PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Optimization of leading-edge undulation of a NACA 65(12)-10
aerofoil for noise reduction and aerodynamic enhancement
Jung-Hoon KIM1; Kwing-So CHOI1;

Giovanni LACAGNINA2; Phillip JOSEPH2;
Seyed Mohammad HASHEMINEJAD3; Tze Pei CHONG3;
Muhammad Farrukh SHAHAB4; Mohammad OMIDYEGANEH4; Alfredo PINELLI4
1

University of Nottingham, UK
University of Southampton, UK
3Brunel University, UK
4
City, University of London, UK

2

ABSTRACT
Leading-edge undulations or tubercles of humpback whale flippers have been known as one of biomimetic
technologies adaptable to flow control of aerofoils, particularly at post stall conditions. These leading-edge
undulations are also known to reduce noise resulting from an interaction with on-coming turbulence. We
have recently carried out a parametric study of a NACA 65(12)-10 aerofoil with a view to optimise theamplitude and the wavelength of leading-edge undulations for noise reduction and aerodynamicenhancement. A 3x3 test matrix composing of three amplitudes (h = 3%, 6% and 12% chord) and three
wavelengths ( = 10%, 20% and 30% chord) was used in the investigation, where lift, drag and noise were
measured at the Reynolds number of 105. In this test, a turbulence-generating grid was installed at the inlet of
the test section to increase the turbulence level in the freestream and to promote transition to turbulence near
the leading edge of aerofoils without a need for a trip device. Within the test matrix considered, we found thatthe best improvement in CL,max is given with the greatest wavelength and amplitude, whereas the maximum
noise reduction is obtained with the small wavelength and the large amplitude.
Keywords: Leading-edge undulation, NACA 65(12)-10, Lift, Drag, Noise

1. INTRODUCTION
Energy and environmental problems have become so critical to our current and future life that vast
areas of scientists and engineers tackle these problems. Surely, these challenges are also significant
motivations for most of researches in fluid mechanics. Among these, studies on low Reynolds flows
around aero- or hydro-foils have long been carried out with this aim for the use of engineering
applications such as propellers, windmills, helicopters, spoilers in automobiles, etc (1). Apart from theextensive studies on the generic shapes of an aerofoil associated with the boundary layer separation (2),many auxiliary methods have been devised to overcome the limit of their performances (3). These
control methods can be categorised in different way, one of which divides them into active and passive
ones depending on whether power are required for the control or not (1). Various active methods
include plasma actuators for momentum addition (4) or streamwise vortical structure generation (5),synthetic jets (6), pneumatic blowing or suction (7), acoustic excitations (8), etc. Although the active
methods have such advantages like comparatively high effectiveness and targeted controllability intime and space, passive control methods are attractive alternatives as they are because of the relative
simplicity for the realization, less cost and no power requirement although it could have an adverse
effect on the performance on off-design conditions for the actuators. The devices or mechanisms
developed for passive control over low Reynolds number flows around foils include tripping wires toenergise boundary layer for the promotion of transition to turbulence (9), Gurney flaps (10), vortex
generators (11), etc. Nature inspires scientists or engineers in developing flow control methods one ofwhich is tubercle or leading edge undulations discovered from the pectoral flipper of a Humpback
whale.
The detailed morphology on Humpback whale’s flippers was evaluated in (12) as an ellipticallytapered, symmetrical aerofoil with leading edge undulations (LEU) and the measurements of the liftand drag of their test models were made in (13) which reported that the LEU delayed stall angle,

