Abbas Khavaran

ASRC Aerospace Corporation, Cleveland, Ohio

James Bridges 

Glenn Research Center, Cleveland, Ohio

Jet Noise Scaling in Dual Stream Nozzles 

NASA/TM—2010-216887

November 2010

AIAA–2010–3968
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Abbas Khavaran

ASRC Aerospace Corporation, Cleveland, Ohio

James Bridges 

Glenn Research Center, Cleveland, Ohio

Jet Noise Scaling in Dual Stream Nozzles 

NASA/TM—2010-216887

November 2010

AIAA–2010–3968

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

16th Aeroacoustics Conference

cosponsored by the American Institute of Aeronautics and Astronautics and 

the Confederation of European Aerospace Societies

Stockholm, Sweden, June 7–9, 2010
Acknowledgments

The Fundamental Aeronautics Subsonic Fixed Wing (SFW) and Supersonic Projects (SUP) at NASA supported this work. 

The authors would like to acknowledge Dr. Milo Dahl, acoustics branch, NASA Glenn Research Center, 

for his thorough and constructive comments.

Available from

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7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

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Available electronically at http://gltrs.grc.nasa.gov

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 

This report is a formal draft or working 

paper, intended to solicit comments and 

ideas from a technical peer group.
NASA/TM—2010-216887 1

Jet Noise Scaling in Dual Stream Nozzles

Abbas Khavaran

ASRC Aerospace Corporation

Cleveland, Ohio 44135

James Bridges 

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

Power spectral laws in dual stream jets are studied by considering such flows a superposition of 

appropriate single-stream coaxial jets. Noise generation in each mixing region is modeled using spectral 

power laws developed earlier for single stream jets as a function of jet temperature and observer angle.

Similarity arguments indicate that jet noise in dual stream nozzles may be considered as a composite of 

four single stream jets representing primary/secondary, secondary/ambient, transition, and fully mixed 

zones. Frequency filter are designed to highlight spectral contribution from each jet. Predictions are 

provided at an area ratio of 2.0—bypass ratio from 0.80 to 3.40, and are compared with measurements 

within a wide range of velocity and temperature ratios. These models suggest that the low frequency noise 

in unheated jets is dominated by the fully mixed region at all velocity ratios, while the high frequency 

noise is dominated by the secondary when the velocity ratio is larger than 0.80. Transition and fully 

mixed jets equally dominate the low frequency noise in heated jets. At velocity ratios less than 0.50, the 

high frequency noise from primary/bypass becomes a significant contributing factor similar to that in the 

secondary/ambient jet. 

Nomenclature

A Jet exit area

B Intercept parameter

c Sound speed

D Jet diameter

Di Inner diameter in the secondary jet

De Effective diameter

cp Specific heat at constant pressure

f , f * Frequency, characteristic frequency

h, ho Static and stagnation enthalpy

m Mass flow rate

M Mach number

n Velocity power factor

T, T o Static and stagnation temperature

U Mean axial velocity

δ Diameter ratio (Di/Dp)

γ Specific heat ratio

λA, λv Area and velocity ratio—secondary divided by primary 

λT Static temperature ratio—primary divided by secondary

θ Polar angle from inlet axis

ρ Density
NASA/TM—2010-216887 2

ξ Normalized frequency (f / f *)

η Normalized radial distance

Subscripts

p Primary jet (core)

s Secondary jet (bypass)

e Transition jet

m Fully mixed jet

Superscripts

(p) Primary jet condition

(s) Secondary jet condition

(m) Mixed jet condition

1.0 Introduction

Development of robust and high fidelity jet noise prediction models applicable to dual stream flows is 

of great interest to turbofan engine designers. RANS-based jet noise prediction models that use variants of 

Lilley’s acoustic analogy are computationally intensive, and require dedicated flow solvers to provide 

input for sources of jet noise in heated flows. Additionally, such methods are difficult to implement in an 

iterative fashion in conjunction with multi-disciplinary design, analysis, and optimization tools. In an 

earlier study, an extensive set of high quality jet noise measurements gathered at the AeroAcoustic 

Propulsion Laboratory (AAPL) at the NASA Glenn Research Center (Refs. 1, 2, and 3) was used to 

develop intensity-scaling laws for the jet mixing noise in single stream jets. The result is a very robust 

code, labeled sJet (for Single stream Jets), that implements the intensity laws and scales the jet noise 

power spectral density from a limited bank of subsonic conditions to a user specified set of conditions that 

include supersonic jets (Refs. 4 and 5). It is well known that supersonic jets at imperfectly expanded 

pressures emit two distinct noise components, i.e., the jet mixing noise and the broadband shock 

associated noise (BBSN). The scaling laws were additionally extended to the broadband shock associated 

noise (Ref. 5) when the jet mixing noise was subtracted from the total spectrum in order to isolate the 

BBSN component. Subsequently a semi-empirical model was proposed for this noise component that 

used a known peak-amplitude and frequency, combined with appropriate spectral attenuation on either 

side from the peak.

