Clifford A. Brown and James Bridges

Glenn Research Center, Cleveland, Ohio

Acoustic Efficiency of Azimuthal Modes

in Jet Noise Using Chevron Nozzles

NASA/TM—2006-214364

December 2006

AIAA–2006–2654
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Cambridge, Massachusetts, May 8–10, 2006

Clifford A. Brown and James Bridges

Glenn Research Center, Cleveland, Ohio

Acoustic Efficiency of Azimuthal Modes

in Jet Noise Using Chevron Nozzles

NASA/TM—2006-214364

December 2006

AIAA–2006–2654
Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

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Level of Review: This material has been technically reviewed by technical management.
NASA/TM—2006-214364 1 

Acoustic Efficiency of Azimuthal Modes in 

Jet Noise Using Chevron Nozzles 

Clifford A. Brown and James Bridges 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

The link between azimuthal modes in jet turbulence and in the acoustic sound field has been 

examined in cold, round jets. Chevron nozzles, however, impart an azimuthal structure on the jet with a 

shape dependent on the number, length and penetration angle of the chevrons. Two particular chevron 

nozzles, with 3 and 4 primary chevrons respectively, and a round baseline nozzle are compared at both 

cold and hot jet conditions to determine how chevrons impact the modal structure of the flow and how 

that change relates to the sound field. The results show that, although the chevrons have a large impact on 

the azimuthal shape of the mean axial velocity, the impact of chevrons on the azimuthal structure of the 

fluctuating axial velocity is small at the cold jet condition and smaller still at the hot jet condition. This is 

supported by results in the azimuthal structure of the sound field, which also shows little difference in 

between the two chevron nozzles and the baseline nozzle in the distribution of energy across the 

azimuthal modes measured. 

Motivation 

Historically, most concepts envisioned to reduce jet noise have not reduced the total acoustic power 

of the jet. Rather, these designs, if they do not increase the total noise, simply translate the acoustic power 

from one frequency to another, more advantageous, frequency or from one observer angle to another, less 

critical, observer angle. This illustrates the robust nature of noise generation by a jet and explains why the 

greatest success in noise reduction has been achieved by lowering the jet velocity while maintaining 

thrust by increased bypass ratio. Several studies have considered the production of jet noise using a modal 

decomposition of jet and its corresponding sound field. Michalke and Fuchs addressed the problem 

theoretically by expanding the source term from Lighthill’s equation, cast in cylindrical coordinates, in 

azimuthal angle as a Fourier series. The result showed that only the lowest order terms, corresponding to 

the lowest order azimuthal modes, are efficient producers of sound. Michalke and Fuchs also measured 

pressure correlations in the jet to support their theoretical finding and showed that the lowest terms 

dominate the turbulent source quantity in a low speed jet (ref. 1). Experimentally, by computing the 

Fourier coefficients of fluctuating jet pressure measurements near the jet shear layer, Armstrong et al.

showed that the lowest order modes dominate in the near field of the jet (ref. 2). While these results 

established the modal energy distribution in the near field turbulence, Juve et al. measured the modal 

content in the acoustic far field at three observation angles and showed the dominance of the lowest three 

azimuthal modes in this region (ref. 3). These experiments were all conducted on cold, round jets. Do 

these results hold for a non-round or a hot jet? 

Research shows that chevron nozzles reduce low frequency noise at aft angles while increasing high 

frequency noise at broadside angles relative to the jet (ref. 4). However, it will be shown that chevron 

nozzles also force flow energy into higher azimuthal modes than typically found, in significant strength, 

in a round nozzle. Examining both the near and far field azimuthal components from different chevron 

nozzles allows further analysis of the correlation between turbulent fluctuations and radiated sound as a 

function of azimuthal mode. If, for example, a chevron nozzle enhances the flow energy in mode m = 3, 

does that lead to a corresponding increase in mode m = 3 sound radiated to the far field or is m = 3 simply 

incapable of producing significantly more far field sound regardless of the flow energy it contains? Using 
NASA/TM—2006-214364 2 

particle image velocimetry (PIV) for near field flow measurements and an array of microphones located 

on a series of rings for mid-field acoustic measurements, this research further investigates the relationship 

between flow energy and sound production, using azimuthal modes, in round and chevron nozzles at hot 

and cold jet conditions. 

Test Hardware 

Jet Rig 

Tests were conducted on the Small Hot Jet Acoustic Rig (SHJAR) located in the AeroAcoustic 

Propulsion Laboratory (AAPL) at the NASA Glenn Research Center. The SHJAR uses remotely located 

compressors and a hydrogen burning combustor to provide heated air to single-flow nozzles at 

temperatures up to 1300 °F and at pressures up to 150 psi. Noise generated by flow through piping and 

control valves is removed using a baffled muffler and the flow is conditioned using screens to create clean 

and quiet conditions at the nozzle exit. Acoustic data repeatability has been determined to be within 

0.5 dB in one-third octave bands at all frequencies. The SHJAR is housed in the AAPL, a 60 ft radius 

geodesic dome lined with sound absorbing wedges creating an anechoic environment above 200 Hz. 