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increased lift and decreased drag. On the contrary, when the LEU were applied to the test model of thesame cross-section with that in (13) but of infinite span without taper, the maximum lift coefficient(C Lmax ) of the aerofoil with LEU was reduced or equal to the aerofoil with smooth leading edge
although the lift in post-stall was dramatically increased (14). For most of studies where twodimensional infinite span of aerofoils were tested (15-17), the CLmax was not increased whereas stall
was delayed compared to the corresponding smooth leading-edged aerofoils.
In addition to the effects of LEU on aerodynamic performances, their aeroacoustic effects have also
been investigated. Adoption of LEU in the flat plate was shown in (18) to reduce aerofoil turbulenceinteraction noise and optimum wavelength of LEU was identified in (19) with regard to the transverse
integral length scale. It is reported in (20) that peak and adjacent broadband noise coming from theaerofoil in the flow without artificial increase of turbulence were reduced by adopting LEU.
In our previous study, two dimensional infinite span of a NACA 65(12) -10 aerofoil, which iscambered and whose type of separation (21) is trailing edge separation at 105 of Reynolds number
based on its chord length, was employed to investigate the effects of various cross sectional shapeswith the amplitude and the wavelength of leading edge profile on the planform. As continuation of thiswork, the present study will demonstrate the results on the optimization of the two parameters in terms
of aerodynamic and aeroacoustic performances.

2. Experimental Setup
2.1 Aerodynamic Force Measurement Facility
Aerodynamic force measurements were carried out in an open-return wind tunnel at the Universityof Nottingham. The dimension of the test section is 0.91 m wide x 0.75 m high and 1.5 m long. In thesetests, a vertically installed aerofoil model was positioned at the mid-span, 0.1 m above the floor and
0.7 m downstream from the inlet of the test section. A schematic of the experimental set-up is shown in
Figure 1. The aerofoil was connected to a force balance by an aluminium strut which was covered byan aerodynamic shaped fairing fixed to the wind tunnel floor. A circular plate in 150 mm diameter was
attached to the bottom of the aerofoil, which was set in a circular hole provided by a 360 mm x 260 mm
rectangular endplate. This allows the aerofoil to rotate through its transverse axis to change the angleof attack during the measurements. The top endplate, which is identical to the bottom endplate but
without a hole, was fixed at the top of the aerofoil with a 2 mm gap. Each endplate had an elliptic
leading edge with a major-to-minor axis ratio of 6 to 1. A 3-component force transducer (Kyowa,
LSM-B-SA1, rated capacity: 10 N) was used to measure the drag and the lift on the aerofoil. The force
balance was mounted on a turntable which was connected through a 2:1 gear to a stepping motor. The
minimum angle of rotation of the turntable was 0.45 degree.

(a)

(b)

Figure 1 (a) A schematic of the experimental set-up (not to scale) and (b) the grid geometry. The
unit for distance is mm.
In order to promote early transition of the boundary layer over an aerofoil, a perforated plate witha mesh size (M) of 25 mm was installed in a wind tunnel 0.56 m upstream of the rotational axis of theaerofoil models. The open-air ratio of this turbulence generating grid was 0.64. The mesh geometry is
shown in Figure 1(b). The turbulence intensity and the longitudinal integral length scale at x/M = 22,
where the aerofoil was installed, were 4.3% and 13 mm, respectively. The integral length scale wasobtained using the method described in (22) and the ratio of nearly unity between the integral scale to5352

the plate thickness appears effective in promoting transition (23). Without the grid, the turbulence
intensity at the same freestream speed was 0.3 %.
A NACA 65(12)-10 aerofoil with 100 mm chord length and 500 mm span, therefore the aspect ratio
5, was selected as a baseline case. The radius at the trailing edge was 0.5% of the chord length. Figure
2 shows the cross section at the peak (blue) and the trough (red) of the aerofoil with LEU. A solid anddashed green line are the camber lines at the peak and the trough section, respectively. This profile wasselected in the current optimization as it showed the highest lift coefficient among the LEU profiles
tested. For the optimization of wavelength and amplitude of the sinusoidal leading-edge undulation, 9aerofoils with 3 variations in h (3%, 6% and 12% chord) and 3 variations  (10%, 20% and 30% chord),
were fabricated by a 3D printer, Zortrax M300 using Z HIPS (high impact polystyrene).
b
a
=

