new on the noise reduction mechanism of a ﬂat plate serrated...

On the noise reduction mechanism of a flat plate

serrated trailing edge

Danielle J. Moreau1 and Con J. Doolan2

The University of Adelaide, South Australia, Australia 5005

This paper presents the results of an experimental investigation exploring the noise re-

duction potential of sawtooth trailing edge serrations on a flat plate at low-to-moderate

Reynolds number (1.6× 105 < Rec < 4.2× 105). Acoustic measurements have been taken

using a flat plate with both sharp and serrated trailing edges in an anechoic wind

tunnel. Trailing edge serrations are found to achieve reductions of up to 13 dB in the

narrowband noise levels and this is mainly due to attenuation of vortex shedding at

the trailing edge. Velocity data have also been measured in the very near trailing edge

wake using hot-wire anemometry and these data are related to the far-field noise mea-

surements to give insight into the trailing edge serration noise reduction mechanism.

The results show that for this particular configuration, the noise reduction mechanism

of trailing edge serrations is dominated by their influence on the hydrodynamic field at

the source location. Therefore the assumption that the turbulent field is unaffected by

the serrations is not valid and explains why theory is not able to explain experimental

observations.

I. Introduction

Trailing edge noise is considered to be a major noise source in many aerodynamic applications

for which sound production is problematic, such as fans, rotors, propellers, wind turbines and

1 Postdoctoral Research Associate, School of Mechanical Engineering, [email protected], AIAA mem-ber

2 Associate Professor, School of Mechanical Engineering, [email protected], AIAA Senior member

1

underwater vehicles [1–3]. Brooks et al. [4] classified airfoil self-noise mechanisms into five categories

and showed that four of the five noise generation mechanisms are due to the interaction of flow

disturbances with the trailing edge. Other studies [5, 6] have shown that trailing edge noise levels

can be reduced by modifying the trailing edge geometry so that flow disturbances are scattered

into sound with reduced efficiency. In [5] it is also noted that other studies [7–9] have shown a

reduction in the radiated noise can be achieved with mechanisms that reduce the correlation length

of turbulence near the trailing edge. Modifying the trailing edge with the application of serrations

has been shown theoretically [5, 6], numerically [10, 11] and experimentally [3, 12–21] to reduce the

trailing edge noise radiated into the far-field.

Howe [5, 6] derived an analytical noise radiation model for a flat plate serrated trailing edge in

low Mach number flow. According to Howe’s [5, 6] theory, trailing edge noise can be significantly

reduced with the addition of trailing edge serrations due to a reduction in the effective spanwise

length of the trailing edge that contributes to noise generation. Howe’s [5, 6] theory states that

the magnitude of this noise reduction is dependent on the height and geometrical wavelength of the

serrations and on the frequency of sound. The sound generated by large eddies whose length scales

are greater than the amplitude of the serrations (low frequency sound) is unaffected by the presence

of the serrations and hence significant noise reductions are only expected in the high frequency

region.

A number of experimental studies on trailing edge serrations have examined their effect on full

scale wind turbine blades or wind tunnel scale airfoil models at high Reynolds numbers (Rec >

5 × 105, based on chord) [3, 12–17]. Oerlemans et al. [3, 15] investigated the reduction of trailing

edge noise from a NACA 64418 airfoil and the blades of a full scale 2.3 MW wind turbine by

shape optimisation and the application of trailing edge serrations. At high Reynolds numbers

(Rec ≈ 1.6 × 106), optimising the airfoil shape for low noise emission and adding trailing edge

serrations achieved an average reduction of ∼ 6 dB in the radiated noise levels over a variety of

flow conditions. Trailing edge serrations applied to a full-scale wind turbine blade were found to

decrease noise levels by ∼ 3 dB at frequencies below 1 kHz and increase the noise levels above this

frequency without any adverse effect on aerodynamic performance. Gruber et al. [17] examined the

2

noise reduction achieved with sawtooth serrations on a NACA 651-210 airfoil at Reynolds numbers

of 2.0× 105 < Rec < 8.3× 105 and found that noise reductions of up to 7 dB were achieved at low

frequencies (< 2 kHz) and an increase in noise level was observed at high frequencies. The frequency

delimiting a noise reduction and a noise increase was found to correspond to a constant Strouhal

number of Stδ = 1, where Stδ is Strouhal number based on boundary layer thickness.

Previous investigations on trailing edge serrations suggest they are a valid means of airfoil self-

noise reduction. The mechanism responsible for this noise reduction is, however, still unclear. Howe’s

model [6] provides some insight into the serration noise reduction mechanism but all experimental

studies conducted on trailing edge serrations in the past have reported some discrepancy between

their measurements and Howe’s theory. In all cases, the predicted noise reduction levels far exceeded

those measured. In addition, contrary to Howe’s [6] theory, trailing edge serrations on airfoils have

been found to produce a noise reduction at low frequencies and a noise increase at high frequencies

[3, 13–17]. In deriving the serration noise reduction model, Howe [6] made a number of assumptions

and approximations. One such assumption is that the surface pressure frequency spectrum close

to the trailing edge is unchanged by the presence of trailing edge serrations; however, a number

of experimental studies have speculated that this assumption is inaccurate [14, 16]. This suggests

that there is a need to further investigate the physical mechanisms by which trailing edge serrations

reduce airfoil self-noise.

