Interaction of a Laminar Boundary Layer

with a Cylindrical Roughness Element

near an Airfoil Leading Edge

B. Plogmann∗, W. Wurz†, and E. Kramer‡

University of Stuttgart, D-70569 Stuttgart, Germany

Surface roughness elements in the leading edge region of airfoils can cause laminar toturbulent boundary layer transition resulting in a loss in lift and a significant increase inaerodynamic drag. Especially wind turbine blades are affected since there is no mainte-nance. The present investigation is devoted to the interaction of a laminar boundary layerwith a single, three-dimensional roughness element of cylindrical shape. Experiments wereconducted in a very low turbulence wind tunnel. A two-dimensional airfoil section similarto the NACA 643-418 was employed at a typical Reynolds number (Re=6,000,000) for windturbine applications. The roughness element is placed in the leading edge region. Down-stream of the roughness element hot-wire boundary layer measurements were performedin a close to zero pressure gradient boundary layer. Discrete roughness heights in a rangefrom 0 to 150 percent of the boundary layer displacement thickness were investigated. Forroughness heights less than 20 percent of the displacement thickness no significant interac-tion with the laminar boundary layer is evident. In a range from 30 to 50 percent, clearly,an increasing mean flow distortion and the growth of boundary layer disturbances can beobserved, however, not leading to boundary layer transition within the measurement re-gion. For roughness heights higher than 75 percent of the boundary layer displacementthickness by pass transition occurs.

Nomenclature

H12 = δ1/δ2 shape factor sBE arc length of BE 72Re = u∞c/ν chord based Reynolds number u∞ free stream velocityReh = uhh/ν roughness Reynolds number uδ local boundary layer edge velocityTu = u′/u∞ longitudinal turbulence level uh velocity at the height of the roughnesscBE chord length of BE 72 β spanwise wavenumbercNA chord length of NACA 643-418 δ1 displacement thicknessdr roughness diameter δ2 momentum thicknessh roughness height ν kinematic viscosity

I. Introduction

An increasing importance of wind turbines in the generation of electricity enforces the design of highlyefficient wind turbine blades. One of the main challenges in the blade design is premature transition due tosurface roughness in the airfoil leading edge region. Such surface roughness can be caused by insects, dust,salt or surface corrosion. As a consequence of boundary layer transition being shifted upstream, the lift isdecreased while the aerodynamic drag is significantly increased. Hence, the performance and, therewith, thepower output of the wind turbine are considerably decreased.

∗Research engineer, Institute of Aerodynamics and Gas Dynamics†Senior Researcher, Institute of Aerodynamics and Gas Dynamics‡Professor, Head of the Institute of Aerodynamics and Gas Dynamics.

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AIAA 2012-3077

Copyright © 2012 by Benjamin Plogmann. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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In general, three different roughness types depending on their shape can be distinguished: two-dimensionalroughness steps, three-dimensional isolated roughness elements1 and distributed roughness elements.2 More-over, a separation into different roughness heights in relation to the boundary layer displacement thicknessis suggestive, since flow phenomena leading to transition downstream of the roughness alter significantly notonly with the shape but also with increasing roughness height in relation to the boundary layer displacementthickness. Based on the transition mechanism, three different roughness heights can be distinguished: low(i),medium(ii) and high(iii) roughness elements.

For low (i) roughness heights, which are typically below 5 percent of the boundary layer displacementthickness, base flow velocity variations caused by the roughness element are small. Boundary layer distur-bances are predominately excited via receptivity.3,4 For roughness heights below a certain threshold valuethe disturbance amplitude is seen to scale linearly with the roughness height.5,6 For two-dimensional rough-ness elements this threshold is about 5 percent of the boundary layer displacement thickness,7 whereas forthree-dimensional roughness elements investigations by De Paula8 hint at a threshold of 20 percent.

When the roughness height is located in a medium range (ii), the receptivity process becomes nonlinear.7

Also, there is a distinct mean flow distortion that can lead to a modified stability behavior of the flowdownstream of the roughness. For a two-dimensional roughness element three-dimensional structures onlyarise during boundary layer transition, whereas a three-dimensional roughness element highly favors thedirect development of three-dimensional structures at or very close to the roughness. As described by Tani1

and Tobak and Peak,9 different vortical structures (horse-shoe shaped vortex wrapped around the front sideof the roughness and a pair of spiral filaments rising vertically in the wake of the roughness) were observed.The vortical structures evolving in the wake of the roughness are likely to originate from velocity streaks(regions of high or low mean velocity in spanwise direction). The stability of these vortical structures wasnumerically studied for a ’quiet’ (in terms of absence of additional boundary layer disturbances) boundarylayer flow interacting with a small height roughness element.10,11 These investigations showed the flow tobecome inviscidly unstable if the strength of the distortion created by the vortices exceeded a thresholdvalue.11 For distortions higher than the threshold value, strongly nonlinear effects with frequencies for themost unstable instabilities much higher than for the viscous Tollmien-Schlichting(TS)-instability were seento occur.

