometry [13]. Herean isolated 3D cylindrical roughness element is used, which could be raised above a flat surface by using a solenoid.
Results contain streamwise velocity measurements for cylinder-present and cylinder-absent conditions and indicate astrongly decelerated region in the near wake and an accelerated region in the far wake along the lateral centerline.
The far-wake accelerated region was accompanied by decelerated regions on each side of the centerline. This effect
was attributed to a possible wall-normal momentum transport mechanism induced by the trailing vortex; with adownward flow of faster-moving fluid at the centerline and and an upward flow of slower fluid at off-axis locations.
This observation is perhaps the first experimental validation of the lift-up mechanism and transient growth prior to
the full development of the theory.
These findings have been enhanced by numerous other flow-visualization studies that culminate with the well-known
experiment of Acarlar and Smith [12]. However, these studies do not provide much quantitative information about
these vortices neither on their streamwise evolution nor on their spanwise distribution. The current experiments
aim to provide a quantitative description of the flow topology in the roughness wake, also suitable for receptivity
quantification studies.
FACILITY AND TECHNIQUESThe experiments closely follow the previous work by White and coworkers[1, 3, 7, 8, 9] in terms of experimental setup.
The facility used for the experiments is the Case Wind Tunnel, an open-return facility with a 0.71 m×0.71 m×2.7 m
test section and a maximum operation speed of 25 m/s. The test section features an externally-mounted, computercontrolled hotwire traverse mechanism with microstepping motors that move hotwire sensors in three perpendicular
directions with micron-step resolution. Restricted to a high-pass frequency of 1 Hz, the turbulent u 0rms level is 0.05%
of the freestream speed.
Measurements are obtained in the boundary layer of a polished flat aluminum plate. The plate has a 25-mm-longelliptical leading edge and the stagnation streamline is controlled by a 300-mm-long trailing-edge flap. The boundary
layer’s virtual leading edge location and the effective unit Reynolds number are estimated using a nonlinear leastsquares fit to the boundary layer’s displacement and momentum thickness distribution along the surface [2]. The
nominal freestream speed is 12.2 m/s; the unit Reynolds number is Re0 = 764×103 m−1 and the virtual leading edge
(xvle ) is 5 ± 2 mm upstream of the physical leading edge. Great care is exercised in the alignment of the flat plate
which is essential to ensure a zero-pressure-gradient flow. The mean shape factor is found as H = 2.56, meaning aslightly accelerated flow. However, this is within acceptable limits from the zero-pressure-gradient value [10].
Transient disturbances are generated using a spanwise array of cylindrical roughness elements. Fig. 2 illustrates theflat plate, the coordinate system and the roughness array. The array is located 300 mm downstream of the plate’s
physical leading edge and consists of 6.35-mm-diameter aluminum discs that are applied to the flat surface using
spray glue. The discs and the glue have a total thickness of 724 µm when applied on the surface and a subcritical
Rek value of 209. Based on the k/D value of this roughness height, Rek,crit is expected to lie between 250 and 275[18, 19]. Under similar conditions, roughness-induced breakdown is observed at Re k = 254 [4]. The elements werespaced λk = 3D = 19 mm apart in the spanwise (z) direction and measurements were taken covering the wake offour elements. The parameters used for the experiments are summarized in Table 1.
Table 1: Summary of experiment parameters.
Rek
209