h

=

18

Figure 2 The cross sectional profile (blue) and the camber line (green) in the peak and the trough(red) profile with the camber line (dashed green) for the NACA 65(12)-10 with LEU.
2.2 Noise Measurement Facility
Acoustic measurements of the aerofoil have been carried on in the open jet wind tunnel facility of
ISVR, at the University of Southampton. It is housed in an anechoic chamber of dimensions 8 m x 8 m
x 8 m, whose walls are acoustically treated with glass-wool wedges to reach the lowest cut-off
frequency of 80 Hz. A large nozzle, 500 mm high and 350 mm wide, was used so that the flow
curvature and downwash deflection effects of an open wind tunnel can be miminised. The ratio
between the geometrical angle 𝛼𝑔𝑒𝑜𝑚 and the effective one 𝛼𝑒𝑓𝑓 in the current experiment is about
1.35. Two side plates were located one chord-length downstream the nozzle to maintain thetwo-dimensionality of the flow. A detailed description of the facility can be found in (24).
An array of eight half-inch condenser microphones (B&K type 4189), located at a distance of 1.2 m
at the mid span of the aerofoil, delivered the free-field noise measurements. The emission angles of the
microphones, relative to the downstream direction of the jet axis, were in the range of 40 to 130
degrees. Finally, each noise measurement lasted for 20 s at the sampling frequency of 40 kHz.

3. Results
3.1 Aerodynamic Performance
Figure 3 shows the lift and drag coefficients as a function of the angle of attack of an aerofoil withleading-edge undulation with different wavelength . Note that the force coefficients are normalized
by the planform area of each aerofoil. Experimental uncertainties are shown by error bars for thebaseline case in Figure 3 (a). The uncertainties in the freestream velocity, force measurements andangle alignment are considered to be ±0.5% FS, ±0.3% FS and ±0.3°, respectively. The Root Sum
Square method (25) was used to estimate the combined errors. The errors in the lift coefficient were
estimated to be 0.8 % at  = 15.3° and 2.7% at  = 5.4°. On the other hand, the errors in the dragcoefficients were 6.5% at  = 15.3° and 11% at  = 5.4°.
For aerofoils with LEU with a turbulence-generating grid installed in the wind tunnel (Figure 3 (a),(c) and (e)) C L starts to deviate from baseline data at about  = 5°. For example, C L of LEU with h/C= 3% and C = 10% reduces after  = 5°, then increases near the maximum lift angle and reduces
again after stall. Previous investigations on a similar LEU (14, 16) also indicated a reduction in C L in
pre-stall angles, which was due to the earlier separation around the trough section (17). C L of LEU with
h/C = 3% and C = 20% or 30%, on the other hand, continue increasing up to the maximum lift angle.
However, C L of these aerofoils (h/C = 3%) do not outperform the baseline in post-stall angles. C D
curves of LEU with h/C = 3% collapse to the baseline data up to  = 18°, but a drag improvement canbe found in post-stall angles. C L and C D behaviour with h/C = 6% (Figure 3 (c)) is similar to that with
h/C = 3%. With h/C = 12% (Figure 3 (e)) C L with C = 10% reduces for all angles of attack. This may

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implicate that there exists an optimum LEU configuration for C Lmax within the range of wavelengthand amplitude being tested. C D of these aerofoils for  between 12° and 18° increases slightly ascompared to that of the baseline, which may be caused by an earlier separation in the trough (17). Withan increase in h/C (Figure 3 (e) and (f)), the difference in C L at the maximum lift and post-stall angles
became larger between different wavelengths tested, particularly with the grid.
The baseline result without grid (Figure 3 (b), (d) and (f)) is strongly influenced by laminar
separation bubbles at the leading edge, giving a flat C L curve between  = 10° to 16°. The stall angle
is reduced without a grid, however. As compared to the baseline result, aerofoils with LEU arenaturally “tripped” at the leading edge even without grid. Therefore, C L and C D curves without gird aresimilar to those with grid.

CLCD(a) h/C = 3%, with Gridb) h/C = 3%, without Grid(c) h/C = 6%, with Grid(d) h/C = 6%, without Grid(e) h/C = 12%, with Grid(f) h/C = 12%, without Grid

Figure 3 Lift and drag coefficients of the aerofoils with the LEU: (a) h/C = 3%, with Grid; (b) h/C= 3%, without Grid; (c) h/C = 6%, with Grid; (d) h/C = 6%, without Grid; (e) h/C = 12%, with
Grid; (f) h/C = 12%, without Grid.