Recently, Ergin and White12 found, that roughness induced disturbances in a ’quiet’ boundary layermay undergo transient growth for medium sized roughness elements. However, transient disturbance growthwas seen to be strongly dependent on the boundary layer receptivity process at the roughness, since initialdisturbance amplitude and the energy distribution among the initial modes are determined by the roughness.

For roughness heights close to or larger than the displacement thickness (iii), transition is observed tooccur immediately downstream of the roughness. This process is also often referred to as bypass transitionand inherent with a strong mean flow distortion, causing strongly nonlinear effects. The first detailed inves-tigations of a high roughness element (mainly a hemisphere was used) interacting with a laminar boundarylayer were conducted by Acalar and Smith13 and Klebanoff et al.14 Different mechanisms appeared to leadto turbulence in the inner (close to the surface) and outer region, which is hinted at by two inflection pointsin the mean flow velocity profile. Vortices close to the surface were seen to provide a strong mixing of highand low speed regions leading to turbulent flow, which is also propagating into the outer region. In the outerregion hairpin vortices were observed for roughness heights above a critical value. However, the vorticalstructures were seen to strongly depend on the roughness shape.

The present experiments focus on the interaction of a laminar boundary layer with a single, three-dimensional roughness element of cylindrical shape. A close alignment of the experimental parameters tooperational conditions of wind turbines is intended. Experiments are, therefore, performed on an airfoil in theclose vicinity of the leading edge. Hence, the effect of pressure gradient can also be covered. The chord basedReynolds number was chosen to Re=6,000,000. In order to account for different initial turbulence levels in thefree stream, the model is equipped with a disturbance source upstream of the roughness element. Therewith,controlled disturbances in a wide frequency and spanwise wave number spectrum can be introduced into thelaminar boundary layer. Hence, the interaction of both a ’quiet’ and a ’disturbed’ boundary layer with theroughness element can be studied. The present experiments are, in a first step, devoted to the interaction ofa ’quiet’ boundary layer with the roughness element. In order to cover the changing mechanisms leading totransition downstream of the roughness element, roughness heights up to 150 percent of the boundary layerdisplacement thickness are investigated.

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II. Experimental Setup

A. Laminar Wind Tunnel

The experiments were carried out in the Laminar Wind Tunnel (LWT) of the Institute of Aerodynamics andGas Dynamics (IAG) in Stuttgart.15 The LWT is an open-return wind tunnel of Eiffel type (Fig. 1). Severalscreens in the inlet section of the LWT and an effective contraction ratio of 20:1 result in an extremelylow longitudinal turbulence level of Tu = 2 · 10−4 obtained in a frequency range of f = 10 − 5000 Hzfor a free stream velocity of u∞ = 30 m/s.16 Up to 98 percent of the turbulence level are within afrequency range from f = 10 − 150 Hz. For higher frequencies velocity fluctuations are in the same or-der of magnitude as the electronic noise of standard hot-wire measurement technique. The closed test

Figure 1. Side view of the Laminar Wind Tunnel(LWT) of the Institute of Aerodynamics and Gas Dy-namics (IAG), acoustical damping marked red.

section exhibits a cross section of 0.73× 2.73 m2 anda length of 3.15 m. The airfoil models are mountedvertically with a spanwise length of 0.73 m. Gapsin-between the model and the wind tunnel walls arecarefully sealed. The diffusor section of the LWT isequipped with noise absorbing foam, significantly re-ducing the background noise propagating upstreamfrom the fan into the test section.17

B. Airfoil Design

Usually, experimental investigations in an airfoil leading edge region at high Reynolds number are verycomplicated because of a thin boundary layer and high surface curvature. In the present experimentsthe model is, therefore, geometrically scaled by a factor of 8 in comparison to standard sized wind tun-nel models (c = 0.6 m). Therewith, experiments can be conducted both at a typical Reynolds numberfor wind turbine applications (Re=6,000,000) and at low free stream velocity (u∞ = 20 m/s). Further-more, the boundary layer thickness is significantly increased (compared to standard dimensions) allowingfor access with standard measurement techniques. Advantage is taken from the fact that only the leadingedge region is of interest for the interaction of the laminar boundary layer and the roughness element.

cp

-1.5

-1

-0.5

0

0.5

1

BE 72NACA 64 3-418

x [m]

y[m

]

0 1 2 3 4 5-0.5

0

0.5

Figure 2. Comparison of the shape and the pressuredistribution of the BE 72 and the NACA 643-418 fora free stream velocity of u∞ = 20 m/s.