The present work attempts to develop a similar intensity-scaling methodology for jet mixing noise in 

turbofan engines. Such an effort represents a formidable task due to the order of increase in parameters 

involved compared to those in single stream flows. In addition to the gas dynamic parameters, the 

geometrical details of a dual stream nozzle influence the generation of both mixing noise and the 

broadband shock noise. From an aerodynamic point of view, a detailed study of the mean flow and 

turbulence should be emphasized as a guide in understating the noise generation mechanism in such 

flows. This is accomplished by holding one jet at a fixed operating condition while incrementally 

changing the second jet. Naturally, any noise-modeling recipe is expected to asymptotically approach a 

single stream jet when either the primary or the secondary dominates the jet exhaust.

Stone et al. (Refs. 6 and 7) studied jet noise from co-annular nozzles with and without a center-body 

plug. Using an extensive data set at nozzle bypass ratios from 5 to 14 they proceeded with component 

extraction and proposed semi-empirical correlations for what they considered as important noise 

components. Stone modeled his single-stream round jet predictions on Lighthill’s general scaling law in 

cold jets, and added some empiricism for effects such as refraction and temperature effect. These models 

are currently coded into the NASA Aircraft Noise Prediction Program (ANOPP) and provide a first 

estimate of jet noise from turbofan engines.
NASA/TM—2010-216887 3

Fisher et al. (Ref. 8) pioneered a scaling approach for jet noise in dual stream flows from a fluid 

mechanics perspective of such streams. In the light of velocity and turbulence measurements, they divided 

a coaxial dual stream jet into several noise-generating segments. Although these noise-producing regions 

beard some resemblance to those suggested by Stone, they differed in their noise modeling details. Later, 

Fisher extended the model to heated jets (Ref. 9) with a dipole-equivalent correction term that represented 

the temperature effect in the transition jet. These studies were limited in their scope and applicability of 

the velocity, area, and temperature ratio between the two streams, and did not examine important 

geometrical details such as a recessed secondary that is typical of the present turbofan engine designs.

The objective of the present study is to construct a composite spectrum for the jet mixing noise by 

considering a dual stream jet as a superposition of un-correlated single-stream equivalent jets. Each single 

stream jet is regarded as a component in the context of its spectral contribution to the total noise. 

Component noise is determined per velocity scaling laws. These laws state that turbulent mixing noise in 

a single stream jet scales with some power of the mean exit velocity, referred to as the velocity exponent 

or velocity power factor n. Since velocity exponents vary with jet temperature (Ref. 5), we expect that a 

composite spectrum should equally hold at different temperatures without additional adjustments. Each 

component noise undergoes a spectral filtering that reflects pertinent turbulence scales in that region of 

the jet. Filter functions (high- or low-pass filters) are determined by a combination of physical reasoning 

and iteration within the bounds of the available jet parameters.

The single-stream jet noise prediction model adopted for this work is briefly reviewed in Section 2.0, 

and is followed by a review of the similarity arguments in dual stream subsonic jets. These discussions 

lay grounds for component splitting and spectral filtering in Section 3.0. Spectral predictions in dual 

stream jets are presented in Section 4.0 at area ratio of 2, which include both unheated and heated primary 

flows (stagnation temperature ratio of 1.0 to 2.67), and at nozzle bypass ratios from 0.80 to 3.40. A 

summary of the results and direction for the follow-on research is given in Section 5.0.

2.0 Method of Approach

We start with the velocity power laws for the turbulent mixing noise in shock-free single-stream jets.

In a previous study, an extensive matrix of jet noise spectral data acquired from the Small Hot Jet 

Acoustic Rig (SHJAR) (Refs. 1, 2, and 3) at the NASA Glenn Research Center was used to develop 

velocity power laws in single stream jets. Power spectral density PSD for the turbulent mixing noise was 

shown to scale from one jet velocity to the next, on a Strouhal frequency basis as (Ref. 4)

( ) ( ) ( ) ( ) ( ( ) ( )) 2 ,

2 1 2 1 2 1 2 1 , , , , 10 , , o n T o o o o PSD T U PSD T U Log U U B T B T θ θ − θ = + θ −θ . (1)

Parameters n and B are referred to as the velocity power factor and the intercept parameter. These 

parameters were determined from SHJAR measurements as a function of angle and jet temperature as 

seen in Figure 1.