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(a)

(b)

Figure 4 Contours of the differences in % values of the C Lmax between the aerofoil with the LEU andthe baseline normalized by that of the baseline: (a) With grid; (b) Without grid.
Figure 4 is a contour map to show the percentage change of C Lmax with LEU, which are normalized
by the baseline C Lmax ‘with grid’ and ‘without grid’ in (a) and (b), respectively. The contour lines wereobtained by interpolating 9 data points which are indicated by red circles. The figure shows that C Lmax
is increased by increasing /C of LEU, but the increment is insensitive to the change in h/C for C <20%. As /C increases further, C Lmax increases with an increase in h/C. C Lmax for an aerofoil with /C= 30% and h/C = 12% is increased by about 10 % with or without grid. The differences in maximum lift
angle between the aerofoils with LEU and the baseline are shown in Figure 5. A similarity in behaviour
between Figure 4 and Figure 5 suggests that an increase in C Lmax by LEU is accompanied by anincrease in the maximum lift angle. While there is no significant change by LEU with grid (Figure5(a)), the maximum lift-angle is increased by up to 6 degrees by LEU without grid.

(a)

(b)

Figure 5 Contours for the maximum lift-angle change between the aerofoil with the LEU and thebaseline: (a) With grid; (b) Without grid.
3.2 Aeroacoustic Performance
Figure 6 shows spectra of sound power level for the baseline aerofoil at three different effective angles
at the freestream velocity of 20 m/s with and without the grid. The three effective angle of attack which are
3.7°, 14.8° and 22.3° represent pre-stall, stall and post-stall, respectively. The comparisons of the spectrums
between with the grid (solid lines) and without the grid (dashed lines) indicate significant increase in thenoise spectra by the interaction with the oncoming turbulent flow over the self-noise. The hump in the
spectrum for ‘𝛼𝑒𝑓𝑓 = 3.7°, No Grid’ (blue dashed) is also found in (26) which explains that the noise iscaused by the interaction between Tollmien–Schlichting (T-S) wave convected downstream and thestationary laminar separation bubble on the aerofoil. Our previous studies also showed the separation
bubble on the baseline aerofoil in this range of angle of attack. At 𝛼𝑒𝑓𝑓 = 14.8° near stall, the amplitudes

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between 100 Hz and 1000 Hz were higher than those at 𝛼𝑒𝑓𝑓 = 22.3° beyond stall. Below 40 Hz, small
increases are observed with the angle of attack. For the present test cases without the grid, our previous
studies showed that separation / stall noise (27) corresponded to the noise spectrum in 40 Hz and 2000 Hz.

Figure 6 Sound Power Level for the baseline aerofoil at three representative angles of attack at thefreestream velocity of 20 m/s with and without the grid.
Figure 7 shows the effects of LEU on the overall sound power level obtained from the integration of
the spectra between 40 Hz and 2000 Hz. In each graph, variations of the overall sound power level with
angle of attack were plotted for the LEU with 3 different wavelengths and the constant amplitude. For
comparison, the variations of the noise from the baseline with the angle of attack are repeatedly shownin black in each figure. The noise data for the ‘Grid’ and ‘No Grid’ are designated by solid and dashedlines, respectively. For the cases of the ‘Grid’, the comparison of the noise profiles between thesefigures reveals that some values of h/C are effective in reducing the interaction noise with theoncoming turbulence and that the reductions are seen to increase with h/C although the reductions are
not big enough to reach the noise levels of the case of ‘No Grid’. Unlikely the cases for ‘Grid’, thenoise profiles show complex shapes depending on the angle of attack. Between 0° and 8° where boththe low frequency separation/stall (40 ~ 100 Hz) and the mid frequency T/S wave-separation bubble
interaction noise (200 ~ 2000 Hz) dominate in the spectrum, the LEUs having C = 20% and 30% with
h/C = 6% and all thetested with h/C = 12% were effective in reducing the overall noise. Between 8°
and 12° where highest L/D takes place, the overall noise appears to increase by the LEUs compared to
the noise of the baseline. Beyond 18°, their effects on noise appear to have some relations with thoseon lift. This point may be indicated in Figure 8 which shows OAPWL vs. C L of the aerofoils with
LEU. OAPWL and C L are the difference of OAPWL and C L from the aerofoil with LEU to thebaseline. The cross correlation coefficient between them was 0.63.