Further details about the SHJAR including documentation of rig noise, background noise, nozzle 

boundary layer measurements, baseline data set, and comparisons to other jet rigs may be found in 

references 5 and 6. 

Models 

A series of chevron nozzle extensions were developed to parametrically explore the impact of 

different chevron parameters (chevron number, penetration angle, and length) on jet noise. The design 

methodology for this nozzle set is described in reference 4. Nozzles tested range from a round baseline 

nozzle to a 10-chevron configuration with chevron penetration angles from 0° to 18.2°. All nozzles in this 

set had a 2-in. exit diameter (Dj). During the test, flow and acoustic data was not collected for all nozzles 

at all conditions. Two chevron nozzles, which produce three and four lobed flow cross section, and one 

round baseline nozzle are presented here. Pictures of these nozzles are shown in figure 1. The first 

chevron nozzle, designated FCC001, has three primary chevrons and a 5° penetration angle. The second 

chevron nozzle, designated FCC002, has four primary chevrons and a 5° penetration angle. The round 

baseline nozzle is designated SMC000. Both chevron nozzle incorporated serrated (“fractal”) edges, a 

feature which is not considered of primary importance here. 

Figure 1.—The three nozzles presented in this paper are FCC001 (left), SMC000

 baseline (middle), and FCC002 (right). FCC001 has three primary chevrons

 with smaller chevrons cut into the edges and FCC002 has four primary

 chevrons also with small chevrons cut into the edges. 
NASA/TM—2006-214364 3 

Data Acquisition and Processing 

Flow Measurements 

The three components of jet velocity (u, v, w) were measured using Stereoscopic Particle Image 

Velocimetry (PIV), in the cross-stream plane, at 12 locations along the jet axis. The jet flow was seeded 

with alumina particles (~0.5 m diameter) injected upstream of the combustor. The ambient air 

surrounding the nozzle was seeded using a commercial fog machine (oil drop ~0.2 m diameter). Light 

was supplied by dual-head Nd: YAG laser. Two 2048 by 2048 pixel cross-correlation cameras, ultimately 

giving a 215 by 160 mm field of view, were placed an angle to the light sheet to capture the three velocity 

components (u, v, w). A total of 200 image pairs were recorded at each point. Data processing, using code 

developed at NASA (ref. 7), was used to combine the images from each camera to create the 

instantaneous three-dimensional velocity maps yielding a final resolution of 1.58 mm (0.03Dj) in the 

cross-stream plane and 1.17 mm (0.02Dj) in the stream-wise plane. Outlying vectors were discarded using 

both hard velocity limits and Chauvenet’s criterion for data clean up. Further details on the PIV setup and 

procedure for calculating the instantaneous velocity maps are available in reference 8. 

Once the instantaneous velocity maps are obtained, turbulence statistics and modal energy are 

calculated. First, time averaged mean ( u ,v ,w ) and fluctuating ( u = u  u ,v = v  v ,w = w  w) 

components of the three velocity vectors are calculated for each instantaneous resolved vector. Next, to 

facilitate calculating azimuthal mode energy, the fluctuating axial velocity (w’) is mapped, using bilinear 

interpolation, from the native Cartesian coordinate system to a polar coordinate system, placing 125 

velocity vectors (equally spaced in azimuthal angle with = 0.05 radians  28.6°) on 64 constant radius 

rings (from 1 to 65 mm radius). Azimuthal modes were calculated using only the fluctuating axial 

velocity (w’), which as the largest velocity component approximates the turbulent kinetic energy. The 

power in each azimuthal mode is determined by computing the Fourier transform, in azimuthal angle at 

each radius, for each of the instantaneous velocity maps and ensemble averaging the results. This process 

is repeated for each measured plane. 

Acoustic Measurements 

Acoustic modes were measured using microphones placed on rings around the jet axis. The array, 

which was originally designed and used as a three-dimensional phased array, contained 80 microphones 

(Bruel & Kjaer 0.25 in. type 4939) on 15 rings. The microphones were evenly spaced in azimuthal angle 

on each ring with the first microphone offset 18° from the first microphone on the previous ring (fig. 2). 

The first 10 rings, nearest to the nozzle exit, had six microphones each while the remaining rings had four 

microphones each (table I). The ring radius started at 35 in. near the nozzle exit and expanded to 50 in. at 

the downstream most ring. This put the array in the jet mid-field (50 Dj was determined to be far field for 

this jet (ref. 6)). Data was recorded simultaneously on all channels, continuously sampled at 50 kHz 

(20 kHz bandwidth) for 20 sec using a DataMAX Instrumentation Recorder from R.C. Electronics. Bruel 

& Kjaer Nexus (type 2690) amplifiers provided signal conditioning and amplification. Jet and ambient 

conditions were recorded using the facility ESCORT computer system. 