Re0 [1/m](764 ± 4) × 103

k [mm]
0.724

xk [mm]300

xvle [mm]-5±2λk [mm]19

3
Ankara International Aerospace Conference∆z [mm]0.5

D [mm]
6.35

AIAC-2007-019

Ergin

Roughness Arrayy

Measurement Plane
x
z
λk

xk

Figure 2: Schematic illustration of the flat plate and the roughness array.
The hotwire measurements are obtained in planes perpendicular to the flow direction. In each measurement plane the
spanwise movements of the hotwire probes are constant; the 19 mm spacing is covered in 38 steps. The wall-normal
step is variable with 400-µm steps outside the boundary layer (starting at approximately η = 8) and progressively
smaller steps are used within the boundary layer. Once a cutoff velocity of 14%U inf is reached, the sensors are moved
away from the plate to their original position. This scanning technique is similar to what was used in Ref. [3].
Measuring the spanwise velocity requires the placement of at least two slanted hotwires with different angularorientations at the same measurement location. For this purpose, a new hotwire sting design is used which supports
one straight sensor in the freestream (Dantec 55P11) and three sensors in the boundary layer. The boundary-layer
sensors are positioned in a trident design with one straight sensor in the middle (Dantec 55P15) and two slanted(Dantec 55P12) hotwire sensors mounted 9.5 mm one either side of the the center probe. Using a separation that is
an integer multiple of the spanwise step (0.5 mm for this experiment) permits all three boundary layer sensors to beplaced at the same measurement location at three different spanwise traverse steps. Naturally, this requires excellentalignment of the flat surface with the traverse plane and the sensors with respect to each other.
Velocity and angular calibrations of all four sensors are performed simultaneously. The calibration constants and theyaw coefficient are computed by using the King’s Law and Hinze’s[20] formula:
¡
¢n
¡
¢1/2
Ve = A + B E 2 = Ṽ cos2 α + k 2 sin2 α(1)

In these equations A, B and n are calibration constants, Ṽ is the freestream speed during the calibration procedure,
Ve is the effective cooling velocity, E is the hotwire voltage, α is the sensor’s yaw angle and k is the sensor’s yaw
coefficient. The yaw coefficient is assumed to be constant [16]. This equation predicts the effective cooling velocity
to within 1% for yaw angles between 0◦ and 70◦ and the error reaches only 15% for a yaw angle of 90◦ [11]. A
nonlinear least-square fit is performed to find A, B, n and k values for each sensor, and typical values are presented
in Table 2. The precise determination of the yaw coefficient, k requires a very accurate knowledge of the wire angle,
α, and the value of the calculated yaw coefficient k 2 is very sensitive to a yaw angle error, ∆α. Fortunately, theindividual uncertainties from α and k cancel each other in Hinze’s formula, reducing the combined uncertainty on
the right-hand-side of Eqn. 1 to less than 1% for −1◦ ≤ ∆α ≤ 1◦ [11].

Table 2: Typical calibration constants observed during experiments.
SensorFreestream
Boundary Layer
Slanted 1
Slanted 2A-1.591-1.419-1.546-1.879

B
0.582
0.538
0.551
0.665

n
2.258
2.377
2.328
2.209

k
—
—
0.160
0.180

4
Ankara International Aerospace Conference

AIAC-2007-019

Ergin

DATA ANALYSIS
During data acquisition, the voltage readings from four sensors are converted to effective cooling velocities using thecalibration constants in Eqn. 1. The effective cooling velocities from all boundary layer sensors are normalized by thefreestream velocity and these are recorded together with the yaw coefficients of slanted sensors for further analysis.
Multiple component velocity data is analyzed by decomposing the steady streamwise and spanwise velocity fields intoa steady, spanwise-invariant basic state and a steady disturbance as:
U (x, y, z)=

U (x, y) + U 0 (x, y, z)W (x, y, z)=W (x, y) + W 0 (x, y, z).

(2)

Although the basic state for a flat plate flow is the Blasius boundary layer profile, it is more appropriate to use
an experimental basic state, which is the average of the boundary layer profiles at the midpoint of two roughness
elements. This basic state is most representative of the theoretical Blasius profile and is 2D, meaning W = 0.
The effective cooling velocity of a heated wire yawed in a 2D flow is given by Hinze’s formula; V e2 = Un2 +k 2 Ut2 , where
Un and Ut are the normal and tangential velocity components on each slanted wire. In the present measurements,
these can be represented by U and W components as; Un = (U cos α − W sin α) and Ut = (U sin α + W cos α).
Substituting for Un and Ut in Hinze’s formula results in an equation for Ve2 = f (U, W, k 2 , α), where Ve2 , k 2 and α
are known and U and W are unknown. For a single α value, this is a single equation with two unknowns. Therefore,a second equation can be obtained by introducing another wire angle. In short, combining measurements of a single
point from the two slant wires provides U and W . Defining a flow angle β = tan −1 (W/U ), Eqn. 3 is obtained,
which can be solved for tan β. Once the flow angle is determined, the determination of U and W components ofthe flow vector follows a simple substitution.
(R2 ab − at ) tan2 β + (R2 bb − bt ) tan β + (R2 cb − ct ) = 0
where

at,b = tan

22αt,b + kt,b
,

(3)