Therefore, the pressure distribution in the rear partcan be changed in order to significantly reduce thechord length of the model.

Hence, a new airfoil section (BE 72) was developed(Fig. 2). In the leading edge region the pressure dis-tribution of the BE 72 is designed to match the oneof the NACA 643-418 at Re=6,000,000, which can beregarded a typical airfoil section for wind turbine ap-plications. For the design three angles of attack cor-responding to a boundary layer with favorable, closeto zero and adverse pressure gradient were selected.The pressure rise in the rear part was significantly in-creased in order to reduce the chord length. The finalchord length of the BE 72 is cBE = 2.4 m resultingin a chord based Reynolds number of Re=3,000,000.However, as can be seen from Fig. 2 the pressure dis-tributions of the BE 72 for x/cBE = 0 − 0.4 andof the NACA 643-418 for x/cNA = 0 − 0.2 corre-spond very well. Hence, results of the present exper-iments (conducted only in the leading edge region)can be attributed to a chord based Reynolds numberof Re=6,000,000. In the following streamwise posi-tions are given with respect to the chord length (cBE)or the arc length (sBE) of the BE 72 airfoil section.

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C. Airfoil Model

The BE 72 model (Fig. 3) was manufactured in two parts. The leading edge section (x/cBE = 0 − 0.4)was built in negative technique using numerically controlled milled molds. The shells of the upper andlower surface are built from reinforced fiber-glass with 5 mm wall thickness. In the measurement region(0.1 ≤ x/cBE ≤ 0.4) a highly polished brass sheet bended to the model contour is inserted. Additionally, themeasurement region is equipped with 63 pressure orifices allowing for the measurement of the static pressuredistribution. The rear part (x/cBE = 0.4 − 1) of the model was built in positive technique with a core ofpolyurethane foam, which is covered with several layers of fiber-glass. Both model parts are assembled witha laser-cut template to ensure the correct model shape. After wet-sanding and polishing, the remaining RMSsurface roughness heights are in the order of 0.5 µm (measured with a precision surface measuring system).

A movable roughness element of cylindrical shape and a diameter of dr = 20 mm is integrated into the

Figure 3. BE 72 model mounted vertically in thetest section with boundary layer traverse for hot-wiremeasurements.

model at a streamwise location of x/cBE = 0.15. Thesurface of the roughness element is adjusted to themodel shape. During the experiments the roughnesselement can be displaced in a range from h/δ1,ref =0−2 using a linear actuator. The actuator is equippedwith an encoder for closed-loop positioning with aminimal incremental motion ≤ 0.1 µm. Addition-ally, the roughness height is measured and monitoredwith a laser-triangulation system with a resolution of0.15 µm corresponding to 0.2 percent of the bound-ary layer displacement thickness at the position of theroughness element (δ1,ref ).

Moreover, a disturbance source is integrated intothe model at x/cBE = 0.1. Therewith, controlledTS-wave disturbances can be excited in the bound-ary layer upstream of the roughness element througha small slit (width=0.2 mm). However, the use ofthis disturbance source is intended for future investi-gations.

D. Data Acquisition and Processing

Measurements have been performed with a constant-temperature hot-wire anemometer. A boundary layerprobe of type 55P15 with a 5 µm wire was used. The hot-wire calibration is based on the King’s lawwith the coefficients optimized for a minimum standard deviation. The hot-wire probe is mounted to atraversing system allowing for automatic boundary layer scans both in wall normal and spanwise direction.Additionally, the traverse is equipped with a static pressure probe, which is used to measure the velocity atthe boundary layer edge. The hot-wire probe was operated with a DISA 55M10 bridge using an overheatratio of 1.8. The hot-wire signal was split into AC and DC part (Fig. 4). For the low-pass filtering an activelow-pass with a cut-off frequency of fc = 1 Hz was used. The AC part was high pass filtered with a passiveRC-filter and amplified with low noise amplifiers. Due to a high sampling rate (fs = 15625 Hz) and a strongdecay of the spectral density in the high frequency range no anti-aliasing filter was necessary. The AC and

CTA

1 Hz

Low Pass

50 Hz

High Pass

USB AD Converter

Amplifier

Data Acquisition PC

Roughness Actuator /

Position Sensor

HW Traversing System

Figure 4. Schematic of the data acquisition setup.

DC signal were acquired at the same time with an18-Bit USB AD-converter.

For each measurement point a total of 32768 sam-ples were recorded. In the post processing the AC partis corrected for the frequency response of the high-pass filter and the amplification ratio. AC and DCpart are, then, summed up in order to calculate ve-locities from the voltage signal. For the spectral anal-ysis the fluctuation velocities are split into 8 blocksof 4096 samples. Each block is Fast Fourier Trans-formed and averages are taken in the frequency do-main. Spanwise wavenumber spectra were processed

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from the spanwise amplitude distribution neglecting the phase information, since it is random without con-trolled disturbance generation upstream of the roughness element. Hence, spanwise wavenumber spectra aresymmetric with respect to the spanwise wavenumber β.