TABLE I.—SETUP INFORMATION FOR THE 

MICROPHONE ARRAY USED TO ACQUIRE 

THE MODAL ACOUSTIC MEASUREMENTS. 

[Only the rings used to acquire the data 

presented are shown in the table.] 

Ring X, Radius, Nmics 1, 

3 0.00 35.0 6 36 

4 4.00 35.75 6 54 

9 24.75 39.5 6 24 

10 31.25 40.75 6 42 
NASA/TM—2006-214364 4 

Figure 2.—Microphone ring array. 

–3

Correlation

9

6

7

8

5

4

3

2

1

0

–1

–2

Correlation

10

8

6

4

2

0

–2

–4

Time, s

0.0000 0.0006 0.0002 0.0004 0.0008 0.0010

Figure 3.—Cross correlations used to determine the time offset between two rings near 90° relative to the jet

 axis (left) and near 125° relative to the jet axis (right) at an acoustic Mach 0.9, cold jet condition using the

 round baseline nozzle (SMC000). The axial spacing of the rings grows downstream leading to the increase

 in time offset at these locations.

Time, s

0.0000 0.0006 0.0002 0.0004 0.0008 0.0010

If data from only one ring is used to calculate the modal content of the sound field, the results will be 

limited to the lower order azimuthal modes (0, 1, and 2). Therefore, to determine the modal content of the 

sound field in the higher modes of interest, it is necessary to combine data from multiple rings. The 

azimuthal angle offset and close axial spacing between rings assists this combination, but using data from 

multiple rings does reduce the ability of the array to resolve high frequencies. To combine data from 

multiple rings, a cross correlation between microphones, at the nearest possible azimuthal angle on 

different rings, is used to get a time offset between the rings (fig. 3). This accounts for the different 

propagation lengths from the source to the microphones at different axial and radial positions. The 
NASA/TM—2006-214364 5 

–3.0

Phase angle, radians

3.0

1.5

2.0

2.5

1.0

0.5

0.0

–0.5

–1.0

–1.5

–2.0

–2.5

–3.0

Phase angle, radians

3.0

1.5

2.0

2.5

1.0

0.5

0.0

–0.5

–1.0

–1.5

–2.0

–2.5

Strouhal frequency, fD/U

0 3 1 2 4

Strouhal frequency, fD/U

0 3 1 2 4

Figure 4.—Cross spectrum phase angle from microphones located on rings near 90° relative to the jet axis

 (left) and at approximately 125° relative to the jet axis (right) for the round baseline nozzle (SMC000) and

 at an acoustic Mach number 0.9, cold jet condition. The high frequency limit of the array is determined at

 the point where the phase angle appears to become random. At 90° (left) this change occurs around

 Strouhal frequency 1.2 and at 125° (right) it occurs near Strouhal frequency 1.6. 

Array

frequency

limit

Array

frequency

limit

frequency limit of the array is determined at the frequency where the cross spectrum phase angle, between 

microphones on the different rings, becomes random, as opposed to varying smoothly. In order to resolve 

at least Strouhal frequency 1, only data from two rings could be combined, limiting the highest azimuthal 

mode that could be resolved to m = 5. Figure 4 shows cross spectrum phase angle plots for two ring 

locations, one near 90° and the other near 125° relative to the jet axis, for a cold, acoustic Mach 0.9 jet 

condition. The 90° plot shows a Strouhal frequency limit of 1.2 while the 125° data shows a Strouhal 

frequency limit of 1.6. 

Once the data from the rings is combined, the azimuthal modal distribution of the acoustic field is 

calculated. First, direct integration of the Fourier series, in azimuthal angle, at each point in time is 

calculated. The direct integration method is necessary due to the uneven spacing of the microphones in 

azimuthal angle. The results, which are time series data divided into spatial modes, are then processed 

using a standard fast Fourier transform routine in time. The result is modal spectra in space and time. 

Results 

Flow Analysis 

Steroscopic Particle Image Velocimetry (PIV) was employed to measure the three velocity 

components in a cold, acoustic Mach Ma = 0.9 jet using the SMC000, FCC001 and FCC002 nozzles and 

in a hot Ma=0.9, temperature ratio Ts,j/Ta = 2.70 jet using the SMC000 and FCC001. The time averaged 

axial velocity at 6 cross sectional planes for each case are shown in figure 5. The three lobes in the 

FCC001 plume and the four lobes in the FCC002 plume, created by the number of primary chevrons in 

each case, is clearly observable in the mean flow data. Note the distance of 1 to 2 jet diameters (Dj) 

required for the lobes to fully develop as it takes some distance for the vorticies generated by the chevrons 

to form and grow. Once developed, however, clear differences in the mean flow data are observed at 

location x/Dj = 2.0 and, although diminished by further mixing, exist out to the final plane at x/Dj = 15.0 

where the plume shape from the chevron nozzles approaches the baseline. The addition of heat to the 