When jets become supersonic, the basic shape of the spectrum at small aft angles changes with jet 

velocity. This is due to the presence of the instability-related noise that increasingly dominates the aft 

angles at supersonic speeds. The jet mixing noise along sideline and forward angles would still scale 

according to the power law (1) provided that U is replaced with a fully expanded jet velocity, and an 

additional term 10Log(Aj2/Aj1) is added to the right-hand-side of Equation (1)—where Aj is the fully 

expanded jet area. The total noise in supersonic shock-containing jets includes an additional component 

attributed to the broadband shock associated noise. The intensity of BBSN depends on the difference 

between the fully expanded jet Mach number and the design Mach number. Similar to the jet mixing 

noise, intensity scaling of shock noise requires two parameters m(θ,To

) and Bshock(θ,To) referred to as 

intensity exponent and the intercept parameter (see Figure 2).

When jet noise in considered as a superposition of multiple equivalent single-stream jets, Equation (1) 

is applicable to each jet through parameters U, T and D that best represent that component stream.
NASA/TM—2010-216887 4

Figure 1.—Velocity power exponent n and intercept parameter B as a function of angle and stagnation temperature 

ratio in single stream jets (parameter B is evaluated as lossless dB at 100D Arc).

Figure 2.—Shock noise intensity exponent m and intercept factor B in single stream convergent nozzles (parameter B

is evaluated as lossless dB at 100D Arc).

2.1 Fully Mixed Jet

The similarity arguments discussed in the next section conclude that a dual stream jet could be 

divided into three regions (four zones) as sketched in Figure 3. The initial mixing region consists of two 

zones that reflect the mixing between primary/secondary and secondary/ambient streams. A transition 

region where the two mixing layers merge, and subsequently a fully mixed region further downstream 

follow this. Noise generation from each of the four zones is addressed through an equivalent single stream 

jet with three parameters U, T and D. In this section we discuss these parameters as related to the fully 

mixed region of the jet.
NASA/TM—2010-216887 5

Figure 3.—Schematic of a dual stream jet showing mixing zones primary/bypass, 

bypass/ambient, the transition, and the fully mixed region.

Let the primary (or core), the secondary (or bypass), and the fully mixed streams in a dual stream jet 

be identified by subscripts p, s and m respectively. The one-dimensional conservation equations plus the 

equation of state (assuming a constant static pressure) are written as

222

(mass)

(momentum)

(energy)

(state)

p p p s ss m mm

p p p s s s m mm

oo o p p p p s ss s m mm m

p p ss mm

U A UA U A

UA UA UA

U hA UhA U h A

TTT

ρ +ρ =ρ

ρ +ρ =ρ

ρ +ρ =ρ

ρ =ρ =ρ

(2) 

where stagnation enthalpy is 2 2 o o h cT U cT =+ = p p , and c R p =γ γ− ( 1) . For simplicity, we use the 

following definitions

, ,

, . o

s s V A

p p

o p p s T T o sp s

U A

U A

T T

T T

λ≡ λ≡

ρ λ≡ = λ ≡

ρ

(3)

The fully mixed jet conditions are solved from eqns. (2) and (3) as

( )

2

2

2

2 ( ) 2

( ) ( ) 2

1 , 1

1 , 1

1 ,

1 . 2

o

m V A T

p V AT

o

m V AT T

o

p V AT

m m p m V AT

p p m p

p o o m m mm p pp

o o p m

p m p pp p p p

U

U

T

T

A D U

A D U

T T TU U c

T T TT U c c

+λ λ λ = +λ λ λ

+λ λ λ λ = +λ λ λ

  ρ  

= = +λ λ λ    

ρ      

ρ  

==+ −  

ρ  

(4)

The specific heat ratios γ

(p) and γ(s) in the primary and the secondary are evaluated at their respective 

temperatures, and are used to evaluate the mixed specific heat ratio ( ) ( ) ( ) ( ) () mp s m m mm p s ps γ = γ +γ +    , 

where m is the mass flow rate.
NASA/TM—2010-216887 6

2.2 Similarity in Subsonic Coaxial Jets

Dual stream jets at subsonic conditions have been examined experimentally by a number of 

investigators. Ideas presented here, and similarly proposed by Fisher et al. (Ref. 8), are founded on 

measurements of Ko and Kwan (Ref. 10) obtained at low subsonic conditions. They tested a 

0.18-Mach number unheated primary jet Up = 197 fps combined with a secondary jet at velocity ratios of 

Us /Up = 0.70, 0.50, 0.30. Using an appropriately defined non-dimensional radial distance, they identified 

four distinct zones based on similarity arguments (see Figure 3). The initial mixing region consists of two 

zones, and ends near the termination point of the secondary potential core. Similarity of the velocity 

profile could be shown for both the primary and the secondary jets when the local mean velocity ratio 

(U – Us)/(Up –Us) is plotted versus normalized radial distance ηp = (y – y0.5)/(y0.9 – y0.1) for the primary, 

and U/Us versus ηs = (y – Ds/2)/x for the secondary flow (see Abramovich, Ref. 11). The second region, 

identified as the transition region starts at the end of the secondary potential core. This is the region where 

the two jets mix. The potential core of the primary flow could persist through the transition region and 

stretch farther into the subsequent fully mixed region depending on the velocity ratio of the two streams.