III. Results and Discussion

A. Base Flow Characteristics

The present experiments were performed for a boundary layer with close to zero pressure gradient. Thepressure distribution in the leading edge region (0 ≤ x/cBE ≤ 0.4) was obtained from 63 pressure orificesusing a PSI pressure scanning system (ESP 64 HD). Measurements were taken with the boundary-layertraversing system placed inside the test section (Fig. 3) to account for its influence. The comparison ofthe pressure distributions obtained with the traverse placed at x/cBE = 0.18 and at x/cBE = 0.40 showsthe upstream influence of the traversing system to be small (Fig. 5). A constant offset in-between themeasured and the calculated (XFOIL18) pressure distribution can be observed showing lower cp values inthe measurements. Likely, the local free stream velocity in the test section is increased due to blockageeffects caused by the large size of the model in relation to the test section. However, the characteristic ofthe pressure distribution within the measurement region remains unchanged, since the pressure gradient isclose to zero, both for the measured and calculated values.

In the following, the measured pressure distribution was used for the calculation of boundary-layer profileswith a finite-difference scheme according to Cebeci and Smith.19 Both for the boundary layer displacementthickness δ1 and the shape factor H12 measured and calculated values are in reasonably good agreement(Fig. 6). The displacement thickness at the position of the roughness element is δ1,ref = 0.72 mm. Theshape factor is nearly constant and very close to the value for the Blasius boundary layer (H12 = 2.591)within the measurement region. In agreement with the pressure distribution, the local boundary layeredge velocity (obtained with the pressure probe at the boundary layer traverse) is nearly constant in themeasurement region. Moreover, a very good consistency of the non-dimensionalized boundary layer profilescan be observed (Fig. 7). In the following, both the height of the roughness element and the wall normalcoordinate y are non-dimensionalized with the displacement thickness at the roughness position (δ1,ref ),whereas the streamwise and the spanwise coordinate are non-dimensionalized with the roughness diameterdr. The streamwise distance ∆s is measured with respect to the center of the roughness element. Mean flowvelocities are related to the local boundary layer edge velocity (uδ).

0 0.1 0.2 0.3 0.4

-1.4

-1.2

-1

-0.8

-0.6 HW Traverse at x/c=0.18HW Traverse at x/c = 0.4

x/c [-]

cp [-

]

0 0.1 0.2 0.3 0.4

-1.4

-1.2

-1

-0.8

-0.6

Xfoil Calculation

Figure 5. Comparison of measuredand calculated (XFOIL) pressuredistributions on the upper surfaceof the BE 72.

s/d r [-]

δ 1 [m

m],

H12

[-]

uδ [m

/s]

-5 0 5 10 150

0.5

1

1.5

2

2.5

3

3.5

4

0

5

10

15

20

25

30

-5 0 5 10 150

0.5

1

1.5

2

2.5

3

3.5

4

δ1

H12

uδ

Figure 6. Comparison of measured(symbol) and calculated (line) dis-placement thickness, shape factorand local free stream velocity.

u/u δ[-]

y/δ 1 [

-]

0 0.5 10

1

2

3

4

5

s/d r = -3.25s/d r = -1.25s/d r = 1.25s/d r = 3.75s/d r = 6.25s/d r = 8.75s/d r = 11.25s/d r = 13.75

Figure 7. Streamwise developmentof the non-dimensionalized bound-ary layer profiles for zero roughnessheight.

B. Mean Flow Distortion and Shape Factor

Fig. 8 shows the mean flow distortion caused by the interaction of the laminar boundary layer with theroughness element for three different roughness heights measured aft of the roughness on the centerline.For roughness heights below h/δ1,ref = 0.2 (Fig. 8a) the mean flow distortion is within 1-2 percent. Thiscorresponds to the range of the measurement uncertainty. The mean flow is, therefore, not considerably

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∆u/u δ [-]

y/δ 1,

ref [-

]

-0.3 -0.2 -0.1 00

1

2

3

4

5∆s /d r = 0.75∆s /d r = 1.25∆s /d r = 1.75∆s /d r = 2.25∆s /d r = 2.75∆s /d r = 3.25∆s /d r = 3.75

a ) h/δ1,ref = 0.2

∆u/u δ [-]y/

δ 1,re

f [-

]

-0.3 -0.2 -0.1 00

1

2

3

4

5∆s /d r = 0.75∆s /d r = 1.25∆s /d r = 1.75∆s /d r = 2.25∆s /d r = 2.75∆s /d r = 3.25∆s /d r = 3.75∆s /d r = 4.25

b ) h/δ1,ref = 0.5

∆u/u δ [-]

y/δ 1,

ref [-

]