FCC001 nozzle cases reduces the size and definition of the lobes, creating flow field that is similar to the 
NASA/TM—2006-214364 6 

Figure 5.—Mean axial velocity at 6 cross stream planes for the SMC000, FCC001, and FCC002 nozzles at a 

 acoustic Mach 0.9, cold jet condition (left) and for the SMC000 and FCC001 nozzles at an acoustic Mach 0.9, 

 temperature ratio Ts, j/Ta = 2.70 jet condition (right). 

x/Dj = 0.1 

SMC000 FCC001 SMC000 FCC001 FCC002 

x/Dj = 1.0 

x/Dj = 2.0 

x/Dj = 5.0 

x/Dj = 8.0 

x/Dj = 15.0 

W, m/s

0 40 80 120 160 200 240 280 

round SMC000 nozzle case at the downstream planes. While this examination of the axial mean flow 

gives an idea of the plume shape, the primary interest is in the behavior of the axial velocity fluctuations, 

which may differ from the behavior of the mean flow. 

The fluctuating component of axial velocity (w’) was used to analyze the azimuthal modes in the jet 

plume. The results (fig. 6 for cold flow, fig. 7 for hot flow) show several things. First, data from the round 

baseline SMC000 nozzle shows qualitative agreement with linear stability theory. Each azimuthal mode 

(above mode m = 0, which is reduced by subtraction of the mean flow) saturates closer to the nozzle exit 

and at lower amplitude compared to the previous mode. Data from the chevron nozzles in the cold flow 
NASA/TM—2006-214364 7 

130 

Mode power, dB 

135 

140 

145 

150 

155 

160 

165 

130 

Mode power, dB 

135 

140 

145 

150 

155 

160 

165 

m = 1 m = 2 

Mode 

m = 0 

Cold 

SMC000 

FCC001 

FCC002 

m = 3 m = 5 m = 4 

130 

Mode power, dB 

135 

140 

145 

150 

155 

160 

165 

130 

Mode power, dB 

135 

140 

145 

150 

155 

160 

165 

130 

10 15 20 0 5 10 15 20 0 5 10 15 20 

z/Dj z/Dj z/Dj

z/Dj z/Dj z/Dj

0 5 

0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Mode power, dB 

135 

140 

145 

150 

155 

160 

165 

130 

Mode power, dB 

135 

140 

145 

150 

155 

160 

165 

Figure 6.—Fluctuating axial velocity power (dB) in modes 0 to 5 at the nozzle lipline radius, as a function of 

 axial distance for the SMC000 (red), FCC001 (blue), and FCC002 (green) nozzles at a Ma = 0.9, cold jet. 

130 

Mode power, dB 

135 

140 

145 

150 

155 

160 

165 

130 

Mode power, dB 

135 

140 

145 

150 

155 

160 

165 

m = 1 m = 2 

Mode 

m = 0 

Ts, j/Ta = 2.70 

SMC000 

FCC001 

m = 3 m = 5 m = 4 

130 

Mode power, dB 

135 

140 

145 

150 

155 

160 

165 

130 

Mode power, dB 

135 

140 

145 

150 

155 

160 

165 

130 

10 15 20 0 5 10 15 20 0 5 10 15 20 

z/Dj z/Dj z/Dj

z/Dj z/Dj z/Dj

0 5 

0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Mode power, dB 

135 

140 

145 

150 

155 

160 

165 

130 

Mode power, dB 

135 

140 

145 

150 

155 

160 

165 

Figure 7.—Fluctuating axial velocity power (dB) in azimuthal modes 0 to 5 at the nozzle lipline radius from the 

 SMC000 (orange) and FCC001 (light blue) nozzles at a Ma = 0.9, Ts, j/Ta = 2.70 jet. 
NASA/TM—2006-214364 8 

185 

Mode power, dB 190 

195 

200 Mode 

m = 0 m = 3 m = 4 

135 

Mode power, dB 

140 

145 

150 

155 

160 

165 

185 

135 

z/Dj z/Dj z/Dj

0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Mode power, dB 

140 

145 

150 

155 

160 

165 

185 

180 180 

175 175 

170 170 

Figure 8.—Azimuthal mode power (dB) based on total axial velocity for the SMC000, FCC001, and FCC002 

 nozzle at Ma = 0.9, cold jet conditions. Azimuthal modes m = 0 (left, note change in y-axis range), m = 3 

 (middle), and m = 4 (right) are shown. Using total axial velocity for the azimuthal mode decomposition 

 shows the expected increase in the m = 3 data for the 3-chevron, FCC001 nozzle and in the m = 4 data 

 for the 4-chevron FCC002 nozzle. 