This paper presents the results of an experimental study that explores the noise reduction

potential of sawtooth trailing edge serrations on a flat plate at low-to-moderate Reynolds number

(1.6 × 105 < Rec < 4.2 × 105). This experimental study has relevance to applications employing

small sized airfoils such as small scale wind turbines, unmanned air vehicles (UAVs) and computer

and automotive fans, all of which operate at lower Reynolds numbers. Acoustic test data have been

measured for a flat plate with both sharp and serrated trailing edges in an anechoic wind tunnel.

In addition, velocity data about the flat plate trailing edge have been measured using hot-wire

anemometry, providing information on the turbulent noise sources. The overall aims of this paper

are: (1) to present acoustic and flow data for two different serration geometries at a variety of flow

speeds; (2) to compare experimental measurements with theoretical noise reductions predicted using

3

the theory of Howe [5, 6]; and (3) to investigate how serrations affect noise production at the trailing

edge.

This paper is structured as follows: Section II presents the theoretical background; the exper-

imental method is described in Section III; Section IV presents the experimental results including

far-field acoustic data, comparison with the theoretical predictions of Howe [6] and velocity spectra

in the wake; and the conclusion is given in Section V.

II. Theoretical background

Howe [6] derived an analytical model to predict the effect on noise radiation of sawtooth serra-

tions at the trailing edge of a flat plate in low Mach number flow. The acoustic pressure frequency

spectrum, Φ(x, ω), of a flat plate with a serrated trailing edge at an observer location a distance |x|

from the trailing edge is given by [6]

Φ(x, ω)

(ρv2∗)2(l/c0)(δ/|x|)2

=

(

Cmπ

)

sin2(

θ

2

)

sin(α)Ψ(ω), (1)

where ρ is the fluid density, v∗ ≈ 0.03U∞, l is the plate span, c0 is the speed of sound, δ is

the boundary layer thickness, Cm ≈ 0.1553, θ and α are the polar and azimuthal observer angles

respectively, Ψ(ω) is the non-dimensional edge noise spectrum and ω = 2πf , where f is the frequency.

The polar and azimuthal observer angles, θ and α, are defined according to the co-ordinate system

of Fig. 1.

The serrated trailing edge investigated here has a root-to-tip amplitude of 2h and wavelength of

λ, as shown in Fig. 2. The non-dimensional edge spectrum for the serrated trailing edge is defined

as

Ψ(ω) =

(

1 +1

2ǫ∂

∂ǫ

)

f

(

ωδ

Uc,h

λ,h

δ; ǫ

)

, (2)

where

f

(

ωδ

Uc,h

λ,h

δ; ǫ

)

=1

AB + ǫ2

(

1 +64(h/λ)3(δ/h)

(

cosh(C√A+ ǫ2)− cos(2ωh/Uc)

)

(√A+ ǫ2)(AB + ǫ2) sinh(C

√A+ ǫ2)

)

, (3)

A = (ωδ/Uc)2, B = 1+ (4h/λ)2, C = λ/2δ and ǫ = 1.33. For the case when h → 0, Eqs. (2) and (3)

reduce to the following non-dimensional edge spectrum for an unserrated trailing edge

Ψ(ω) =A

(A+ ǫ2)2. (4)

4

According to Howe’s [6] theory, when the acoustic frequency is high such that ωh/U∞ >> 1,

the theoretical maximum reduction in radiated mean square pressure is proportional to 10 log10[1+

(4h/λ)2] for serrations with a sawtooth profile. The largest noise reductions occur when the dimen-

sions of the serrations are of the order of the turbulent boundary layer thickness and when the angle

between the mean flow and the local tangent to the wetted surface is less than 45◦. This suggests

that sharper serrations with a smaller wavelength to amplitude ratio, λ/h, will result in greater

noise reduction.

x

z

y

Trailing edge

Plate

Observer x

Fig. 1 Flat plate co-ordinate system.

Flow

2h

Tip of sawtooth

Root of sawtooth

Plate

Fig. 2 Sawtooth serrations at the trailing edge of a flat plate with root-to-tip amplitude of 2h

and wavelength of λ.

5

III. Experimental method

A. Anechoic wind tunnel facility

Experiments were performed in the anechoic wind tunnel at the University of Adelaide. The

anechoic wind tunnel test chamber is 1.4 m × 1.4 m × 1.6 m (internal dimensions) and has walls

that are acoustically treated with foam wedges to approximate a free environment at frequencies

above 250 Hz. The facility contains a contraction outlet that is rectangular in cross-section with

dimensions of 75 mm x 275 mm. The maximum flow velocity of the free jet is ∼ 40 m/s and the

free-stream turbulence intensity is 0.33% [22].

