Milo D. Dahl

Glenn Research Center, Cleveland, Ohio

Predictions of Supersonic Jet Mixing and 

Shock-Associated Noise Compared 

With Measured Far-Field Data 

NASA/TM—2010-216328

May 2010
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Milo D. Dahl

Glenn Research Center, Cleveland, Ohio

Predictions of Supersonic Jet Mixing and 

Shock-Associated Noise Compared 

With Measured Far-Field Data 

NASA/TM—2010-216328

May 2010

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
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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. 
Predictions of Supersonic Jet Mixing and Shock-Associated Noise

Compared with Measured Far-Field Data

Abstract

Codes for predicting supersonic jet mixing and broadband shock-associated noise were assessed using

a database containing noise measurements of a jet issuing from a convergent nozzle. Two types of codes

were used to make predictions. Fast running codes containing empirical models were used to compute

both the mixing noise component and the shock-associated noise component of the jet noise spectrum.

One Reynolds-averaged, Navier-Stokes-based code was used to compute only the shock-associated noise.

To enable the comparisons of the predicted component spectra with data, the measured total jet noise

spectra were separated into mixing noise and shock-associated noise components. Comparisons were

made for 1/3-octave spectra and some power spectral densities using data from jets operating at 24

conditions covering essentially 6 fully expanded Mach numbers with 4 total temperature ratios.

1 Introduction

Computational codes that attempt to predict jet noise vary from the near instantly computed empirical

models to numerically intensive, extremely long running, direct simulations. The empirical models are

limited in their ability to predict the radiated jet noise beyond the relatively small set of geometries and

operating conditions with which they were developed. At the other extreme, the computationally intensive

models may simulate all the proper physics for noise predictions, but running them is so costly that they

currently have little practical usage. In between these two are found attempts to increase the practical ability

to predict jet noise by using more sophisticated numerical tools and physical models that achieve results in

an acceptable amount of time.

In general, a jet noise model must predict the radiated noise from all the sources that exist throughout

the range of useful jet operating conditions. At lower speeds, the noise may be characterized as coming from

the fine-scale turbulence in the flow. As the speed increases, the noise due to coherent, large-scale turbulence

becomes significant starting in the directions off the downstream jet axis. Near sonic conditions and above

cause pressure imbalances in the flow, creating shocks. The interaction between turbulence and shocks creates

an additional source of noise that radiates over a broad range of higher frequencies and predominantly in

the direction upstream of the nozzle exit. If coherent feedback occurs, then intense screeching can also be

present. These are all potential sources of radiated jet noise. An approach to making jet noise predictions

is to model the sources separately. Then assuming incoherent sources, the radiated noise from each source

is combined in the far field to obtain the total noise. Alternatively, some or all of the jet noise sources are

computed simultaneously to obtain the total radiated noise. Once a modeling tool has been developed, it

must be validated by comparing predictions to experimentally measured data.

As part of a larger study to assess NASA’s capability to predict aircraft noise,1empirical and acoustic

analogy based tools were used to predict jet noise and the results were compared to measured data over a wide

range of operating conditions.2 The jet experiments used nozzle geometries including convergent, convergentdivergent, internal mixer, separate flow, and chevron configurations operating with Mach numbers from 0.3

to 2.0 and temperatures from 0.8 to 3.0 times the ambient temperatures. The predicted jet noise included

both mixing noise, for all jet operating conditions, and broadband shock-associated noise, for supersonic jet

operating conditions. The general conclusions were that the empirical tools could make successful overall

sound pressure level predictions for a broad range of nozzle geometries and operating conditions while the

acoustic analogy tools were successful for a very limited range of operating conditions using a single stream

NASA/TM—2010-216328 1

Milo D. Dahl 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 
nozzle. No attempt was made in the above study to separately assess the ability to predict the broadband

shock-associated noise generated during supersonic jet conditions. This report includes separate assessments

of mixing noise and broadband shock-associated noise prediction codes. Jet noise predictions from older

and more recent models are compared to a set of acoustic measurements from supersonic, shock-containing

jets at a variety of jet speeds and temperatures. Predictions are made for both mixing noise sources and

shock-associated noise sources.