The transition region is highlighted mainly by an absence of any similarity velocity profile.

Following this region, similarity of the local mean velocity is displayed again in the fourth or the fully 

mixed region. Eldred et al. (Ref. 12) defined a radial parameter ηe = (y – De/2)/xe to show similarity for 

mean velocity ratio U/Up in this region. The virtual origin for this jet is xe = x – ∆x, where shift ∆x is 

measured relative to the primary exit, and depends on the secondary-to-primary velocity ratio λV. The 

effective diameter De (see Eq. (10)) is defined for an equivalent jet of velocity Up having an identical 

thrust as that of the dual stream jet. In the following section, we define the fully mixed diameter Dm for a 

dual stream nozzle. Since diameter ratio De/Dm is a fixed number, the similarity of local mean velocity 

U/Up should equivalently hold relative to the radial parameter ηm = (y – Dm/2)/xm in the fully mixed 

region.

Of primary interest in any jet noise prediction algorithm is the source strength, i.e., the turbulence 

intensity distribution. Figure 4, reproduced from data of (Ref. 10), shows turbulence intensity as a 

percentage of the primary jet velocity at selective stream-wise locations from near the exit at 0.5Dp to

8Dp.

The peak turbulence in the fully mixed region is nearly 11.75 percent of the primary velocity as seen 

in Figure 4. Using test condition parameters λV = 0.70, λT = 1.0, and λA = 2.67 in the conservation 

equations, the mixed flow parameters are evaluated as Dm/Dp = 1.89 and Um/Up = 0.80. Therefore the peak 

turbulence as a percentage of the fully mixed velocity is ~ 14.7 percent, similar to a single stream jet. This 

provides an impetus to treat this region as a single stream jet for noise considerations—although an 

appropriate filter would be required to tone down its high frequency content.

In the transition zone ( x D/ 6.0 p  ), the peak turbulence is typified by ~ 7 percent (at y Dp  0.6 ) 

relative to primary jet velocity, or nearly 60 percent of the peak turbulence if this zone were to be treated 

as a single stream jet at the primary jet conditions (Up, Tp). For this reason the turbulence intensity level is 

attenuated by a factor of 0.60 and the region is treated as a single stream jet with an effective diameter De

resulting in a similar thrust as the dual stream jet. Additionally, a high frequency filter will be introduced 

to moderate its high frequency noise so that the combined spectra from the transition and the initial 

mixing regions agree with measurements at high frequency.

We now turn our attention to the initial mixing region in Figure 3. As for the secondary jet, 

measurements of Ko and Kwan (Ref. 10, Figure 6) show similarity of turbulence intensity u′/Us versus 

radial parameter ηs at each velocity ratio λV in the secondary mixing region. As λV increases, the 

turbulence ratio approaches ~14 percent, similar to a single stream jet. Deviations from similarity appear 

mostly in the inner part of the mixing region (ηs < 0), while the outer part ηs < 0 conforms closely with 

the single stream jet similarity at all λV. Consequently, it seems appropriate to treat this mixing region as a 

single stream jet at the secondary conditions, and with a suitable filter to tone down its low frequency 

content— as this noise component is due primarily to the large vortices in the fully mixed jet. Further,
NASA/TM—2010-216887 7

Figure 4.—Radial distribution of turbulence intensity in a dual 

stream jet at λV = 0.70, and at axial locations, x/Dp = 0.50, 1.0, 

2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 (Ref. 10).

the filter could also be tailored to represent the effect of the lip thickness (i.e., the radial separation 

between the secondary nozzle inner radius and the primary lip).

Next, we consider the primary and secondary stream shear layer within the initial mixing region. This 

mixing zone resembles that of a jet discharging into a moving ambient with velocity Us. As shown in 

(Ref. 10, Figure 7), similarity is observed for turbulence intensity u′/(Up – Us) versus normalized radial 

distance ηp. Unlike the secondary shear layer, the slight deviation from single stream jet similarity is 

measured on the positive side of ηp. Due to reduced shear, this mixing layer contributes little to the 

overall jet noise spectra, however, from a modeling standpoint, it should be compatible with the limiting 

case as λV → 0 so we can recover the single stream jet noise spectra.

In the next section, we discuss the frequency filters designed for each noise-generating region so that 

in combination they can afford a dual stream jet noise spectrum at a range of angles and operating 

conditions. This includes both isothermal and heated flows and jets with an inverted velocity profiles (i.e.,

λV > 1).

3.0 Frequency Filters

The exhaust geometry in a dual stream coaxial jet is sketched in Figure 5. In general, the inner 

diameter of the outer nozzle is larger than the diameter of the inner stream due to the wall thickness or a 

recessed secondary, and/or other geometrical considerations. The flow area ratio can be expressed as

2

2

2 , s i

A

p p

D D

D D

λ = −δ δ≡ . (5)

When the two streams discharge at the same axial location the wall thickness should be kept to a 

minimum (i.e., δ → 1) to avoid a wake and discontinuity in the nozzle profile at the exit that could lead to 

discrete tones. 