B. Test model

The flat plate model used in this study is composed of a main steel body and a detachable

trailing edge plate made from brushed aluminum, as shown in Fig. 3. The main body has a span of

450 mm and a thickness of 6 mm. The leading edge (LE) of the main body is elliptical with a semi-

major axis of 8 mm and a semi-minor axis of 3 mm while the trailing edge (TE) is asymmetrically

bevelled at an angle of 12◦. Three 0.5 mm thick trailing edge plates were used (one at a time):

one with a straight, unserrated configuration and two with serrations. The flat plate model with

the straight unserrated trailing edge is used as the reference configuration for all tests and so will

be referred to as the reference plate hereafter. Two different serration geometries are compared

in this study, both with root-to-tip amplitude of 2h = 30 mm: one with a wavelength of λ = 3

mm (λ/h = 0.2, termed narrow serrations) and the other with λ = 9 mm (λ/h = 0.6, termed wide

serrations). The root of the serrations is aligned with the trailing edge of the main body so that only

the serrated component of the trailing edge plate is exposed to the flow. The area of the reference

plate is equivalent to that of the flat plate with serrated trailing edges giving the same effective

wetted surface area in all three test cases. The serrated and reference plate models all have the

same mean chord of 165 mm.

The trailing edge plate is fastened to the main body with 24 M2 × 0.4 screws. These screws

protruded slightly (< 0.4 mm) into the flow below the lower flat surface of the plate model; however,

this was consistent for all three plate configurations. Hot-wire measurements within the boundary

6

3 mm

8 mm

LE

TE

0.5 mm

12

Main body

Trailing edge plate

Fig. 3 Schematic diagram of the flat plate model.

layer on the lower flat surface of the plate downstream of the screws confirmed that any flow

disturbances created at the screws dissipated well before the trailing edge. The method of trailing

edge attachment used in this study avoids bluntness at the root of the serrations that may produce

vortex shedding and a tonal noise component. The flat plate model was held between two side plates

and attached to the contraction at zero angle of attack as shown in Fig. 4. The span of the flat

plate models extends beyond the width of the contraction outlet to eliminate the noise produced by

the interaction of the side plate boundary layers with the model leading edge.

In a previous study by the authors [23], the noise produced by two different reference plate

models (with straight trailing edge) were compared. One plate had a span equal to the width of

the contraction outlet (275 mm) and was held between two side plates that were aligned with the

contraction edges. The second plate had a span of 450 mm as shown in Fig. 4. The noise radiated

by the two plates was found to be highly comparable over the entire frequency range of interest

(250 Hz - 10 kHz) indicating that the dominant source of noise is turbulent boundary layer trailing

edge noise. It is also worth mentioning that in another study [22], the authors have experimentally

analyzed the cross-correlation of noise measured above the leading and trailing edges of the reference

plate at U∞ = 15 − 38 m/s to show that trailing edge noise significantly dominates the radiated

sound field over the noise produced at the leading edge.

C. Measurement techniques

Unless otherwise stated, acoustic measurements were recorded at a single observer location using

a B&K 1/2" microphone (Model No. 4190) located 554 mm directly below the trailing edge of the

7

Fig. 4 The flat plate model with wide trailing edge serrations held between the side plates

and attached to the contraction outlet.

reference plate. The accuracy in the microphone sound pressure level is ±1 dB based on its free field

response (as stated in the transducer documentation). Hot-wire anemometry was used to obtain

unsteady velocity data in the wake of the serrated and reference plate models. A TSI 1210-T1.5

single wire probe with wire length of L = 1.27 mm and a wire diameter of d = 3.81 µm was used in

experiments. The sensor was connected to a TSI IFA300 constant temperature anemometer system

and positioned using a Dantec automatic traverse with 6.25 µm positional accuracy. The traverse

allowed continuous movement in the streamwise (x), spanwise (y) and vertical (z) directions. The

co-ordinate system used in this study is shown in Fig. 1. The origin of the co-ordinate system is

located at the centre of the trailing edge of the reference plate.

Experiments were conducted at zero angle of attack and at free-stream velocities between

U∞ = 15 and 38 m/s corresponding to Reynolds numbers, Rec = 1.6 × 105 and 4.2 × 105, respec-

tively. Acoustic and flow data were recorded for each flat plate model using a National Instruments

PCI-4472 board at a sampling frequency of 5 × 104 Hz for a sample time of 8 s and 4 s, respec-

tively. Data are presented in either one-third-octave band or narrowband format with a frequency

resolution of 8 Hz. Narrowband spectra have been calculated using Welch’s averaged modified

periodogram method of spectral estimation with a Hamming window function and 75% overlap.

8

According to Bendat and Piersol [24], the 95% confidence interval on the narrowband autospectral

density is therefore -0.74/+0.81 dB/Hz for the acoustic measurements and 10−0.1/100.1 m2/s for

the velocity measurements. One-third-octave band spectra have been calculated using a filter bank

from time series data. Mean velocity profiles at the flat plate trailing edge are also presented and

the uncertainty in the mean velocity is less than 7% for a 95% confidence interval [24].