-0.3 -0.2 -0.1 00

1

2

3

4

5∆s /d r = 0.75∆s /d r = 1.25∆s /d r = 1.75∆s /d r = 2.25∆s /d r = 2.75∆s /d r = 3.25∆s /d r = 3.75

c ) h/δ1,ref = 0.75

Figure 8. Streamwise development of mean flow distortion on roughness centerline for three different roughnessheights.

changed through the interaction with the roughness element. The comparison to two-dimensional roughnesselements7 shows that a significant mean flow distortion can only be observed at increased roughness heightsfor a single three-dimensional roughness elements. The shape factor immediately downstream of the rough-ness element shows only a slight increase (H12 = 2.63) for h/δ1,ref = 0.2 in comparison to the base flow(Fig. 9). Further downstream (∆s/dr = 2.75) no considerable difference in the shape factor for h/δ1,ref = 0and h/δ1,ref = 0.2 is evident.

A significant increase of the mean flow distortion is observed for 0.3 ≤ h/δ1,ref ≤ 0.5 (Fig. 8b) resulting inan inflectional nature of the boundary layer profiles downstream of the cylindrical roughness element (Fig. 10).

∆s/d r [-]

H12

[-]

0 5 10 151

2

3

4

5h / δ1,ref = 0 h / δ1,ref = 0.1h / δ1,ref = 0.2h / δ1,ref = 0.3h / δ1,ref = 0.4h / δ1,ref = 0.5h / δ1,ref = 0.75h / δ1,ref = 1.00h / δ1,ref = 1.25h / δ1,ref = 1.50

∆s/d r [-]

H12

[-]

0 2 4 6

2.6

2.8

3

3.2

Figure 9. Streamwise development of the shape factoron centerline for different roughness heights.

The maximum distortion (∆u/uδ = 0.15) is presentin the near wall region close to y = h = 0.5 δ1,refimmediately downstream of the roughness. Clearly,the mean flow distortion is decreasing in the down-stream development until the boundary layer profilecoincides within the measurement uncertainty withthe base flow profiles at ∆s/dr = 3.75. Hence, theinflectional nature of the boundary layer profile isstabilized within a relatively short streamwise dis-tance. This observation is consistent with the stream-wise development of the shape factor, which is signif-icantly increased directly downstream of the rough-ness (H12 = 3.2) before decreasing again to approxi-mately H12 = 2.59. The roughness Reynolds numberfor h/δ1,ref = 0.5 is Rh = 195.

H12

[-]

0 2 4 60

1

2

3

4

h/δ1,ref = 0.5h/δ1,ref = 0.75

∆s/d r [-]

y/δ 1,

ref [-

]

0 2 4 60

1

2

3

4

Figure 10. Boundary layer profiles (line) and shapefactor (line with dot) on centerline aft of the rough-ness for h/δ1,ref = 0.5 (black) and h/δ1,ref = 0.75 (red).

A further increase of the roughness height toh/δ1,ref = 0.75 results in a maximum of 30 percentmean flow distortion in relation to the velocity at theboundary layer edge (uδ) in the close vicinity of theroughness element. The comparison to h/δ1,ref = 0.5shows the maximum being shifted off the wall to ap-proximately y = h = 0.75 δ1,ref . Hence, the maxi-mum distortion is located at a wall normal positioncorresponding to the roughness height for h/δ1,ref =0.5 and for h/δ1,ref = 0.75, respectively. Comparingthe boundary layer profiles immediately downstreamof the roughness, an increased inflectional nature forh/δ1,ref = 0.75 is evident (Fig. 10). In downstreamdirection the mean flow distortion is first decreasing,

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∆s/d r [-]

z/d

r [-]

-1 0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

1.2

1.4

h/δ1,ref = 0.75h/δ1,ref = 1.00h/δ1,ref = 1.25h/δ1,ref = 1.50

roug

hnes

s el

emen

t

R.M.S < 10-2

R.M.S > 10-2

Figure 11. Spanwise extend of turbulentregion downstream of the roughness el-ement at y/δ1, ref = 0.3.

resulting in an increased stability of the boundary layer profiles.However, transition is seen to occur within a relatively shortstreamwise distance (∆s/dr = 4.75) aft of the roughness. Theroughness Reynolds number for this case is Rh = 432. This value isslightly lower than the values reported by Tani1 (Reh = 500−800)for a cylindrical roughness element and in good agreement with thevalue (Reh = 440) deduced from Gregory and Walker.20