Cold 

SMC000 

FCC001 

FCC002 

cases shows each azimuthal mode peaking closer to the nozzle exit compared to the same mode from the 

baseline nozzle. This behavior is consistent with the increased mixing near the nozzle exit, generated by 

the chevrons, observed in the mean flow data. In the hot flow cases (fig. 7), shows the azimuthal modes 

from both the SMC000 baseline nozzle and from the FCC001 chevron nozzle peaking at approximately 

the same axial location. This indicates that the heat is playing the primary role in shortening the mixing 

region with the chevrons playing a secondary role. While these results are expected, several other 

observations were not predicted. 

The initial concept was that chevrons add energy to the unsteady azimuthal modes in the jet plume by 

generating vorticies that change with time. If this idea is correct the FCC001 chevron nozzle should 

produce an amplified azimuthal mode m = 3 and the FCC002 chevron nozzle should produce an 

amplified m = 4, corresponding to the number of primary chevrons on each nozzle respectively, compared 

to the baseline nozzle (SMC000). While observation of the mean flow planes supports this theory, 

figure 6 shows that chevrons only slightly change the amplitude of these azimuthal modes computed 

using fluctuating axial velocity. In fact, the greatest amplification occurs at azimuthal mode m = 2 in the 

3 chevron nozzle and at azimuthal mode m = 3 in the 4 chevron nozzle. This could be because these 

chevron nozzles use a chevron on chevron pattern that alters the azimuthal structure of the plume or 

because all chevrons are not generating fluctuations at the same instant leading to fewer vortices at any 

one time. Computing the modal decomposition using total axial velocity (fig. 8), however, shows the 

chevrons are generating the amplified modes initially expected. Thus, the chevrons do impart the 

expected azimuthal modes into the flow, but they work primarily on the mean flow component and have 

minimal affect on the fluctuating component. If this translates to the sound field, the azimuthal mode 

distribution of sound from the chevron nozzles should be similar to the baseline nozzle. 

Acoustic Analysis 

Previous analyses of azimuthal modes in round jets in the far field found that the lowest order modes 

are the most significant producers of sound (ref. 3). With the increased interest in chevron nozzles, data 

was analyzed to determine if this is also true for chevron nozzles, which by their nature alter the 

azimuthal shape of the jet. Acoustic far field and mid-field ring array data was collected from two 

chevron nozzles and one round baseline nozzle. While not pertaining directly to the azimuthal structure 

of the sound field, the far field data (fig. 9) provides the first point of consideration for the effect of the 

chevrons. It shows that these chevron nozzles increase noise levels at both the 90° and 125° angles 
NASA/TM—2006-214364 9 

1/3 octave spl, dB 

95 

90 

85 

80 

75 

70 

65 

60 

1/3 octave spl, dB 

95 

100 

90 

85 

80 

75 

70 

65 

60 

SMC000 

FCC001 

FCC002 

SMC000 

FCC001 

FCC002 

SMC000 

FCC001 

SMC000 

FCC001 

Figure 9.—Far field acoustic results for nozzles SMC000, FCC001, and FCC002 at a Ma = 0.9, cold jet condition 

 (top) and at a Ma = 0.9, Ts, j

/Ta = 2.70 jet condition (bottom) measured at 90° (left) and 125° (right) relative to 

 the jet axis. Data has been transformed to a lossless condition and scaled to a distance of 100* Dj. 

Strouhal frequency, fDj

/Uj

10–2 10–1 100 102 

Strouhal frequency, fDj/Uj

10–2 10–1 100 102 

102 103 104 105 

102 103 104 105 

Frequency, Hz 

Frequency, Hz 

1/3 octave spl, dB 

95 

90 

85 

80 

75 

70 

65 

60 

1/3 octave spl, dB 

95 

100 

90 

85 

80 

75 

70 

65 

60 

relative to the jet axis. The noise increase due to the chevrons is more in the cold jet condition compared 

to the hot jet condition, agreeing with the flow velocity analysis showing that chevrons are a secondary 

effect to heat. 

The modal structure of the sound field was calculated for azimuthal mode 0 to 5 for frequencies up to 

approximately Strouhal frequency 1.2, the limit of the azimuthal array. The results are presented in 

figures 10 and 11 for nozzles SMC000, FCC001, and FCC002 at the cold, Ma = 0.9 jet condition. 