2
bt,b = 2 tan αt,b (kt,b− 1),

2
ct,b = tan2 αt,b kt,b
+1

and

R=

Ve,t cos αb
Ve,b cos αtWith the available streamwise and spanwise velocity components, the wall-normal velocity component, V , or thewall-normal velocity perturbation, V 0 can be obtained by using the appropriate form of the continuity equation,
where the first order derivatives are approximated by central differences. Assuming constant step size in x and z, theperturbation continuity equation takes the following form:
µ

∂V 0
∂y

¶

=−
j

µ

0
0
0
W 0 − Wk−1
Ui+1
− Ui−1
+ k+1
2∆x
2∆z

¶

(4)

where i, j and k are the grid indices in the x, y and z directions respectively. Omitting the primes, the continuity
equation for the wall-normal velocity gradient is obtained. Using the no-slip boundary condition on the wall, (V and
V 0 is 0); the wall-normal velocity profile V (y), is calculated. Computation starts at the wall location and moves awayfrom the wall using previously computed Vj values. With all three velocity components available in the 3D domain,
the streamwise vorticity is calculated using ωx = (∂W/∂y − ∂V /∂z).
RESULTSThe results of this experiment include spatially phase-lock averaged U , V , W , and ω x data in a 3D rectangular domain.
The streamwise range is 310 < x < 550 mm which corresponds to a Reynolds number
range of 2.41 × 105 < Rex < 4.24 × 105 . The wall-normal and spanwise domains are 0 < y < 4.7 mm and−9.5 < z < 9.5 mm. The grid has variable spacing in the streamwise direction with ∆x as low as 2.5 mm in thenear wake, gradually increasing to as high as ∆x = 50 mm in the far wake. In the present work 310 < x < 340 mm
will be referred to as the near wake, and 340 < x < 550 mm will be referred to as the far wake. The grid spacing
is constant in the wall-normal and spanwise directions with ∆y = 0.1 mm and ∆z = 0.5 mm. The velocity andvorticity data is presented at each location as a combination of contour lines, colored contours and vectors.
The phase-lock averaged steady flow properties in the roughness wake can be seen in Figures 3 through 5. In thesefigures the flow is into the page, the abscissa is the spanwise direction and the ordinate is the wall-normal direction,
5
Ankara International Aerospace Conference

AIAC-2007-019

Erginboth displayed in mm’s. The projection of the roughness element that generates the disturbance extends between−3.17 < z < 3.17 mm and 0 < y < 0.724 mm. The green contour lines indicate 10% increments of dimensionlessstreamwise velocity U , the vector field represents the dimensionless V and W , and the colored contours represent
the streamwise vorticity intensity. The length of the heavy horizontal lines in the figures’ top right corner is equal
to the length of a vector representing V , W pair equal to 10% of U∞ . The colored contour levels that represent
ωx are shown on the right-hand side of each figure and have the units of m−1 . The limits of the color spectrum isselected such that the contour levels are the same for all figures. Warmer colors (yellow, orange, red etc...) represent
a positive streamwise vorticity (into the page), indicating a clockwise fluid rotation in these figures. Conversely,
the colder colors (blue, turquoise etc...) represent a negative streamwise vorticity (out from the page), indicating acounter-clockwise fluid rotation in the figures. White color indicates zero streamwise vorticity.
F rame 001 ? 03 J un 2005 ? 310mm

w_x
220
200
180
160
140
120
100
80
60
40
20
0
-20
-40
-60
-80
-100
-120
-140
-160
-180
-200
-220