The filters defined subsequently each depend on a cut-off frequency and are designed to tone down 

either the high- or the low-frequency spectral density (dB) as a function of frequency.
NASA/TM—2010-216887 8

Figure 5.—Dual stream coaxial jets.

Let f

* denote a characteristic frequency (defined shortly), and

, 2 f m m

f

ξ≡ = ∗ . (6)

Consider two filter functions as

23 4

1

2 3

2

() 1 , 25 125 250

() 1 . 2 6

F e

F e

−ξ

−ξ

  ξξ ξ ξ = +ξ+ + +    

  ξ ξ ξ = +ξ+ +    

(7)

Each of the four noise producing zones undergoes a filtering that reflects the predominant noisegenerating scales in that zone. The functions defined in Equation (7) work as low- and/or high-pass filters, 

and are determined by iteration and comparison of the predicted spectra with measurements.

3.1 Fully Mixed Region

This jet is defined as a single stream jet at Um, Tm, and Dm. According to the conservation 

Equations (4), the fully mixed diameter ratio Dm/Dp depends on the secondary geometry through area 

ratio λA. Since the secondary jet diameter is uniquely defined through three geometrical parameters 

according to Equation (5), the characteristic frequency f *

in the fully mixed region should additionally 

depend on parameter δ. We introduce a low-pass filter for this noise-generating region as

( ) * 10 1

1 , Filter( ) 10 ( ) m

m

U f f Log F D

  =   = ξ

  δ . (8)

At a fixed λA, a larger δ adds to the secondary jet diameter, which in turn enhances the fully mixed 

diameter and decrease its characteristic frequency.

3.2 The Secondary Jet

This jet is defined through the secondary jet parameters Us, Ts, and Ds, and is expected to contribute 

to the high frequency noise. The required high-pass filter should be compatible with that in the fully 

mixed region to accommodate the limiting case when the primary jet becomes relatively weak. In that 

case, the fully mixed jet and the secondary are identical and the two filters should recover a single jet at 

the secondary conditions. Parameter δ best fits the characteristic frequency in the secondary jet as

( ) * 3 10 1 , Filter( ) 10 1 ( ) s

s

U f f Log F D

  = δ   = −ξ

  (9)
NASA/TM—2010-216887 9

3.3 Transition Jet

Due to the lack of an intrinsic similarity within the region, this jet is relatively more ambiguous and 

requires a more delicate treatment. Per discussions presented earlier, it is best defined as single stream jet 

at Up, Tp, and De. The effective diameter is calculated per equal thrust to that of the dual stream jets

2

2

2 1 e A T V

p

D

D

= +λ λ λ . (10)

Since the maximum turbulence intensity is of the order of 60 percent of the primary jet velocity, the noise 

level needs to be attenuated accordingly by this percentage—raised to some exponent. A proper exponent 

(7/2) is derived from physics-based jet noise modeling (Ref. 13) that scales jet mixing noise versus

turbulence intensity. Additionally, a low-pass filter is used at an appropriate characteristic frequency 

( ( ) )

( ( ) )

3

2 * 7/2 10 10 3

2

3

, Filter( ) 10 (0.60) 10

ˆ 3

A p

e A

U F

f f Log Log D F m

  ξ λ   = = +   λ  

(11)

where m m ˆ = ξ Min , ( ) . The filter, denoted as the second term on the RHS of Equation (11), works more 

effectively as λA increases. Parameter λA in (11) is replaced with its limits at λA > 3 or λA < 1 such that 

1.0 ≤λA ≤ 3.0. When combined with the high frequency noise from the secondary jet, these two noise 

components should be required to match the total high frequency noise in a dual stream nozzle.

3.4 Primary Jet

This jet is defined through parameters Up, Tp, and Dp, and is considered subject to a flight speed of 

U∞ = Us. The required high-pass filter is bound by the limiting requirements at Us → 0.

( ) * 10 1 , Filter( ) 10 1 ( ) p sp f U U D f Log F = − = −ξ (12)

When the secondary jet is relatively insignificant, the fully mixed jet and the primary become identical.

The two jets subject to the proposed filters recover the primary jet, as expected. The only caveat is that a 

virtual transition flow is also in the pictures, and is identical to the primary jet. The filter function in 

Equation (11) suggests an additional contribution from this jet to the total noise spectral density

( ) 7/2 10 1 0.60 0.67 dB Log10 + = .

In the next section, the proposed models are examined at a number of conditions and the jet noise 

spectral density in dual stream nozzles is evaluated as a superposition of the four uncorrelated spectra 

subject to their respective filters.