Figure 10 shows data from the 90° array location where a very gradual increase in the frequency at the 

peak amplitude point is observed as azimuthal mode number increases. Also at the 90° array location, the 

lowest order azimuthal modes (m = 0,1) have the highest peak amplitudes, around Strouhal frequency 0.3, 

by at least 3 dB but, interestingly, azimuthal mode m = 2 has the lowest peak amplitude of the modes 

computed for all three nozzles at the 90° ring location. This is particularly of note in the FCC001 

3-chevron nozzle case where flow analysis showed the m = 2 azimuthal mode having the highest 

amplification further downstream. Azimuthal modes m = 4 and m = 5 have very similar peak amplitudes 

approximately 1 dB above the peak level in mode m = 2. The data presented at the 90° ring location for 
NASA/TM—2006-214364 10 PSD, dB spl

90

95

100

105

110

115

m = 1 m = 2

Mode

m = 0

SMC000

FCC001

FCC002

m = 3 m = 5 m = 4

90

PSD, dB spl

95

100

105

110

115

90

Strouhal frequency, fD/U

102 101 100

Strouhal frequency, fD/U

102 101 100

Strouhal frequency, fD/U

102 101 100

PSD, dB spl

95

100

105

110

115

PSD, dB spl

90

95

100

105

110

115

90

PSD, dB spl

95

100

105

110

115

90

PSD, dB spl

95

100

105

110

115

Strouhal frequency, fD/U

102 101 100

Strouhal frequency, fD/U

102 101 100

Strouhal frequency, fD/U

102 101 100

Figure 10.—Mode power spectral density at 90° relative to the jet axis for nozzles SMC000, FCC001, and

 FCC002 at a Ma = 0.9, cold jet condition. 

PSD, dB spl

90

95

100

105

110

115

m = 1 m = 2

Mode

m = 0

SMC000

FCC001

FCC002

m = 3 m = 5 m = 4

90

PSD, dB spl

95

100

105

110

115

90

Strouhal frequency, fD/U

102 101 100

Strouhal frequency, fD/U

102 101 100

Strouhal frequency, fD/U

102 101 100

PSD, dB spl

95

100

105

110

115

PSD, dB spl

90

95

100

105

110

115

90

PSD, dB spl

95

100

105

110

115

90

PSD, dB spl

95

100

105

110

115

Figure 11.—Mode power spectral density at 125° relative to the jet axis for the SMC000, FCC001, and

 FCC002 nozzles at a Ma = 0.9, cold jet condition. 

Strouhal frequency, fD/U

102 101 100

Strouhal frequency, fD/U

102 101 100

Strouhal frequency, fD/U

102 101 100
NASA/TM—2006-214364 11 

all modes shows very little difference between the two chevron nozzles, both only being shifted to higher 

amplitudes compared to the round baseline nozzle. Data from the 125° microphone ring (fig. 11) also 

shows the chevron nozzles having a higher peak amplitude compared to the baseline nozzle in azimuthal 

modes m = 1,2,3 but, unlike the 90° location, similar peak amplitudes at modes m = 0,4,5. The baseline 

still shows reduced noise at frequencies above the peak amplitude frequency. The other significant 

difference between the 90° and 125° locations is in azimuthal mode m = 2, which is greater than modes 

m = 3,4,5 leaving a steady decrease in amplitude as azimuthal mode increases. Data at the 125° ring 

location also shows little difference between the two chevron nozzles. 

Data recorded for the SMC000 and FCC001 nozzles at a Ma = 0.9, Ts,j/Ta = 2.70 jet condition is 

presented in figures 12 and 13. At this jet condition, the noise difference between the chevron nozzle 

(FCC001) and the baseline nozzle is reduced at all modes compared to data from the cold jet condition 

(figs. 10 and 11). This fits with both the flow analysis and the far field acoustic results that showed the 

round jet better approximates the hot chevron jet than at the cold jet condition. Also of note, the reduction 

in azimuthal mode m = 2 observed in the cold jet at the 90° location does not occur in the heated jet and 

azimuthal mode m = 5 is more amplified relative to the lower order modes m = 2,3,4. Nothing in the flow 

data analysis indicates why mode m = 5 should be amplified above the lower order modes. Azimuthal 

modes m = 0 and m = 1 continue to have amplitudes well above all higher modes with a Strouhal 

frequency at peak amplitude of 0.2 (m = 0) and 0.3 (m = 1), respectively. There is no shift in noise 

distribution between modes when comparing the chevron and baseline nozzles at the hot jet condition. 

Data collected by Juve et al. showed only the lowest order azimuthal modes are significant in the 

acoustic far field of a round jet (ref. 3). Data from the round baseline nozzle analyzed during this study 

from the SHJAR showed a more balanced distribution of energy across the lowest 3 to 4 azimuthal PSD, dB spl

85

90

95

100

105

110

m = 1 m = 2

Mode

m = 0

SMC000

FCC001

m = 3 m = 5 m = 4

85

PSD, dB spl

90

95

100

105

110

85

Strouhal frequency, fD/U

102 101 100

Strouhal frequency, fD/U

102 101 100

Strouhal frequency, fD/U

102 101 100

PSD, dB spl

90

95

100

105

110

PSD, dB spl

85

90

95

100

105

110

85

PSD, dB spl

90

95

100

105

110

85

PSD, dB spl

90

95

100

105

110

Strouhal frequency, fD/U

102 101 100

Strouhal frequency, fD/U

102 101 100

Strouhal frequency, fD/U

102 101 100

Figure 12.—Mode power spectral density for the SMC000 and FCC001 nozzles at a Ma = 0.9, Ts, j/Ta = 2.70

 jet condition measured at 90° relative to the jet axis. 
NASA/TM—2006-214364 12 PSD, dB spl