IV. Experimental results

A. Acoustic data

1. Reference plate acoustic spectra

The far-field acoustic spectra for the reference plate with a straight trailing edge at free-stream

velocities between U∞ = 15 and 38 m/s are shown in Fig. 5. This figure shows a clear trend with

broadband noise levels decreasing for a reduction in flow velocity. This is particularly evident at

lower frequencies (< 1 kHz) where high noise levels are measured. In addition, a broad peak is

observed in the noise spectra at high frequencies (at 8.5 kHz for U∞ = 38 m/s) and this peak

reduces in frequency and amplitude with decreasing flow speed.

Frequency, kHz

Spe

ctra

l den

sity

, dB

re

(20

µPa)

2 /H

z

0.3 1 100

20

40

60

8038 m/s35 m/s30 m/s25 m/s20 m/s15 m/s

Fig. 5 Far-field acoustic spectra for the reference plate with a straight trailing edge at flow

speeds of U∞ = 15− 38 m/s.

The high frequency peak observed in the reference plate noise spectra in Fig. 5 is attributed

to vortex shedding from the trailing edge. According to Blake [1], narrowband blunt trailing edge

vortex shedding noise is negligible if the trailing edge is sufficiently sharp such that the bluntness

9

parameter t/δ∗ < 0.3 where t is the thickness of the trailing edge and δ∗ is the boundary layer

displacement thickness. While the boundary layer properties have not been directly measured at all

flow speeds in this study, they can be approximated using the expressions for a turbulent boundary

layer at zero pressure gradient on a flat plate as follows [25]

δ = 8δ∗, (5)

and

δ

c=

0.37

Re1/5c

, (6)

where δ is the boundary layer thickness and c is the plate chord. Table 1 shows the flat plate

boundary layer properties and bluntness parameter calculated using Eqns. (5) and (6) at flow speeds

between U∞ = 15 and 38 m/s. The mean velocity profile for the reference plate at U∞ = 38 m/s is

presented later in Section IV B 2 and shows good agreement with the estimated boundary properties

given in this table. As stated in Table 1, the bluntness parameter t/δ∗ > 0.3 for all free-stream

velocities between U∞ = 15 and 38 m/s indicating that narrowband noise contributions due to blunt

trailing edge vortex shedding can be expected.

The centre frequency, fc, of the vortex shedding peak in the noise spectra (see Fig. 5) and the

associated Strouhal number based on trailing edge thickness, Stt = fct/U∞, are also given in Table

1. Between U∞ = 15 and 38 m/s, the vortex shedding peak occurs at a Strouhal number of between

0.08 and 0.11. This is in agreement with the findings of Herr and Dobrzynski [26] who also reported

flat plate blunt trailing edge vortex shedding noise to occur at Stt ≈ 0.1.

2. Noise reduction achieved with trailing edge serrations

Figure 6 shows the narrowband far-field acoustic spectra for the reference plate and the two

plates with trailing edge serrations at free stream velocities of U∞ = 15 and 38 m/s. The background

noise spectra are also shown in these figures for comparison. Figure 6 shows that both serration

geometries reduce the high frequency trailing edge vortex shedding noise component. Reductions of

up to 13 dB are achieved at frequencies where trailing edge vortex shedding noise is dominant.

For clearer comparison, Figs. 7 and 8 show one-third-octave band spectra for the reference plate

10

Table 1 Flat plate boundary layer properties and centre frequency, fc, and Strouhal number,

Stt, of the trailing edge vortex shedding noise peak for U∞ = 15− 38 m/s.

U∞, m/s δ, mm δ∗, mm t/δ∗ fc, Hz Stt = fct/U∞

38 4.7 0.53 0.84 8540 0.11

35 4.8 0.60 0.82 7750 0.11

30 5.0 0.62 0.80 6680 0.11

25 5.2 0.64 0.77 4900 0.10

20 5.4 0.67 0.74 3980 0.10

15 5.7 0.71 0.70 2530 0.08

Frequency, kHz

Spe

ctra

l den

sity

, dB

re

(20

µPa)

2 /H

z

0.3 1 100

20

40

60

80ReferenceNarrow serrationsWide serrationsBackground

(a)

Frequency, kHz

Spe

ctra

l den

sity

, dB

re

(20

µPa)

2 /H

z

0.3 1 100

20

40

60

80ReferenceNarrow serrationsWide serrationsBackground

(b)

Fig. 6 Far field acoustic spectra for the reference plate and the plates with trailing edge

serrations compared to background noise levels at U∞ of (a) 38 and (b) 15 m/s.

and the flat plate with trailing edge serrations at flow speeds between U∞ = 15 and 38 m/s. In

Figs. 7 and 8, the one-third-octave band spectra have been normalised according to

Lp1/3norm = Lp1/3 − 50 log10(M)− 10 log10(δb/r2), (7)

where Lp1/3 is the far-field acoustic spectra in one-third-octave bands, M is free-stream Mach

number, δ is the boundary layer thickness given in Table 1, b is the length of the wetted span and r

is the radial distance from the reference plate trailing edge to the observer location. The normalised

one-third-octave band spectra in Figs. 7 and 8 are plotted against Strouhal number based on trailing

edge boundary layer thickness, Stδ = fδ/U∞.