4.0 Numerical Results

Turbulent mixing noise from the four aforementioned zones are combined to form a composite 

spectrum as follows:

i. Appropriate equivalent single jet parameters U, T and D are supplied to the sJet code that predicts 

the turbulent mixing noise in single-stream jets according to the velocity power laws. Four 

predicted component noise tables are stored as 1/3-Octave lossless spectra.
NASA/TM—2010-216887 10

ii. Each component noise undergoes a low- or high-pass filter.

iii. A composite spectrum is formed as:

primary secondary transition fully-mixed /10 ( /10) ( /10) ( /10) ( /10) 10 10 10 10 10 SPL SPL SPL SPL SPL =+ + + . (13)

In addition to the jet mixing noise, broadband shock associated noise could be a significant factor if either 

of the two streams is imperfectly expanded (Ref. 14).

Next acoustic measurements are compared with predictions at a range of temperatures and subsonic 

pressure ratios in the two streams. 

4.1 Coaxial Jet Noise Data (Fisher et al.)

These measurements were reported by Fisher et al. (Refs. 8, 9, and 15) and were carried out in the 

large anechoic chamber at the Defense Research Agency (DRA) in the United Kingdom to investigate 

flow/noise characteristics of coaxial jets. The nozzles consist of co-planar primary and secondary jets at

Dp = 1.307 in., Ds = 2.291 in. and λA = 2.0, and with a measured discharge coefficient close to unity.

Details of the experimental setup are provided in (Ref. 8). Noise data presented here have been scanned 

from the publicly available reports and the AIAA references (Refs. 8, 9, and 15).

A sample of 11 set points is listed in Table 1, each identified by a run number that will be used in the 

presentation. All cases are subsonic, with a maximum nozzle pressure ratio of 1.79 at Run no. P038. The 

bypass ratio varies from 1.0 (Run no. P038) to 3.38 (Run no. P043).

BPR m m = =λ λ λ s p V AT   (14)

Spectral data at several run conditions were provided at 90° only, while most were reported at three inlet 

angles of 40°, 90° and 140°. The stagnation temperature ratio in the primary stream is 1.0 at each of the 

first eight measurement points, and is subsequently increased to 2.0 and 2.67 at the last three set points. 

The secondary flow remains unheated throughout.

Predictions are presented as lossless, 1/3-Octave sound pressure level (SPL) on a 6 m (236.2 in.) arc. 

TABLE 1.—COANNULAR NOZZLE TEST CONDITIONS (REF. 9), λA= 2.0

Run

no.

Primary Secondary λV λT

NPR To - R U - fps M NPR To - R U - fps M

P018 1.241 540.0 623.2 0.56 1.570 540.0 885.6 0.83 1.42 1.07

P019 1.318 540.0 701.2 0.64 1.117 540.0 448.7 0.40 0.64 1.00

P023 1.190 543.0 561.5 0.50 1.186 543.1 557.6 0.50 0.99 1.00

P027 1.244 541.8 626.8 0.57 1.186 542.5 557.6 0.50 0.89 0.98

P028 1.325 541.6 708.5 0.64 1.186 542.3 557.6 0.50 0.79 0.97

P032 1.424 543.2 791.8 0.73 1.186 543.6 557.6 0.50 0.70 0.95

P035 1.570 528.8 876.4 0.83 1.192 528.7 557.6 0.50 0.63 0.93

P038 1.791 532.6 990.2 0.95 1.191 532.6 557.6 050 0.56 0.89

P040 1.146 1080.0 705.2 0.45 1.187 540.0 557.6 0.50 0.79 2.02

P042 1.233 1080.0 869.2 0.56 1.180 540.0 547.6 0.49 0.63 1.98

P043 1.169 1440.0 869.2 0.48 1.180 540.0 557.6 0.49 0.63 2.68

Jet noise prediction and comparisons with measurements at set point conditions of Table 1 are 

presented in Figure 6 to Figure 16.

Several conclusions are drawn from these predictions:

1. Lowest velocity ratio (i.e., λv = 0.56 at Run no. P038), high-frequency noise in the primary is 

comparable to that in the secondary/ambient.
NASA/TM—2010-216887 11

2. In jets with an unheated primary, a fully mixed jet dominates the low-frequency noise at all 

conditions. Addition of heat to the primary jet results in the enhancement of low frequency noise 

in the transition region. 

3. The high frequency noise is completely dominated by the secondary jet when velocity ratio 

exceeds 0.60.

4. Transition jet dominates the mid-frequency span in most cases. At a constant primary velocity, 

this jet makes a stronger contribution as the velocity ratio is lowered.

5. At the high velocity ratio λv > 1, the secondary jet completely dominates the mid- to high-frequency 

noise. The fully mixed jet determines the low-frequency noise as before (Figure 6 and Figure 8).