4

y

3

2

1

0

-5

0

5

z

Figure 3: Steady flow properties in the near wake at x = 310 mm.
First, the results in the near wake is explained. Immediately downstream of the roughness array, at x = 310 mm, thesteady flow properties are shown in Fig. 3. Here, the streamwise velocity contours indicate a decelerated region in
the wake of the roughness element. The deceleration is symmetric around the roughness centerline and compact in aregion directly behind the roughness element, lower in the boundary layer. The locations higher in the boundary layer
are not effected by the presence of roughness as much as the lower portions. Second, the V and W velocities are
directed downward (towards the plate) along the centerline (z = 0). As they approach the plate, they are directedsideways, away from the centerline. Then they change direction one more time around z = ±3.5 mm and turnupwards (away from the plate) creating two streamwise vortex cores at approximately y ≈ 1.0 mm. An interestingobservation can be made about the spanwise location of the vortex cores: These appear to be around z ≈ ±2.75 mm,
which is not directly along the edges of the roughness (z ≈ ±3.17 mm), but a small distance closer to the centerline,
which is consistent with previous observations [21]. The rotation direction also agrees with the trailing legs of ahorseshoe vortex as indicated in Fig. 1. Thus, from this point forward, this vortex pair will be called the horseshoe
pair. Expected symmetries can also be seen in Fig. 3; there is little or no spanwise velocity along the centerline, oralong both edges of the spanwise wavelength (z = ±9.5 mm). The vector magnitudes are less than 5% and only one
pair of vortex eyes is distinctly visible.
At x = 350 mm, the steady streamwise velocity contours display accelerated flow regions along both sides (z ≈±3 mm) of the roughness, and decelerated flow regions along the centerline (Fig. 4). The V , W field is similar tothat in Fig. 3, with increased velocity vector magnitudes and increased streamwise vorticity intensities. The maximum
vorticity intensity is observed at x = 340 mm [2]. Between x = 310 mm and x = 350 mm, the decelerated region in
the wake along the centerline is gradually accelerating, because of the downward flow along the centerline producedby the two legs of the horseshoe vortex: The −V velocity along the centerline carries the high momentum fluid fromhigher parts in the boundary layer to the lower parts, as explained by the lift-up mechanism [14].
Here, it is interesting to note a secondary pair of vortex outside of the existing horseshoe pair. The rotation of
the secondary vortex pair is opposite in direction to that of the horseshoe pair, and this can be observed from thecrossflow velocity vectors and the ωx intensities. These observations remain in agreement with previous results, which
identifies up to three plies of vortex pairs [21]. Additionally, the rotation directions indicated in the section cut in6
Ankara International Aerospace Conference

AIAC-2007-019

Ergin

F rame 001 ? 03 J un 2005 ? 350mm

w_x
220
200
180
160
140
120
100
80
60
40
20
0
-20
-40
-60
-80
-100
-120
-140
-160
-180
-200
-220

4

y

3

2

1

0

-5

0

5

z

Figure 4: Steady flow properties at x = 350 mm.
F rame 001 ? 03 J un 2005 ? 500mm

w_x
220
200
180
160
140
120
100
80
60
40
20
0
-20
-40
-60
-80
-100
-120
-140
-160
-180
-200
-220

4

y

3

2

1

0

-5

0

5

z

Figure 5: Steady flow properties in the far wake at x = 500 mm.
Fig. 1 are similar to the measured directions in Fig. 4. A careful investigation of Fig. 1 reveals that the secondary
vortex pair appears at a certain downstream distance and not directly in the wake of roughness. In the results of thepresent work, the secondary vortex is not present at x = 310 mm, (Fig. 3), is barely visible at x = 320 mm [2], andis more obvious further downstream at x = 350 mm.
The steady flow properties in the far wake at x = 500 mm are shown in Fig. 5 where the streamwise velocity along
the centerline is further accelerated when compared to x = 350 mm. In addition to this, it gradually diffuses inthe spanwise direction with increasing downstream distance, covering a larger spanwise region and the magnitude ofωx continue its monotonic decay in the far wake. It is apparent that the perturbations generated by the roughness
elements develop and get stronger in the first 40-50 mm and start their decay approximately 50 mm downstream of
the array location. This transient behavior is attributed to a competition between an unsteady disturbance growthmechanism and a steady disturbance decay mechanism [1]. In other words, the disturbed laminar flow observed in
the present experiment is a result of a stronger decaying steady flow and a weaker unsteady flow.
The global distribution of the streamwise velocity component, U , is visualized in Fig. 6. In this figure, two surfacesof constant velocity are shown in a perspective view in the 3D measurement domain. The lower (turquoise) surface
represents the 20% of U∞ and the upper (yellow) surface represents 80% of U∞ . In the near wake, there is adecelerated region directly behind the roughness element and this region is more emphasized on the lower surface,than the upper surface. The accelerated regions along both edges of the roughness element appear at a very shortdownstream distance in the near wake and these lead to the streaky structures further downstream. The streaky
7
Ankara International Aerospace Conference

AIAC-2007-019

Ergin

Y
X

Z

4

y

3
550

2
500

1
450
0
-10

400

x

-5
0

z

350
5
10

300

Figure 6: Iso-velocity surfaces of 20% and 80% of U∞ .