Following a brief description of the experiments and a presentation of the spectral data obtained from the

experiments, a summary of the various jet noise prediction models assessed herein is given. The jet mixing

noise prediction models are empirical in nature and depend on their underlying experimental database. The

broadband shock-associated noise models have varying degrees of empiricism, but only a Reynolds-averaged,

Navier-Stokes (RANS) based model uses flow field calculations as a part of the jet noise prediction scheme.

This allows nozzle geometry and flow field conditions outside of the experimental database to be used in

making jet noise predictions. The RANS-based broadband shock-associated noise model is new and only an

initial assessment for single-stream, round jets is provided here to compare with previous model predictions.

2 Experimental Setup

The experimental jet noise spectral data used in this study were acquired during an extensive test program

conducted using the Small Hot Jet Acoustic Rig (SHJAR) at the NASA Glenn Research Center. The

SHJAR is a single-stream, hot jet rig installed within the AeroAcoustic Propulsion Laboratory, a 65-foot

geodesic dome lined with acoustic absorbing material to provide anechoic conditions for noise testing at all

frequencies above 200 Hz. More information on this facility may be found in Bridges & Brown3 and other

reports describe the types of data and the quality of the data collected during testing in this facility.4–6

Khavaran & Bridges7 discuss details of the test results from the program to measure the noise from jets

at a variety of nozzle pressure ratios and total temperatures. Tables are given that describe the different

nozzles used and the variety of operating conditions tested. A subset of that data is used here consisting of

noise data from supersonic jets issuing from a 2.0-inch exit diameter, circular, convergent nozzle. The nozzle,

designated as smc021, is a modified version of the smc000 baseline convergent nozzle with a 5-degree conic

contraction and a 0.04-inch thick lip, see Figure 1. The smc021 nozzle had a sharp edge lip with notches cut

into the edge. These nozzles are shown in Figure 2. The purpose of the modifications was to minimize the

screech noise observed in the smc000 nozzle spectral data.

To assess the various shock-containing jet noise prediction models, the data were collected using the

smc021 nozzle operated at the 24 conditions listed in Table 1. The operating conditions are grouped according

to constant total temperatures. However, the operating condition parameters were recorded at the time the

acoustic data were measured, hence, the numbers in the table reflect the slight variations in conditions that

occurred during the testing. The table column headings are given as follows:

Rdg – designates the experimental reading number used to label the various operating conditions.

Tt/T∞ – the nozzle flow total temperature to ambient temperature ratio.

NPR – the nozzle pressure ratio defined as the nozzle flow total pressure divided by the ambient

pressure.

Mj – the fully expanded jet Mach number computed using the equation

Mj =

 2

γj − 1

 NPR

γj−1

γj − 1

 1

2

(1)

Vj/c∞ – the acoustic Mach number is the ratio of the fully expanded jet velocity to the ambient

speed of sound. The fully expanded jet velocity is computed from Mj using the fully expanded

speed of sound

cj =

p

γj R Tj (2)

and the fully expanded temperature

Tj =

Tt

1 +

γj − 1

2

M2

j

(3)

NASA/TM—2010-216328 2
β – the shock noise parameter

β =

q

M2

j − 1 (4)

γj – the ratio of specific heats at the fully expanded jet conditions. It is based on assuming that

the jet flow is a calorically imperfect, thermally perfect gas. It is computed by iteration using

equations (180), (43), and (44) in the ‘Ames Tables’8 where NPR and Tt are fixed and known

and the resulting Mach number is Mj .

T∞ – the ambient temperature in degrees Kelvin.

p∞ – the ambient pressure in Pascals.

c∞ – the ambient speed of sound in meters per second computed from the equation

c∞ =

p

γ R T∞ (5)

where γ = 1.4 and R = 286.959 m2/(s2K).