(a) h/C = 3%(b) h/C = 6%(c) h/C = 12%

Figure 7 Variations of overall sound power level with attack angle: (a) h/C = 3%; (b) h/C = 6%; (c)h/C = 12%. Blue, red and green lines designate C = 10%, 20%, 30%, respectively, whereas
those of the baseline in black are repeatedly shown for comparison. Solid and dashed lines denotefor ‘Grid’ and ‘No Grid’, respectively. Integration was made between 40 and 2000 Hz.

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Figure 8 OAPWL vs. C L for aerofoils
Figure 9 Contours of the noise reduction in dB
with the LEU at over 𝛼𝑒𝑓𝑓 = 18° without
by the LEU at 𝛼𝑒𝑓𝑓 = 15° with the grid.
the grid.
Contours of the noise reduction by the leading edge undulation at 𝛼𝑒𝑓𝑓 = 15° with grid is plotted in
Figure 9. It shows that optimal parameters are located at around C = 15% and h/C = 10%. But it is not
so meaningful because the level differences are less than 1 dB in the range of h/C larger than about
3.5%. Taking C L into consideration, too low C and high h/C may not be a good choice as the amountof noise reduction is not big enough. A compromise can be made to be C = 30% and h/C = 6%
considering drag near stall as well as C Lmax and noise reduction.

4. CONCLUSIONSFor the continuation of previous studies on the optimization of the trough section of the leadingedge undulation (LEU) of a NACA 65(12)-10, further explorations on the shape optimization of LEU
were made in terms of the wavelength () and the amplitude (h) by the experimental evaluation of theirlifts, drags and aeroacoustic noises in low Reynolds number (~ 10 5 ) flow. Variations in theirperformances were also investigated in high freestream turbulence intensity (4.2%) flows. The test
matrix for the parametric study was composed of C = (10%, 20%, 30%) and h/C = (3%, 6%, 12%).
With a turbulence-generating grid installed in the wind tunnel, the largest increase of the C Lmax
compared to the baseline was about 10% and the best improvement in C L,max was given with thegreatest wavelength and amplitude. The increases of the C Ls at post-stall angles became greater as hincreased although the aerofoil with the LEU of high ratio of h/ underperformed the baseline in thisrange. The CDs in pre-stall angles increased as h increased and those in post-stall angles increased with
. Without the grid, the increases of the C L in post-stall angles by LEU were greater than those with thegrid. The angles at C Lmax of the aerofoils with LEU increased as the C Lmax increased.
The effects on the aeroacoustic noise between 20 Hz and 2000 Hz which correspond to
separation/stall noise were also evaluated. When the grid was installed, the LEUs reduced overallsound power level compared to the baseline by reducing turbulence interaction noise whose frequency
range was between 150 Hz and 2000 Hz. Without the grid, their effects on noise also depended on theattack angle as well as the parameters of LEU. At low angle of attack, the LEUs with large h wereeffective in reducing T/S waves-separation bubble (T/S-SB) interaction noise. The effects on the noisein the lower frequency range than that of the T/S-SB interaction noise were not consistent. In 𝛼𝑒𝑓𝑓
between about 10° and 15° where the T/S-SB interaction noise disappeared, the noise components
between 150 Hz and 2000 Hz grew larger by the LEU compared to the baseline. Beyond 15 °, i.e. in
post-stall, the effects of the LEU on the noise appeared to be correlated with those on lift coefficient.
For the cases with the grid, the overall noise map integrated between 20 Hz and 2000Hz at
𝛼𝑒𝑓𝑓 =15° which corresponds to the angle near the maximum lift may indicate that largest noise
reduction be achieved by the LEU with high h and . However, taking lift into the consideration, theadvantage of the largest noise reduction is reduced since the C L increase around this parametercompared to baseline goes to nearly zero. A compromise can be made to be C = 30% and h/C = 6%
considering drag near stall as well as C Lmax and noise reduction.

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ACKNOWLEDGEMENTS
This study was supported by EPSRC (Grant Number EP/N018486/1) in the UK.

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