5

w_x
220
200
180
160
140
120
100
80
60
40
20
0
-20
-40
-60
-80
-100
-120
-140
-160
-180
-200
-220

0.3
0.35

0.4

0. 4

structures are initially narrow and gradually cover a larger spanwise region. This finding is in complete agreementwith transient growth theory, because smaller spanwise wavenumbers are expected to grow for a larger distance. The
velocity along z = ±9.5 mm represents the basic state and the boundary layer growth is visible on both ends of the
wavelength for the upper surface.

5

0.35

0.4

0 . 3 0.45
5

0.4 5

0.5
0.4

z

0.35
0

0

.3

0.35

0.4

0.4 5
0.45

0 .4

0.4
0.35

0. 4

0. 4

-5

350

400

450

500

550

x

Figure 7: U and ωx contours 800 µm above the surface.
In Fig. 7 contours of U and ωx are shown in an (x,z) plane 0.8 mm above the flat surface with ωx contour levels
similar to those in Figs. 3 through 5. In Fig. 7 the downstream evolution of ω x intensity of both the counter-rotating
horseshoe and the outer secondary vortex pairs are shown, where the initial growth and final decay is clearly visible.
Consistent with the literature, the inner horseshoe vortex pair starts at z ≈ ±3.0 mm, gradually approaches towards
the centerline in the near wake for a certain streamwise distance and remains parallel afterwards. On the other handthe outer secondary vortex pair seems to diverge from the centerline and becomes parallel with the flow direction.
These results indicate that the roughness-induced horseshoe vortices slowly diffuse in the spanwise direction withincreasing streamwise distance.

8
Ankara International Aerospace Conference

AIAC-2007-019

Ergin

SUMMARY AND CONCLUSIONS
Time-averaged streamwise and spanwise velocity components are measured with high spatial resolution, and thewall-normal velocity component is estimated from these values using a discretized approximation of the continuity
equation. The obtained complete steady velocity disturbance field provides quantitative data suitable for receptivity
quantification using the biorthogonal decomposition technique [6]. These results also identify streamwise-oriented
vortices that play a critical role in lift-up concept, transient and optimal disturbances.
Many aspects of the flow field are in complete agreement with the literature: First, strongly decelerated velocity
profiles are observed in the near wake of the roughness elements and these profiles gradually become accelerated in
the far wake. Second, high-speed streaks appear a short distance downstream of the roughness array aligned withthe spanwise edges of the roughness elements. Third, the V , W vector field and the streamwise vorticity indicate
the trailing legs of the primary horseshoe vortex and the secondary outer vortex. Lastly, the rotation directions andthe fact that the secondary pair appears at a short distance downstream of the roughness array also agree with theprevious observations.
An important concern is regarding the wall-normal extent of the perturbations. The U 0 and W 0 values are expected
to vanish at the edge of the boundary layer, and the wall-normal extent of the current experiments are sufficient
to display this behavior. However, in Figs. 3 through 5 the V 0 and ωx intensities reach the edge of the boundary
layer. This could be an artifact of insufficient wall-normal resolution in the upper parts of the boundary layer during
data acquisition. As mentioned before, the boundary layer scanning technique uses an uneven measurement grid in
the y direction, with larger wall-normal steps outside the boundary layer and gradually decreasing steps within theboundary layer. It is possible that a large wall-normal step, ∆y was used in the region where negative ∂V /∂y values
could have been measured during the experiments, missing these important velocity gradients.
A second concern is related with the location of the vortical structures within the boundary layer. This point is ofextreme importance, because the quantitative and qualitative differences between measured and optimal disturbances
are attributed to the differences in wall-normal locations of the vortex core generated by roughness and the computed
vortex core that produces an optimal disturbance [5]. The cores of the vortices in Figs. 3 through 5 appear to be aty ≈ 1 mm, so that the vortices can be assumed to be localized within the lower parts of the boundary layer. On thecontrary, the vortices that generate optimal disturbances extend well above the boundary layer. The resolution of thefact that V and ωx have non-zero values at the edge of the boundary layer requires further experimental investigation
with higher wall-normal resolution in the upper parts of the boundary layer and with an increased wall-normal range.
ACKNOWLEDGEMENTS
This work is supported by the U.S. Air Force Office of Scientific Research under grant number F49620-02-1-0058.
F.G. Ergin acknowledges the Case School of Engineering for its support through a Case Prime Fellowship and Edward
B. White for many useful comments and suggestions. The moral support provided by Gültap Songur Ergin, M.Sc.
during the progression of this work cannot be left unmentioned.