11

The one-third-octave band spectra at all flow speeds in Fig. 7 show that the narrow serrations

slightly reduce broadband noise levels by up to 2.5 dB at low frequencies (R1). In the mid-frequency

range, a minor noise increase of up to 3 dB is observed with narrow serrations (R2). In the high

frequency region, narrow serrations produce a significant noise reduction of up to 10 dB in the

trailing edge vortex shedding noise component (R3).

The one-third-octave band spectra for the reference plate and the flat plate with wide serrations

are shown in Fig. 8. This figure shows that at all flow speeds between U∞ = 15 and 38 m/s, the

wide serrations attenuate broadband noise levels by up to 3 dB at low frequencies (R1). In the

mid frequency range, wide serrations have little affect on the radiated noise with the noise levels

of the reference plate and the flat plate with wide serrations being approximately equal (R4). At

high frequencies, the wide serrations significantly attenuate the trailing edge vortex shedding noise

component by up to 10 dB (R3).

For both serration geometries in Figs. 7 and 8, the regions of noise attenuation (R1 and R3)

reduce in frequency and amplitude with decreasing flow speed. Comparing Figs. 7 and 8 shows that

wide serrations outperform the narrow ones by achieving higher levels of low frequency attenuation

over a larger frequency range and no noise increase in the mid frequency region.

12

R1 R2 R3

Stδ

Lp1/

3 no

rm, d

B r

e 20

µP

a

0.1 1110

120

130

140

150ReferenceNarrow serrations

(a)

R1 R2 R3

Stδ

Lp1/

3 no

rm, d

B r

e 20

µP

a

0.1 1110

120

130

140


(b)

R1 R2 R3

Stδ

Lp1/

3 no

rm, d

B r

e 20

µP

a

0.1 1110

120

130

140


(c)

R1 R2 R3

Stδ

Lp1/

3 no

rm, d

B r

e 20

µP

a

0.1 1110

120

130

140


(d)

R1 R2 R3

Stδ

Lp1/

3 no

rm, d

B r

e 20

µP

a

0.1 1110

120

130

140


(e)

R1 R2 R3

Stδ

Lp1/

3 no

rm, d

B r

e 20

µP

a

0.1 1110

120

130

140


(f)

Fig. 7 Normalised one-third-octave band spectra for the reference plate and the plate with

narrow serrations at U∞ of (a) 38, (b) 35, (c) 30, (d) 25, (e) 20 and (f) 15 m/s. R1: region

of noise reduction, R2: region of noise increase, R3: region of noise reduction in the blunt

trailing edge vortex shedding component and R4: region of equivalent noise levels.

13

R1 R4 R3

Stδ

Lp1/

3 no

rm, d

B r

e 20

µP

a

0.1 1110

120

130

140

150ReferenceWide serrations

(a)

R1 R4 R3

Stδ

Lp1/

3 no

rm, d

B r

e 20

µP

a

0.1 1110

120

130

140


(b)

R1 R4 R3

Stδ

Lp1/

3 no

rm, d

B r

e 20

µP

a

0.1 1110

120

130

140


(c)

R1 R4 R3

Stδ

Lp1/

3 no

rm, d

B r

e 20

µP

a

0.1 1110

120

130

140


(d)

R1 R4 R3

Stδ

Lp1/

3 no

rm, d

B r

e 20

µP

a

0.1 1110

120

130

140


(e)

R1 R4 R3

Stδ

Lp1/

3 no

rm, d

B r

e 20

µP

a

0.1 1110

120

130

140


(f)

Fig. 8 Normalised one-third-octave band spectra for the reference plate and the plate with

wide serrations at U∞ of (a) 38, (b) 35, (c) 30, (d) 25, (e) 20 and (f) 15 m/s. R1: region

of noise reduction, R2: region of noise increase, R3: region of noise reduction in the blunt

trailing edge vortex shedding component and R4: region of equivalent noise levels.

14

3. Variation in noise reduction with Strouhal number

Figure 9 shows 2D surface plots of the measured attenuation achieved with the trailing edge

serrations at flow speeds between U∞ = 15 and 38 m/s. The attenuation in these figures has been

calculated by dividing the power spectral density of the serrated plates by that of the reference plate.

Three separate regions of noise reduction are identifiable in the attenuation maps in Fig. 9 and each

of these regions is bounded by a constant Strouhal number based on boundary layer thickness at

the trailing edge, δ. For narrow serrations in Fig. 9 (a):

• Stδ < 0.13 : Region of noise attenuation (R1).

• 0.13 < Stδ < 0.7 : Region of noise increase (R2).

• 0.7 < Stδ < 1.4 : Region of attenuation in the blunt trailing edge vortex shedding noise

component (R3).

For wide serrations in Fig. 9 (b):

• Stδ < 0.2 : Region of noise attenuation (R1).