For h ≥ δ1,ref the location of boundary layer transition moveseven further upstream as can be deduced from the shape factor(Fig. 9). It seems that if a threshold for the shape factor in-between H12 = 3.2 − 3.8 is exceeded, by-pass transition is seento occur in the close vicinity of the roughness element. Consider-ing the spanwise extend, in which the laminar boundary layer isaffected by the roughness element total R.M.S values in a frequencyrange (f = 150− 7630 Hz) were calculated. Therewith, a laminarboundary layer can clearly be distinguished from a turbulent one.The threshold R.M.S value to separate the laminar and the turbu-lent state was chosen to 10−2. This value was seen to coincide withthe first increase in the mean flow velocity. Fig. 11 shows the results for different roughness heights. Clearly,the spanwise extend, in which the boundary layer is interacting with the roughness element is considerablyincreasing with the roughness height. However, it seems that the angle of the wedge-shaped turbulent regiondownstream of the roughness element is rather independent of the roughness height, whereas the leadingedge of the wedge-shaped region is significantly moving upstream with increasing roughness height.

In the following further light is shed on the spanwise extend of the mean flow distortion for a roughnesselement of h/δ1,ref = 0.5 (Fig. 12). Immediately downstream of the roughness element (Fig. 12a) a largewake region is present, which extends up to three roughness heights (y/δ1,ref = 1.5) in wall normal direction.The extend of the wake region in spanwise direction (z/dr = ±0.5) is, at first, constricted to the roughnessdiameter. Further downstream (Fig. 12b), no significant mean flow distortion can be observed on thecenterline being in good agreement with the wall normal measurements (Fig. 8b). However, streaks (regionsof high velocity in spanwise direction) can be observed on both sides of the roughness with the maximumamplitude located at z/dr = ±0.5. Similar to the wake region immediately downstream of the roughnessthese streaks can be observed up to three roughness heights in wall normal direction. In the downstreamdevelopment the streak amplitude is seen to decrease again (Fig. 12c). As a result, no mean flow distortioncan be observed in the near wall region (y/δ1,ref = 0.42). For 0.54 ≤ y/δ1,ref ≤ 1.67 a peak valley structureon both sides of the roughness is present, however, with very small amplitudes. These observations hintat the presence of a counter-rotating vortex pair (as indicated in Fig. 12b) on each side of the roughnesselement, respectively. This observation would fit to the flow visualizations of a horseshoe and a pair of spiralfilaments in the wake of a cylindrical roughness element by Legendre and Werle.21

z / dr [-]

u/u

δ[-]

-1.5 -1 -0.5 0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

a ) ∆s/dr = 0.75

z / dr [-]

u/u

δ [

-]

-1.5 -1 -0.5 0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

b ) ∆s/dr = 4.75

z / dr [-]

u/u

δ [

-]

-1.5 -1 -0.5 0 0.5 1 1.50

0.2

0.4

0.6

0.8

1y /δ 1,ref = 0.42y /δ 1,ref = 0.56y /δ 1,ref = 0.83y /δ 1,ref = 1.11y /δ 1,ref = 1.39y /δ 1,ref = 1.67y /δ 1,ref = 3.33

c ) ∆s/dr = 13.75

Figure 12. Streamwise development of spanwise mean flow distortion at different wall-normal positions forh/δ1,ref = 0.5.

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C. Spectral Boundary Layer Characteristics

Fig. 13 shows a comparison of wall normal boundary layer spectra for h/δ1,ref = 0 and h/δ1,ref = 0.5,respectively. Measurements were taken at 3 streamwise positions downstream of the roughness on thecenterline. In all spectra low-frequency disturbances (f = 200− 350 Hz) are evident, which are clearly seento decay in wall normal direction. In streamwise direction, these disturbances are not considerably amplifiedor damped. These observations lead to the conclusion that these low-frequency disturbances can likely beattributed to vibrations of the boundary layer traverse or background noise and are, therefore, not connectedto characteristics of the boundary layer flow.

In case of a laminar boundary layer without roughness element (Fig. 13a) no significant boundary layerdisturbance modes are present immediately downstream of the roughness in the frequency range of the mostamplified TS-waves (f = 450 − 700 Hz) as can be deduced from Fig. 14. Further downstream (Fig. 13c)small amplitude disturbances are seen to grow for (f = 350−550 Hz) predominately in the near wall region.Hints at a second peak are present in the outer region of the boundary layer. These observations fit very wellto the linear stability characteristics as can be seen from the streamwise development of the n-factor withinthe measurement region (Fig. 14). For roughness heights below h/δ1,ref = 0.2 no significant changes to theobservations made for h/δ1,ref = 0 are evident in the wall normal boundary layer spectra on the centerline.This can likely be attributed to the fact that the present experiments are conducted in a very low turbulencewind tunnel.