9
Ankara International Aerospace Conference

AIAC-2007-019

Ergin

References[1] Ergin, F. G. and White, E. B., Unsteady and transitional flows behind roughness elements, AIAA Journal, Vol
44, p:2504-2514, Nov 2006
[2] Ergin, F. G., Roughness Induced Transition, PhD Thesis, Case Western Reserve University, Aug 2005
[3] White, E. B., Rice, J. M., and Ergin, F. G., Receptivity of stationary transient disturbances to surface
roughness, Phys. Fluids, Vol 17, p:064109(12p), Jun 2005
[4] Rice, J. M., Roughness Receptivity and Scaling of Non-Optimal Transient Disturbances, Masters Thesis,
Case Western Reserve University, 2004
[5] , Fransson, J. H. M., Brandt, L., Talamelli A., and Cossu, C., Experimental and theoretical investigation of
the non-modal growth of steady streaks in a flat plate boundary layer, Phys. Fluids, Vol 16, p:3627-3638, Oct
2004[6] Tumin, A., Multimode decomposition of spatially growing perturbations in a two-dimensional boundary layer,
Phys. Fluids, Vol 15, p:2525-2540, Sep 2003
[7] White, E. B. and Ergin, F. G., Receptivity and transient growth of roughness-induced disturbances, AIAAPaper 2003-4243, 2003
[8] White, E. B. and Reshotko, E., Roughness-Induced Transient Growth in a Flat-Plate Boundary Layer, AIAAPaper 2002-0138, 2002
[9] White, E. B., Transient growth of stationary disturbances in a flat plate boundary layer, Phys. Fluids, Vol
14, p:4429-4439, Dec 2002
[10] Saric, W. S., Low-speed boundary layer transition experiments, in coll., Transition: Experiments, Theory andComputation, 1996[11] Bruun, H. H., Hot-Wire Anemometry Principles and Signal Analysis, Oxford University Press, 1995
[12] Acarlar, M.S. and Smith, C.R., A study of hairpin vortices in a laminary boundary layer. Part 1. Hairpin
vortices generated by a hemisphere protuberance, J. Fluid Mech., Vol 175, p:1-41, 1987
[13] Kendall, J. M., Laminar Boundary Layer Velocity Distortion by Surface Roughness: Effect upon Stability,
AIAA Paper 81-0195, 1981[14] Landahl, M. T., A Note on an Algebraic Instability of Inviscid Parallel Shear Flows, J. Fluid Mech., Vol 98,
p:243-251, 1980
[15] Sedney, R., A survey of the effect of small protuberances on boundary-layer flows, AIAA J., Vol 11, p:782-792,
1973[16] Jørgensen, F. E., Directional sensitivity of wire and fibre-film probes, DISA Info., No. 11, 31-37, 1971[17] Morkovin, M. V., On the many faces of transition, Plenum, NY, Viscous Drag Reduction, p:1-31, 1969[18] Tani, I., Boundary-layer transition, Annu. Rev. Fluid Mech., Vol 1, p:169-196, 1969[19] von Doenhoff, A. E. and Braslow, A. L., The effect of distributed surface roughness on laminar flow, Pergamon,
Boundary Layer and Flow Control, Vol 2, p:657-681, 1961
[20] Hinze, J. O., Turbulence. An introduction to its mechanism and theory., McGraw-Hill, 1959
[21] Gregory, N. and Walker, W. S., The effect on transition of isolated surface excrescences in the boundary
layer, Aero. Res. Council, Tech. Report R. & M. 2779, 1956

10
Ankara International Aerospace Conference