90

95

100

105

110

115

m = 1 m = 2

Mode

m = 0

SMC000

FCC001

m = 3 m = 5 m = 4

90

PSD, dB spl

95

100

105

110

115

90

Strouhal frequency, fD/U

102 101 100

Strouhal frequency, fD/U

102 101 100

Strouhal frequency, fD/U

102 101 100

PSD, dB spl

95

100

105

110

115

PSD, dB spl

90

95

100

105

110

115

90

PSD, dB spl

95

100

105

110

115

90

PSD, dB spl

95

100

105

110

115

Strouhal frequency, fD/U

102 101 100

Strouhal frequency, fD/U

102 101 100

Strouhal frequency, fD/U

102 101 100

Figure 13.—Mode power spectral density for the SMC000 and FCC001 nozzles at a Ma = 0.9, Ts, j/Ta = 2.70

 jet conditions measured at 125° relative to the jet axis. Normalized amplitude

Normalized amplitude

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Mode Mode

0 1 2 3 0 1 2 3

Juve et. el.iii

SHJAR

Juve et. el.iii

SHJAR

Figure 14.—Modal distribution of acoustic energy at Strouhal frequency 0.3, measured at 90° (left) and near

 120° (right) (125° for the SHJAR data) relative to the jet axis, for data from Juve et. el.iii and data acquired

 from SHJAR. 

modes. Figure 14 shows a comparison of the Juve data and the SHJAR data at Strouhal frequency 0.3 and 

at 90° and 120° relative to the jet axis (125° in the SHJAR data). At the 90° location, the data shows 

similar levels at azimuthal modes m = 0 and m = 1. The Juve data, however, shows significantly more 

energy in azimuthal mode m = 2 and almost no energy in azimuthal mode m = 3. At the 120° location the 

Juve data has similar levels in the lowest order azimuthal mode, m = 0. The far field data of Juve then 

shows approximately twice the energy in azimuthal modes m = 1 and m = 2 compared to the SHJAR data 

but considerably less energy in mode m = 3. The SHJAR data, therefore, shows that more azimuthal 
NASA/TM—2006-214364 13 

modes may be important producers of sound compared to the Juve data. There are, however, two primary 

differences in the tests that should be remembered when comparing these data sets. First, the Juve data set 

was measured in the far field of the jet (60 to 100 Dj) while the SHJAR data was acquired in the mid-field 

of the jet (approximately 20 Dj). Second, the Juve data was recorded at a Mach 0.4 jet condition with a 

2-cm nozzle diameter. The SHJAR data was acquired at a Mach 0.9 jet condition with a 2-in. nozzle 

diameter leading to a source that is much less compact compared to the Juve jet. 

Conclusions 

Theoretical and experimental studies on round nozzles, both in the near field and far field, has shown 

that the lowest order azimuthal modes dominate the jet. Chevron nozzles, by their very nature, change the 

cross-sectional shape of the jet and, therefore, should the azimuthal structure of plume turbulence. To 

investigate this idea, flow data previously acquired using Particle Image Velocimetry (PIV) in the crossstream plane and acoustic data acquired using a three-dimensional phased array was used to determine the 

modal structure of the turbulent flow and acoustic field for two chevron nozzles and one round baseline 

nozzle. This data set, due to the setup of the phased array, limited the scope to a maximum azimuthal 

mode of m = 5 and a maximum frequency of Strouhal frequency 1.2. 

The PIV data was examined first to quantify the effect of chevrons on the unsteady azimuthal 

structure of the jet. Data from the chevron nozzles then showed that, while the cross-sectional shape does 

change greatly with the number and penetration of the chevrons, the change exists primarily in the mean 

axial flow. When the mean flow is subtracted and power in the azimuthal modes is calculated using the 

fluctuating axial velocity, the modal energy distribution of the chevron nozzles begins to approach that of 

the round baseline nozzle. In the cold jet condition, the axial location of the peak amplitude is shifted 

upstream toward the nozzle exit by the chevrons and some amplifications occurs, though not in the 

azimuthal mode corresponding to the number of chevrons, but to the azimuthal mode one less than the 

number of primary chevrons (i.e., nozzle with 3-primary chevrons showed maximum amplification in 

mode m = 2 compared to the round jet). Data from the hot jet condition showed even smaller differences 

between the chevron and baseline nozzle, illustrating the strong role heat plays in the azimuthal shape of 

the jet. 

Once the flow analysis of the flow data was complete, data from the three-dimensional phased array 

was used to determine modal structure of the acoustic mid-field. Far field acoustic data indicated that the 

chevron nozzles produced more noise than the baseline nozzle at the angle measured with the azimuthal 

array so some increase in amplitude compared to the baseline nozzle was expected due to the chevrons. 