• 0.2 < Stδ < 0.7 : Region of equivalent noise levels (R4).

• 0.7 < Stδ < 1.4 : Region of attenuation in the blunt trailing edge vortex shedding noise

component (R3).

In their experiments on a NACA 651-210 airfoil with trailing edge serrations, Gruber et al.

[17] found that for a range of serration geometries (λ/h = 0.1 − 0.6) the frequency delimiting a

noise reduction and a noise increase followed a constant Strouhal number dependency of Stδ = 1.

This Strouhal number scaling does not describe the trends observed in the flat plate data in Fig. 9.

Discrepancies in the Strouhal number scaling are attributed to significant differences in the geometry

of the airfoil used in the study of Gruber et al. [17] and the flat plate studied here.

4. Noise directivity

Figure 10 shows the sound pressure level directivity pattern for the reference plate and the

plates with trailing edge serrations at three selected one-third octave band centre frequencies at

15

(a) (b)

Fig. 9 Noise reduction achieved with (a) narrow serrations and (b) wide serrations at U∞ =

15 − 38 m/s. Dashed lines are lines of constant Strouhal number, Stδ. R1: region of noise

reduction, R2: region of noise increase, R3: region of noise reduction in the blunt trailing

edge vortex shedding component and R4: region of equivalent noise levels.

U∞ = 38 m/s. To obtain these measurements, the microphone was fastened to the traverse arm and

the traverse was then used to position the microphone at a number of locations on an arc at a radial

distance of 300 mm from the trailing edge of the reference plate. The measurements in Fig. 10 have

been corrected to account for shear layer refraction [27].

At the one-third-octave band centre frequency of 0.4 kHz, Fig. 10 (a) shows that both serration

geometries slightly reduce the noise levels of the reference plate (region R1 in Figs. 7 (a) and 8 (a))

at all angular locations, with the wide serrations outperforming the narrow ones. In Fig. 10 (b)

at 2 kHz, the wide serrations produce equivalent noise levels to the reference plate (region R4 in

Fig. 8 (a)) while a noise increase is observed with the narrow serrations (region R2 in Fig. 7 (a)) at

all angular locations. At 8 kHz in Fig. 10 (c), both serration geometries significantly attenuate the

trailing edge vortex shedding noise component (region R3 in Figs. 7 (a) and 8 (a)) at all angular

locations.

Figure 10 shows that the trailing edge serrations do not significantly modify the directivity of

the radiated trailing edge noise and that their effect on the radiated noise is independent of observer

position. This was found to be the case at all one-third-octave band frequencies, whether a noise

reduction occurred or not.

16

180°

210°

240° 270°

300°

330°

0°

40

60

80

ReferenceNarrow serrationsWide serrations

(a)

180°

210°

240° 270°

300°

330°

0°

40

60

80


(b)

180°

210°

240° 270°

300°

330°

0°

40

60

80


(c)

Fig. 10 Trailing edge noise directivity pattern for the reference plate and the plates with

trailing edge serrations for U∞ = 38 m/s at one-third-octave band centre frequencies of (a)

0.4, (b) 2 and (c) 8 kHz. Dashed circular contours denote the sound pressure level in dB.

Note that the origin is 20 dB. An angular position of 180◦ relates to a position upstream of

the trailing edge at x = −300 mm, y = 0, z = 0, 270◦ relates to a position directly below the

trailing edge at x = 0, y = 0, z = −300 mm and 0◦ relates to a position downstream of the

trailing edge at x = 300 mm, y = 0, z = 0.

5. Comparison with theory

Figure 11 shows 2D surface plots of the noise reduction predicted with Howe’s [6] theory as

presented in Section II for the two different serration geometries used in this study. The predicted

attenuation in Fig. 11 has been calculated by dividing the edge spectra of the serrated plates (Eqs. (2)

and (3)) with that of the reference plate (Eq. (4)). The oscillations in the theoretical noise reduction

map for narrow serrations in Fig. 11 (a) are due to interference between acoustic radiation produced

at the root and the tip of the serrations.

17

(a) (b)

Fig. 11 Noise reduction for (a) the narrow serrations and (b) the wide serrations predicted

with the theory of Howe [6] at U∞ = 15− 38 m/s. Note the differing colorbar scales.

The experimental measurements in Fig. 9 do not agree with Howe’s theory (Fig. 11) in terms of

absolute noise levels or in terms of the variation in noise reduction with flow velocity and frequency.

Compared with measured attenuation levels, the theoretical noise reduction predictions are much

higher and occur over a much larger frequency range at all flow velocities considered in this study.

In addition, some attenuation is measured at low frequencies contrary to Howe’s model that predicts

noise reductions to occur only at high frequencies (ωh/U∞ >> 1). This is however, in agreement

with a number of other experimental studies that have found trailing edge serrations to attenuate

low frequency airfoil self-noise [13, 14, 16, 17].

According to Howe [6], the serration geometry determines the magnitude of the noise reduction.