For roughness heights in a range 0.3 ≤ h/δ1,ref ≤ 0.5 (Fig. 13d) the disturbance level is slightly de-creased in the near wall region immediately downstream of the roughness on the centerline (in comparison toh/δ1,ref = 0). This can likely be explained by the decreased mean flow velocity in the wake of the roughnesselement. However, further downstream (Fig. 13e) a significant growth of boundary layer disturbance modesfor a wide frequency range f = 400 − 1500 Hz can be observed. The most dominant modes, however, arepresent in a frequency range f = 450 − 800 Hz. The maximum amplitude in wall normal direction can beobserved for y/δ1,ref = 0.8− 1.2, while a second peak is evident close to y/δ1,ref = 4. From the comparison

a ) h/δ1,ref = 0, ∆s/dr = 0.75 b ) h/δ1,ref = 0, ∆s/dr = 4.75 c ) h/δ1,ref = 0, ∆s/dr = 13.75

d ) h/δ1,ref = 0.5, ∆s/dr = 0.75 e ) h/δ1,ref = 0.5, ∆s/dr = 4.75 f ) h/δ1,ref = 0.5, ∆s/dr = 13.75

Figure 13. Comparison of the streamwise development of the spectral boundary layer characteristics on theroughness centerline for h/δ1,ref = 0 and h/δ1,ref = 0.5.

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to measurements for h/δ1,ref = 0.3 and h/δ1,ref = 0.4 it can be seen that the peak amplitude of these modessignificantly increases with the roughness height, whereas the frequency range is very similar. Hence, in thestreamwise development disturbances are seen to grow stronger with increasing roughness height.

However, after reaching a maximum amplitude clearly a damping of these disturbance modes begins.The maximum amplitude is located close to ∆s/dr = 4.75 in streamwise direction for all three roughnessheights (h/δ1,ref = 0.3, 0.4, 0.5), respectively, showing the streamwise position of the maximum amplitude tobe independent of the roughness height. All modes with frequencies above f = 550 Hz are strongly dampedresulting in amplitudes lower than the signal to noise ratio as can be seen from Fig. 13f. For h/δ1,ref = 0.5only a slight increase in the boundary layer disturbance level remains in comparison to the base flow case(Fig. 13c) in a lower frequency range (f = 350 − 550 Hz). These lower frequency modes are in the samefrequency range as the modes, which were seen to grow in the base flow case. Furthermore, the peakposition of the disturbance modes is significantly shifted towards the wall in the streamwise developmentas can be seen from the comparison of Fig. 13e and Fig. 13f. Similar observations were made for the lowerroughness heights (h/δ1,ref = 0.3 and h/δ1,ref = 0.4). As a result of the lower absolute peak amplitudesat ∆s/dr = 4.75 the higher frequency modes (f ≥ 550 Hz) were seen to approach the level of the signalto noise ratio already early in the downstream development in comparison to h/δ1,ref = 0.5. Also, theamplitude level of the low frequency modes (f = 350− 550 Hz) was observed to be lower at ∆s/dr = 13.75.Interestingly, a good agreement in the frequency range of the most amplified TS-wave modes (Fig. 14) atthe location of the roughness element and the maximum amplitude modes at ∆s/dr = 4.75 can be observedfor 0.3 ≤ h/δ1,ref ≤ 0.5.

∆s/d r [-]

f [H

z]

0 5 10 15 20 25200

400

600

800

1000n

420

-2-4-6-8-10

roug

hnes

s el

emen

t

Figure 14. Streamwise developmentof n-factor calculated with respect tothe streamwise source position ∆s/dr =−6.25.

In the following further light is shed on the spanwise develop-ment of the disturbance modes introduced by the roughness el-ement with h/δ1,ref = 0.5. Therefore, spanwise boundary layerscans were performed at a wall normal position of y/δ1,ref = 0.83(Fig. 15) at the same streamwise locations as for the wall normalscans on the centerline (Fig. 13). Immediately downstream of theroughness (Fig. 15a) no significant disturbance modes are presenton the centerline as already observed in the wall normal spectrum(Fig. 13d). However, at a spanwise spacing of z/dr = ±0.5 a growthof disturbance modes in two lobes can be observed. The frequencyrange of these modes coincides with the most amplified modes ob-served on the centerline further downstream (Fig. 13e). The maxi-mum amplitude seems to be located close to y/δ1,ref = 0.83 as canbe deduced from several spanwise scans at different wall normal po-sitions. Taking the spanwise mean flow velocity distribution intoaccount shows these lobes to coincide with the regions of the high-est mean flow velocity gradient caused by the wake of the roughnesselement. In the spanwise wavenumber spectrum (Fig. 15d) theselobes result in a peak valley structure, however, clearly dominatedby the 2 two-dimensional mode.