Of particular interest, however, was the distribution of energy between the modes. Data from the cold jet 

showed that, although there was an offset in amplitude when comparing the chevron nozzles to the 

baseline, the acoustic energy was distributed in the chevron nozzles in the same way as the round nozzle. 

In fact, nothing observed in the sound field tied the modal spectra to the number of chevrons. 

Additionally, as expected based on the flow data and far field acoustic data, the hot jet condition exhibited 

only small amplitude differences between the chevron and baseline nozzle. Comparisons to the far field 

data collected by Juve et al. showed significant differences in modal distributions and significant modes 

in the cold, round jet compared to the SHJAR data. These differences may be due to differences in the 

measurement array or in the compactness of the noise source. Finally, the modal decomposition showed 

data in modes m = 2 to m = 5 have similar amplitudes and are within approximately 3 dB of the amplitude 

found in modes m = 0 or m = 1. Thus, at least the first five azimuthal modes may be important in the 

acoustic mid-field of a cold jet. More decrease was found in between azimuthal modes in the acoustic 

mid-field at the hot jet condition. 

Although this study was limited by its use of existing data originally acquired for other purposes, it 

has provided two good observations. First, the time averaged mean flow dominates the lobed structure of 

the jet plume. When the time averaged mean is removed, turbulence from the chevron nozzle resembles 

the turbulence round nozzle in azimuthal modal structure, although the peak location of the modes moves 

upstream. Second, when heat is added to the jet, it plays the primary role in shaping the azimuthal 
NASA/TM—2006-214364 14 

structure of the jet (based on fluctuating axial velocity) leaving the chevrons to take a secondary place. It 

is important to remember that these observations are based on two chevron nozzles, only varying the 

number of primary chevrons on the nozzles. These observations are also only taken at two angles relative 

to the jet axis, 90° and 125°, both away from the peak angle for jet noise. A more complete study using 

nozzles varying chevron number, length and penetration angle and a dedicated far field azimuthal array at 

more angles relative to the jet axis is needed to confirm these results in all cases. 

References 

1. Michalke, A. and Fuchs, H.V., “On turbulence and noise of an axisymmetric shear flow,” J. Fluid 

Mech. 70(1), 179–205, 1975. 

2. Armstrong, Ralph R., Michalke, Alfons, and Fuchs, Helmut V., “Coherent Structures in Jet Turbulence 

and Noise,” AIAA J. 15(7), 1011–1017, 1977. 

3. Juve, Daniel, Sunyach, Michel, and Comte-Bellot, Geneieve, “Filtered Azimuthal Correlations in the 

Acoustics Far Field of a Subsonic Jet,” AIAA J. 17(1), 112–113, 1979. 

4. Bridges, J. and Brown, C.A., “Parametric Testing of Chevrons on Single Flow Hot Jets,” NASA/TM—

2004-213107, 2004. 

5. Bridges, J. and Brown, C.A., “Validation of the Small Hot Jet Rig for Jet Noise Research,” AIAA 

Paper 2005–2846, May 2005. 

6. Brown, C. and Bridges, J., “Small Hot Jet Acoustic Rig Validation,” NASA/TM—2006-214234, 2006. 

7. Wernet, M.P., “Fuzzy Logic Enhanced Digital PIV Processing Software,” NASA/TM—1999-209274, 

1999. 

8. Opalski, Anthony B., Wernet, Mark P., and Bridges, James E., “Chevron Nozzle Performance 

Characterization Using Stereoscopic DPIV,” AIAA Paper 2005–444, 2005. 
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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20

Acoustic Efficiency of Azimuthal Modes in Jet Noise Using Chevron Nozzles

Clifford A. Brown and James Bridges

Jet aircraft noise; Aeroacoustics

Unclassified -Unlimited

Subject Category: 07

The link between azimuthal modes in jet turbulence and in the acoustic sound field has been examined in cold, round

jets. Chevron nozzles, however, impart an azimuthal structure on the jet with a shape dependent on the number, length

and penetration angle of the chevrons. Two particular chevron nozzles, with 3 and 4 primary chevrons respectively, and a

round baseline nozzle are compared at both cold and hot jet conditions to determine how chevrons impact the modal

structure of the flow and how that change relates to the sound field. The results show that, although the chevrons have a

large impact on the azimuthal shape of the mean axial velocity, the impact of chevrons on the azimuthal structure of the

fluctuating axial velocity is small at the cold jet condition and smaller still at the hot jet condition. This is supported by

results in the azimuthal structure of the sound field, which also shows little difference in between the two chevron

nozzles and the baseline nozzle in the distribution of energy across the azimuthal modes measured.

Prepared for the 12th Aeroacoustics Conference cosponsored by the American Institute of Aeronautics and Astronautics

and the Confederation of European Aerospace Societies, Cambridge, Massachusetts, May 8–10, 2006. Responsible person,

Clifford A. Brown, organization code RTA, 216–433–2896.