3 Description of Measured Data and Analysis

The measurements of the noise radiated from the jet were made by 24 microphones. These microphones were

located on an arc 50 nozzle exit diameters from the center of the nozzle exit area and placed at 24 equallyspaced angles. The angles were from 50 to 165 degrees as measured from the upstream inlet centerline to

the nozzle.

As described in Bridges et al.2 and in Khavaran & Bridges,7the time histories for the microphone signals

were processed using the Finite Fourier Transform with suitable averaging and scaling to obtain narrow

band spectral data with amplitude levels adjusted to report results at a radius of 100 nozzle exit diameters.

The atmospheric attenuation inherent in the measured data was removed resulting in lossless spectra. These

spectra contained 8193 points at equally spaced intervals of about 12 Hz. The spectral amplitudes were

normalized by the frequency interval to obtain a power spectral density. Follow-on processing generated

1/12-octave and 1/3-octave spectra as desired.

Jet noise prediction models are available for computing only the mixing noise component, only the broadband shock-associated noise component, or combining the two components to compute the total radiated

jet noise (not including any jet screeching noise in the predictions). Given that only the total radiated jet

noise was measured, Khavaran & Bridges7, 9 developed scaling laws that attempt to separate the total jet

noise into its mixing noise and shock-associated noise components. The results of this spectral component

separation for the Table 1 conditions are shown in Figure 3 for measurements at a 50 degree inlet angle. The

plots show 1/3-octave lossless spectra as a function of the Strouhal number fD/Vj , where, in this case, f is

the 1/3-octave center frequency, D is the nozzle exit diameter, and Vj is the fully expanded jet velocity.

Khavaran & Bridges7, 9 discuss that the smc021 nozzle was designed to reduce screech, but did not

eliminate it. Even at reduced amplitude, the screech was noted to have induced the effect of mixing noise

amplification. This additional noise could be included as part of the velocity-scaled mixing noise or included

as part of the shock-associated noise. The plots show both types of component separation. The total

noise is either the sum of shock-associated noise and mixing noise with amplification or the sum of shockassociated noise with amplification and mixing noise. However, the discussion on jet noise amplification

given in Deneuville & Jacques10 describes the issue as more complicated than this simple noise component

separation suggests. Both the broadband noise due to mixing and due to shock association are affected by the

presence of screech tones as excitation sources. The mixing noise is amplified as a result of excitation’s effect

on the turbulence and as this turbulence passes through the shock structure, the broadband shock-associated

noise is possibly amplified. Currently, there is no certain way to determine the amount of amplification that

is applied to each component. The results shown in Figure 3 suggest that when the shock-associated noise is

distinctly dominant over the mixing noise at the forward angles, the amount of screech present in the current

set of noise data has little affect on the shock-associated noise amplitude. Hence for a first approximation

in these results, the effects of jet noise amplification will be applied only to the mixing noise component for

the purposes of comparing jet mixing noise predictions with measured data in this report and no further

consideration will be given to adding amplification to the shock-associated noise data.

NASA/TM—2010-216328 3
Figures 4 and 5 show the component separation results for measurements at 90 degrees and 120 degrees,

respectively. Mixing noise can be seen to dominate at the lower frequencies and becoming a larger portion of

the spectrum as the directivity angle moves downstream. Conversely, the broadband shock-associated noise

dominates at the higher frequencies and at the upstream angles. After brief descriptions of both mixing noise

and shock-associated noise models, these spectral data from measurements will be compared to predicted

spectra.

4 Description of Jet Noise Prediction Models

The assessment conducted by Bridges et al.2 used predictions computed using one empirical model and

two acoustic analogy models. Far fewer predictions were made with the latter due to the larger amount

of computational resources required, especially that these models require a flow solution computed using

a Reynolds-averaged, Navier-Stokes (RANS) solver. The approach here is also to use models containing

various amounts of empiricism for predicting both the mixing noise component and the shock-associated noise

component of the noise spectrum from supersonic jets with shocks. Then for a subset of data, predictions

are compared to measured data for a recent RANS-based shock-associated noise prediction model.