Further downstream (Fig. 15b), a strong amplification of these disturbance modes can be seen not onlyin the region, in which the lobes were observed directly downstream of the roughness element, but especiallyin the centerline region. Interestingly, the disturbance modes show a ’comb-like’ structure with the mostdominant peaks at frequencies of f = [475, 500, 525, 600, 700] Hz, which are also evident in the spanwisewavenumber spectrum (Fig. 15e). The disturbances induced by the roughness are mainly composed of two-dimensional modes. Small side peaks at a spanwise wavenumber (non-dimensionalized with the roughnessdiameter dr) of approximately β = ±2.4 can be observed for the dominant modes in the ’comb-like’ structurementioned above.

At ∆s/dr = 13.75, clearly, the high frequency modes (f ≥ 550 Hz) are damped in the entire spanwiseextend. However, the spanwise extend of the lower frequency modes (f = 350 − 550 Hz) is considerablyincreased. Two lobes with a spanwise spacing of z/dr = ±0.5 can be observed, in which the disturbanceamplitude is increased. In the outer region (z/dr = ±1.75) two lobes with a significantly reduced disturbancelevel are present leading to a peak valley structure in spanwise direction. As a result peaks in the spanwisewavenumber spectrum can be observed at β = 0.5 and β = 1.08 corresponding to a spanwise wavelengthof 2dr and 0.93dr. However, the spanwise wavenumber spectrum is still dominated by the two-dimensional

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modes.Similar observations concerning the amplification and the spanwise wave numbers of these disturbance

modes were made for the lower roughness heights of h/δ1,ref = 0.3 and h/δ1,ref = 0.4. In accordance withthe observations made on the centerline the absolute amplitudes were seen to increase with the roughnessheight.

a ) ∆s/dr = 0.75 b ) ∆s/dr = 4.75 c ) ∆s/dr = 13.75

d ) ∆s/dr = 0.75 e ) ∆s/dr = 4.75 f ) ∆s/dr = 13.75

Figure 15. Comparison of spanwise boundary layer disturbances amplitudes (top) and spanwise wave numberspectra (bottom) for h/δ1,ref = 0.5.

IV. Conclusion

Boundary layer measurements were conducted downstream of a single, cylindrical roughness elementplaced on an airfoil leading edge. Therefore, a new airfoil section BE 72 was designed in order to allow forexperiments both in the leading edge region and at a typical Reynolds number for wind turbine applications(Re = 6, 000, 000). The pressure distributions of the BE 72 allow for experiments in boundary layers withfavorable, close to zero and adverse pressure gradient. The boundary layer parameters were seen to be ingood agreement with calculations based on the measured pressure distribution.

For low roughness heights (h/δ1,ref ≤ 0.2), no significant interaction of the roughness element and thelaminar boundary layer was evident. The mean flow distortion was within 1-2 percent resulting only in asmall increase of the shape factor (H12 = 2.63) downstream of the roughness element for h/δ1,ref = 0.2 incomparison to the base flow case (H12 = 2.59). Moreover, no increase in the boundary layer disturbancelevel caused by the roughness element could be observed within the measurement region.

A significantly increased mean flow distortion was present for medium sized roughness elements 0.3 ≤

h/δ1,ref ≤ 0.5. As a result, the shape factor immediately downstream of the roughness was considerablyincreased. However, in the downstream development the inflectional nature of the boundary layer profileis stabilized and the shape factor decreases to approximately H12 = 2.59 being equal to the value for thebase flow case (h/δ1,ref = 0). Downstream of the roughness element a significant growth of disturbancemodes was observed in a frequency range from f = 500 − 800 Hz. The energy of these modes was seen

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to be predominantly concentrated in two-dimensional modes. However, after reaching a maximum a strongdamping of these modes was observed. At the same time low-frequency modes (f = 350 − 550 Hz) wereslightly growing with spanwise wavenumber modes corresponding to multiples of the roughness diameter.

For high roughness heights (h/δ1,ref ≥ 0.75) transition was seen to occur in a wedge shape region inthe close vicinity of the roughness element. Regarding the shape factor, it seems that if a threshold ofH12 = 3.2 − 3.8 is exceeded, bypass transition is seen to occur. The spanwise extend of the wedge shapedturbulent region downstream of the roughness element was seen to considerably increase with the roughnessheight.

Future investigations will focus on the interaction of a two-dimensional TS-wave with the roughnesselement at different heights. In addition, the effect of pressure gradient in the leading edge region (favorableand adverse) will be addressed.

V. Acknowledgments

This work is supported by DFG (Deutsche Forschungsgemeinschaft) under grant Wu 265/4-1.

References

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19Cebeci, T. and Smith, A. M. O., “Analysis of Turbulent Boundary Layers,” Academic Press, 1974.20Gregory, N. and Walker, W. S., “The Effect on Transition of Isolated Surface Excrescences in the Boundary Layer,”

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