6. Increasing the secondary jet speed at a constant primary jet velocity enhances the low-frequency 

contribution from the fully mixed region. 

These results required no special treatment in heated jets versus unheated jets. The basic building 

block of the prediction methodology, i.e., single stream jet noise model, accounts for temperature 

variations of both velocity exponent n(θ,To

) and the intercept parameter B(θ,To) according to Figure 1.

As the secondary-to-primary velocity ratio is lowered to below 0.50, the high-frequency noise from 

primary-bypass shear layer dominates the same from other noise generating regions, and dictates the 

high-frequency noise in a dual-stream jet. This is presented at conditions of Table 2 at a velocity ratio of 

λv = 0.45 at a bypass ratio of BPR=0.78. Spectral predictions are shown in Figure 17 at two angles of 60°

and 90°. Unfortunately no measurements were available for comparison at this operating condition.

TABLE 2.—COANNULAR NOZZLE CONDITIONS AT λA= 2.0

Run

no.

Primary Secondary λV λT

NPR To - R U - fps M NPR To - R U - fps M

P001 1.791 540.0 997.5 0.95 1.117 540.0 448.8 0.40 0.45 0.87

Figure 6.—Jet noise spectrum in dual stream unheated jets at 60°, 90° and 140° (Run no. P018, 

Table 1) ∞ = λ= = 1.0, 1.42, 623.2 o T T p vp U fps.
NASA/TM—2010-216887 12

Figure 7.—Jet noise spectrum in dual stream unheated jets at 60°, 90° and 140° (Run no. P019, 

Table 1) ∞ = λ= = 1.0, 0.64, 701.2 o T T p vp U fps.

Figure 8.—Jet noise spectrum in dual stream unheated jets at 60°, 90° and 140° (Run no. P023, 

Table 1) ∞ = λ= = 1.0, 0.99, 561.5 o T T p vp U fps.
NASA/TM—2010-216887 13

Figure 9.—Jet noise spectrum in dual stream unheated jets at 90°, 120° and 140° (Run no. P027, 

Table 1) ∞ = λ= = 1.0, 0.89, 626.8 o T T p vp U fps.

Figure 10.—Jet noise spectrum in dual stream unheated jets at 90°, 120° and 140° (Run no. P028, 

Table 1) ∞ = λ= = 1.0, 0.79, 708.5 o T T p vp U fps.
NASA/TM—2010-216887 14

Figure 11.—Jet noise spectrum in dual stream unheated jets at 90°, 120° and 140° (Run no. P032, 

Table 1) ∞ = λ= = 1.0, 0.70, 791.8 o T T p vp U fps.

Figure 12.—Jet noise spectrum in dual stream unheated jets at 90°, 120° and 140° (Run no. P035, 

Table 1) ∞ = λ= = 1.0, 0.63, 876.4 o T T p vp U fps.
NASA/TM—2010-216887 15

Figure 13.—Jet noise spectrum in dual stream unheated jets at 90°, 120° and 140° (Run no. P038, 

Table 1) ∞ = λ= = 1.0, 0.56, 990.2 o T T p vp U fps.

Figure 14.—Jet noise spectrum in dual stream heated jets at 60°, 90° and 140° (Run no. P040, 

Table 1) ∞ = λ= = 2.0, 0.79, 705.2 o T T p vp U fps.
NASA/TM—2010-216887 16

Figure 15.—Jet noise spectrum in dual stream heated jets at 60°, 90° and 140° (Run no. P042, 

Table 1) ∞ = λ= = 2.0, 0.63, 869.2 o T T p vp U fps.

Figure 16.—Jet noise spectrum in dual stream heated jets at 60°, 90° and 140° (Run no. P043, 

Table 1) ∞ = λ= = 2.67, 0.63, 869.2 o T T p vp U fps.
NASA/TM—2010-216887 17

Figure 17.—Predicted jet noise spectrum in dual stream unheated jets at 60° and 90° (Run no. 

P001, Table 2) ∞ = λ= = 1.0, 0.45, 997.5 o T T p vp U fps.

The prediction model presented here, although quite satisfactory for the test cases examined, remains 

to be validated at other conditions with larger area ratio λA typical of turbofan engines at high bypass ratio 

BPR > 8. Also of interest would be jet noise spectral data in dual stream flows with a heated secondary. In 

such flows, the radial temperature gradient in the bypass stream is expected to enhance the refraction of 

the high-frequency noise and provide a so-called thermal shielding.

5.0 Summary

A jet noise prediction model has been proposed for coaxial dual stream flows that should find 

application in turbofan engines. The model uses a composite of four equivalent single-stream jets, each 

subject to an appropriate filter. Reasonably accurate spectra were produced at all test conditions examined 

in this article. The maximum bypass ratio was about 3.37 at a secondary-to-primary area ratio of 2.0. The 

velocity ratio spanned a wide range of 0.45 to 1.42. The component spectra show that the secondary 

stream completely dominates the mid- to high-frequency noise at the highest velocity ratio. The large 

turbulence scales in the fully mixed region of the jet mostly dominated the low-frequency noise. The 

model relied on quality noise prediction in single-stream jets at both heated and unheated conditions.