The theoretical maximum attenuation in the radiated mean square pressure (in dB) is 10 log10(1 +

(4h/λ)2) for serrations with a sawtooth profile. The noise reduction is therefore expected to increase

as λ/h decreases. For the narrow serrations with λ = 3 mm, the maximum attenuation is predicted

to be 26 dB while for the wide serrations with λ = 9 mm, the maximum theoretical attenuation is

17 dB. As shown in Fig. 11, narrow serrations are predicted to clearly outperform wide serrations in

terms of the level of attenuation achieved at all frequencies and flow speeds. In this study however,

wide serrations were found to achieve higher attenuation levels than narrow serrations which actually

cause a slight noise increase in the mid frequency range (see Figs. 7 - 9). While contrary to Howe’s

[6] theory, this does agree with the experimental findings of Chong et al. [18, 19] who found wider

18

serrations to be the more effective in reducing tonal instability noise at low Reynolds numbers.

B. Velocity data

As the turbulent flow field about the trailing edge is the source of trailing edge noise, velocity

measurements in the near wake of the straight and serrated trailing edges are examined in this

section to gain insight into the mechanism by which serrations affect noise production. While

velocity measurements are presented at the selected flow speed of U∞ = 38 m/s only, measurements

at all other flow speeds follow the same trend.

1. Mean velocity profiles

Figure 12 shows the variation in mean velocity (U/U∞) measured in the vertical (z) direction

with downstream (x) distance for the reference plate and the two plates with trailing edge serrations

at U∞ = 38 m/s. As shown in this figure, the mean velocity profiles for the three trailing edge

geometries differ significantly indicating that trailing edge serrations alter the flow structure in the

near wake. Greater wake flow deflection is observed for the serrated trailing edges compared to the

reference plate and this deflection increases with decreasing serration wavelength.

According to Michel’s criteria [25], transition from laminar to turbulent flow occurs when the

Reynolds number based on momentum thickness, Reθ, exceeds a value of

Reθtr = 1.174

(

1 +22400

Rec

)

Re0.46c , (8)

where Rec is Reynolds number evaluated at distance c. For all three plates, the profiles measured

1 mm downstream of the trailing edge (at x/c = 0.006 for the reference plate and x/c = 0.1 for

the plates with trailing edge serrations) satisfy Michel’s criteria of Reθ > Reθtr. Additionally, the

profiles all have a shape factor of H = 1.2 - 1.4 above and below the trailing edge indicating that

the trailing edge flow is well developed and turbulent on both surfaces of all three plates.

2. Velocity spectra

Figures 13 and 14 show spectral maps of the fluctuating velocity (u′2/Hz) measured in the

spanwise (y) and vertical (z) directions in the near wake of the plate with straight and serrated

19

−0.04 −0.02 0 0.02 0.04

0.4

0.5

0.6

0.7

0.8

0.9

1

z/cU

/U∞

0.0060.100.120.150.21

(a)

−0.04 −0.02 0 0.02 0.040.5

0.6

0.7

0.8

0.9

1

z/c

U/U

∞

0.100.120.150.21

(b)

−0.04 −0.02 0 0.02 0.04

0.5

0.6

0.7

0.8

0.9

1

z/c

U/U

∞

0.100.120.150.21

(c)

Fig. 12 Normalised mean velocity profiles in the wake measured in the vertical (z) direction

at various downstream (x/c) locations at U∞ = 38 m/s for (a) the reference plate, (b) the plate

with narrow serrations and (c) the plate with wide serrations. The profiles in (b) and (c)

have been measured in line with the peak of a serrated tooth.

trailing edges at U∞ = 38 m/s. In these figures, the velocity spectral maps are plotted against

Strouhal number based on width of the wake, Stlw, where the width of the wake, lw, for each

plate has been calculated from the velocity profiles in Fig. 12. A small ridge can be seen in all

velocity spectral maps at approximately Stlw ≈ 2. This is due to a slight dip or “notch” in the hot-

wire anemometer frequency response which does not affect the conclusions drawn from the velocity

measurements.

The spectra for all three plates in Figs. 13 and 14 show high energy levels at low frequencies.

20

This corresponds to the high levels of low frequency trailing edge noise measured in the far-field at

U∞ = 38 m/s (see Fig. 6 (a)). The high levels of low frequency energy are likely due to eddies or

convected flow perturbations in the boundary layer as it negotiates the adverse pressure gradient on

the top beveled surface of the plate. This is evidenced by the spectral maps in Fig. 14 which shows

slightly higher energy levels on the top surface of the plates near the trailing edge than in the region

below the trailing edge.

(a)

(b) (c)

Fig. 13 Velocity spectral maps in the wake measured in the spanwise (y) direction from

centre span at z/c = 0 at U∞ = 38 m/s for (a) the reference plate, (b) the plate with narrow

serrations and (c) the plate with wide serrations. The spectral map in (a) has been measured

at a position of x/c = 0.006 which corresponds to 1 mm downstream from the trailing edge of

the reference plate. The spectral maps in (b) and (c) have been measured at x/c = 0.1 which

corresponds to 1 mm downstream from the serrated trailing edge and a position of y/c = 0

corresponds to the peak of a serrated tooth.