4.1 Mixing Noise Models

As a jet flow issues from a nozzle, the flow mixes with and expands into the surrounding medium. From

the initial shear layer to the downstream developed jet, turbulent eddies develop at various times and of

various sizes, cascading their energy through the flow, emitting unsteady fluctuations that become sound

outside of the jet. Mixing noise models attempt to predict this radiated noise and the empirical models

attempt to predict it over the whole frequency range and at every directivity angle from the jet axis. The

two models used here are both part of NASA’s Aircraft Noise Prediction Program (ANOPP).11 The ANOPP

code assembles noise source prediction modules for engine and airframe components and links them to an

acoustic propagation code to obtain far field noise levels and sound spectra. While complete aircraft system

level noise predictions may be computed using ANOPP, the individual modules within ANOPP may be

used to make component level noise predictions. For the jet mixing noise predictions, the modules named

SGLJET and ST2JET are used.

4.1.1 ANOPP Module SGLJET

The SGLJET module predicts the radiated jet mixing noise for single stream, shock-free, jet flows issuing

from circular, convergent nozzles. It uses the methodology found in the SAE ARP 876 document which

depends on tabulated data obtained from experiments.12

The equation for the far-field, mean-square acoustic pressure contains constants obtained from fitting

experimental data and functions that either represent correlated equations or interpolations of tabulated

values. The general form for the equation is given as

hp

2

i ∝ 1

r

2

Π(ρ

ω

j

, Vj ) D(θ, Vj ) F(Sc, θ, Vj , Tj ) f(Vj , θ, M∞) (6)

The overall acoustic power is given by the Π-function. It is a variation of the classic V8 power law and

attempts to account for the changes in jet density and the deviations from the power law as the jet velocity

changes. Both of these are incorporated through tabulated values of a density exponent ω and a power

deviation factor, both as functions of Vj . The directivity function D is tabulated versus both the directivity

angle θ, measured from the inlet, and the jet velocity Vj . F is the normalized spectral distribution factor that

determines the 1/3-octave spectra for each frequency as a function of the jet velocity, directivity angle, and

temperature. The frequencies of the normalized spectra are given in terms of a corrected Strouhal number

Sc that depends on an empirical function of the jet velocity. Finally, the results may be modified for the

effects of forward velocity through the f-function.

NASA/TM—2010-216328 4
4.1.2 ANOPP Module ST2JET (Mixing)

The ST2JET module predicts jet noise for one or two stream circular nozzles. The nozzles can be either

convergent or convergent-divergent and can be operated at subsonic or supersonic conditions. As such, it

includes both mixing noise and shock-associated noise sources.

For single stream jets, the radiated mixing noise is modeled to come from three sources: 1) The small

scale mixing noise that comes from near the nozzle exit. This noise has relatively high frequency content.

2) The intermediate scale mixing noise that comes from the shear layer as the jet mixes with the ambient

air. This noise contains mid- to high-frequency content. 3) The large scale mixing noise that comes from

the fully developed jet. It contains the lower frequency noise. Though each of these mixing noise source

models have different frequency content and different spectral amplitudes, they all may be represented by

an equation for the far field mean-square acoustic pressure of the form

hp

2

i ∝ 1

r

2

Π(ρj , Vj , M∞) D(θ

0

, Vj ) F(S

0

, θ0) (7)

For each source, the acoustic power function Π is computed using a correlation equation and both the

directivity function D and the spectrum function F are determined from an interpolation of tabulated values.

To be clear, each of the three mixing noise sources has its own set of correlations and tabulated values. The

directivity and spectral functions depend on an effective directivity angle θ

0 and an effective Strouhal number

S

0

. The effective directivity angle has an empirical modification to account for the effects of the jet flow and

the freestream flow on the directivity angle of the noise radiated from the jet. S

0 depends on the effective

directivity angle and includes additional effects due to jet temperature.