Subsequently, no special provisions were needed to account for the temperature effect. High bypass ratio 

jets, and jets with a heated secondary remain to be tested to further validate the model and its filter 

functions.

Of near-term interest is the extension of the model to dual stream jets with a supersonic primary 

and/or secondary, where shock-cell formation and the broadband shock associated noise should 

additionally be taken into consideration. As pointed out in the introduction, the prediction model is 

intended to provide a quick and reasonably accurate noise assessment in coaxial, axisymmetric, dual 

stream configurations, and is, in no way, intended to identify or assess noise benefit/penalty of various 

noise suppression devices. Those concepts need to be studied and possibly modeled in a similar fashion 

within their own parametric space. In such cases, a physics-based jet noise predictions methodology that 

deploys a variant of the Acoustic Analogy, or large eddy simulation may suggest trends that could help 

engine designers with their noise mitigation efforts.

References

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

2005–2846, May 2005.

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

2006.
NASA/TM—2010-216887 18

3. Bridges, J., and Wernet, M.P., “Effect of Temperature on Jet Velocity Spectra,” AIAA–2007–3628, 

2007.

4. Khavaran, A., and Bridges, J., “SHJAR Jet Noise Data and Power Spectral Laws,” NASA/TM—

2009-215608, http://gltrs.grc.nasa.gov, March 2009.

5. Khavaran, A., and Bridges, J., “Development of Jet Noise Power Spectral Laws Using SHJAR Data,” 

AIAA–2009–3378, May 2009. 

6. Stone, J.R., Krejsa, E.A. and Clark, B.J., “Jet Noise Modeling for Coannular Nozzles Including the 

Effects of Chevrons,” NASA/CR—2003-212522, http://gltrs.grc.nasa.gov, September 2009

7. Stone, J.R., Krejsa, E.A. and Clark, B.J., “Semi-Empirical Model for Coannular Nozzle Component 

Noise Extraction and Correlation Including the Effects of Noise Reduction Devices,” AIAA–2003–

1060, 2003.

8. Fisher, M.J., and Preston, G.A., and Bryce, W.D., “A Modeling of the Noise from Simple Co-axial 

Jets,” AIAA–1993–4413, October 1993. 

9. Fisher, M. J., and Preston, G. A., and Mead, C. J., “A Modeling of Noise from Simple Coaxial Jets,” 

AIAA–1996-1666, May 1996.

10. Ko, N.W.M., and Kwan, S.H., “The Initial Region of Subsonic Coaxial Jets,” J. Fluid Mechanics, 

73(2), pp. 305–332, 1976.

11. Abramovich, N., The Theory of Turbulent Jets, M.I.T. Press, 1963.

12. Eldred, K.M., et al., “Far-field noise Generation by Coaxial Flow Jet Exhaust. 1. Detailed 

Discussion,” Wyle Lab Report FAA-RD-71-101, 1971.

13. Khavaran A., and Kenzakowski, D.C., “Noise Generation in Hot Jets,” AIAA–2007–3640, 2007.

14. Viswanathan, K., “Parametric Study of Noise from Dual Stream Nozzles,” J. Fluid Mechanics, 521, 

pp. 35–68, 2004.

15. Fisher, M.J., and Preston, G.A., “The Prediction of Noise from Co-axial Jets,” ISVR Technical 

Report No. 215, University of Southampton, 1993.
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Jet Noise Scaling in Dual Stream Nozzles 

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14. ABSTRACT

Power spectral laws in dual stream jets are studied by considering such flows a superposition of appropriate single-stream coaxial jets. Noise 

generation in each mixing region is modeled using spectral power laws developed earlier for single stream jets as a function of jet 

temperature and observer angle. Similarity arguments indicate that jet noise in dual stream nozzles may be considered as a composite of four 

single stream jets representing primary/secondary, secondary/ambient, transition, and fully mixed zones. Frequency filter are designed to 

highlight spectral contribution from each jet. Predictions are provided at an area ratio of 2.0--bypass ratio from 0.80 to 3.40, and are 

compared with measurements within a wide range of velocity and temperature ratios. These models suggest that the low frequency noise in 

unheated jets is dominated by the fully mixed region at all velocity ratios, while the high frequency noise is dominated by the secondary 

when the velocity ratio is larger than 0.80. Transition and fully mixed jets equally dominate the low frequency noise in heated jets. At 

velocity ratios less than 0.50, the high frequency noise from primary/bypass becomes a significant contributing factor similar to that in the 

secondary/ambient jet. 

15. SUBJECT TERMS

Noise; Aircraft noise; Aerodynamic noise; Acoustics 

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