21

(a)

(b) (c)

Fig. 14 Velocity spectral maps in the wake measured in the vertical (z) direction at centre

span at U∞ = 38 m/s for (a) the reference plate, (b) the plate with narrow serrations and (c)

the plate with wide serrations. The spectral map in (a) has been measured at a position of

x/c = 0.006 which corresponds to 1 mm downstream from the trailing edge of the reference

plate. The spectral maps in (b) and (c) have been measured at x/c = 0.1 which corresponds to

1 mm downstream from the serrated trailing edge, in line with the peak of a serrated tooth.

The spectral maps measured in the spanwise direction in the near wake of the two plates with

serrated trailing edges in Figs. 13 (b) and (c) show features that occur due to flow interaction with

the serrations. Higher levels of turbulent energy are measured at locations that correspond to the

tip of a serrated tooth. This is to be expected as the measurement locations are physically closer

to the model at the tip of a serrated tooth, thus are closer to an attached boundary layer and its

more energetic, small scale turbulence, compared with measurements taken in the space between

two serrated teeth, where the probe is relatively far away from the attached boundary layer and can

22

be considered to be in a wake. Figure 13 shows that the trailing edge serrations affect the flow field

in the vicinity of the trailing edge which is the source of the trailing edge noise in Fig. 6 (a).

The spectral maps for the reference plate in Figs. 13 (a) and 14 (a) support the theory that

vortex shedding at the trailing edge is the source of the broad high frequency peak in the reference

plate noise spectra (see Fig. 5). High energy velocity fluctuations at frequencies corresponding to

those of the broad peak in the reference plate noise measurements are observed along the span and

close to the trailing edge of the reference plate in Figs. 13 (a) and 14 (a) respectively. These high

energy velocity fluctuations are however, not observed in the spectral maps for the flat plate with

serrated trailing edges (see Figs. 13 (b) and (c) and 14 (b) and (c)). This agrees with the noise

spectra in Fig. 6 (a) which shows that serrations attenuate the vortex shedding noise component.

The vertical spectral map for the plate with narrow serrations in Fig. 14 (b) shows higher energy

turbulent fluctuations at mid frequencies (Stlw = 0.16 − 1.6 corresponding to 600 Hz - 6 kHz) on

the top surface of the plate at the trailing edge compared to the reference plate. This corresponds

to noise measurements in Fig. 7 (a) which shows the narrow serrations increase noise in the mid

frequency region. The spectral map for the wide serrations does not display these high energy

mid frequency fluctuations (see Fig. 14 (c)) and correspondingly, no mid frequency noise increase is

observed for this trailing edge geometry (see Fig. 8 (a)).

The velocity measurements in Figs. 12 - 14 show that trailing edge serrations alter the behaviour

of the flow field about the trailing edge and this directly affects noise production. As stated earlier,

Howe’s [6] serration noise reduction model was derived assuming that the surface pressure frequency

spectrum close to the trailing edge is unchanged by the presence of trailing edge serrations. As the

surface pressure spectrum at the trailing edge is driven by the velocity field, the near wake velocity

measurements in Figs. 13 and 14 indicate that the pressure frequency spectrum close to the trailing

edge will be altered by the presence of trailing edge serrations. This helps explain the considerable

theoretical over-prediction of noise reduction observed in this and many other experimental studies

[13, 14, 16, 17]. The results suggest that for this particular configuration (Reynolds number range

and serration and test model geometry), the effect of serrations on noise production is dominated by

changes in the hydrodynamic field rather than changes in the diffraction properties of the trailing

23

edge.

V. Conclusion

This paper has presented results of an experimental investigation of the acoustic and aero-

dynamic effects of trailing edge serrations on a flat plate at low-to-moderate Reynolds number.

Trailing edge serrations were found to minimise broadband noise levels at low frequencies (by up

to 3 dB at the reference measurement location) and achieve significant attenuation (of up to 13 dB

at the reference measurement location) of blunt vortex shedding noise at high frequencies without

modifying the directivity of the radiated noise. The noise reduction achieved with trailing edge

serrations was found to depend on Strouhal number, Stδ = fδ/U∞, and serration wavelength.

Theoretical predictions of the noise reductions using the theory of Howe [6] were in poor agree-

ment with experimental data. Contrary to theory, wide serrations with larger wavelength to ampli-

tude ratio, λ/h, were found to outperform narrow ones by achieving higher attenuation levels and

no noise increase in the mid frequency region.

Unsteady velocity data in the very near wake of the straight and serrated trailing edges suggested

that for this particular configuration, the noise reduction capability of trailing edge serrations is

related to their influence on the hydrodynamic field at the source location rather than on a reduction

in sound radiation efficiency at the trailing edge. Hence the assumption that serrations don’t affect

the turbulence field [6] appears to be invalid and explains the considerable differences observed

between experimental measurements and theoretical predictions.

Acknowledgments

This work has been supported by the Australian Research Council under grant DP1094015 ‘The

mechanics of quiet airfoils’.

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