4.2 Shock-Associated Noise Models

Supersonic jet flows from convergent nozzles are imperfectly expanded creating shocks in the flow. The

turbulence normally created by jet flows interacts with the shock structure producing a noise source in

addition to that produced by turbulent mixing. This source may emit tones, known as screech, and a wide

band of noise called broadband shock-associated noise. This latter noise is of main interest here. Though

considered a broadband noise, shock-associated noise has a characteristic spectrum with a fundamental peak

and has spectral levels that vary with the directivity angle. It is also most dominant at angles upstream

of the nozzle exit. A prediction model for shock-associated noise was first proposed by Harper-Bourne &

Fisher.13 Deneuville14 used ideas from Harper-Bourne & Fisher (HBF) and experimental data to develop

a simplified version of the model. Both models are discussed further and compared to measured data in

Balsa et al.15 Later Tam16, 17 used the physics of large-scale turbulent structures in shock-containing jets

to develop a model for shock-associated noise. Both the HBF and Tam models have been incorporated into

ANOPP as the SAESHK and the TAMSHK modules. In addition to these modules, the ST2JET module

also predicts shock-associated noise. The simplified model from Deneuville was programmed based on the

work of Gliebe et al.18 Finally, a model was recently developed by Morris & Miller19 to use a RANS-based

flow solution as part of a shock-associated noise model.

4.2.1 ANOPP Module SAESHK

The SAESHK module in ANOPP contains the HBF shock-associated noise model as given in the formulas

of the SAE ARP 876 document.12 These formulas closely follow those given in Harper-Bourne & Fisher13

after the equation for the far field pressure spectrum is integrated to obtain the sound pressure spectrum in

1/3-octave bands as described by Balsa et al.15

The form of the equation for the far field mean-square acoustic pressure is given by

hp

2

i ∝ 1

r

2

[1 + W(σ, θ, Vj )] β

η H(σ) (8)

where β is the shock noise parameter defined in equation (4), η is an exponent that is equal to 4 if β ≤ 1

or if β > 1, it equals 1 for unheated jets or 2 for heated jets, σ is a frequency parameter based on shock

cell spacing and Mach number, H is the group source strength spectrum tabulated from measured data, and

W is a shock cell noise source interference function. The interference function uses a tabulated correlation

NASA/TM—2010-216328 5
coefficient spectrum and accounts for the constructive and destructive interference between the shock cell

noise sources.

4.2.2 Simplified Shock-Associated Noise Model

The ‘Simplified’ model is an empirical correlation for the spectrum of shock-associated noise based on two

straight lines that join at the peak of the spectrum.14 The peak frequency is computed from

fp =

0.7 Vj

1.1βD(1 + Mc cos θ)

, (9)

where for no ambient flow Mc = 0.7 Vj/c∞, and the peak sound level is of the form

hp

2

imax ∝

1

r

2

β

4

. (10)

The far field sound spectrum is then given by

hp

2

i = hp

2

imax 

f

fp

n

(11)

where n = 7 for f /fp ≤ 1 and n = −1 for f /fp > 1. The program for this model is taken from the ‘MGB’

code found in Gliebe et al.18

4.2.3 ANOPP Module TAMSHK

The broadband shock-associated noise model of Tam16, 17 is based on the theory that large-scale turbulent

structures generated in the supersonic jet mixing layer interact with the periodic-like shock cell structure that

exists in imperfectly expanded jets. This interaction causes pressure perturbations that radiate as sound.

The large structures are modeled as a sum of instability waves each with their own amplitude envelope

and phase speed characteristics. These characteristics affect the amplitude and directivity of the radiated

noise. The model is applicable to both the under-expanded and the over-expanded jets that can issue from

convergent-divergent nozzles. In this report, it is applied only to convergent nozzle jet flows.

The form for the far field mean-square acoustic pressure is

hp

2

i ∝ 1

r

2

Π(Aj , Mj , Tj ) F(θ, f) (12)

where Π is the overall shock noise acoustic power function and F is the spectral distribution function. Using

the nozzle exit area and the jet Mach number and temperature, the overall acoustic power is computed

from correlated equations based on the theoretical development of equations describing the physical jet flow.

These include equations for the spatial extent of the noise source, the jet core length, the shock cell strength,

and the fully expanded jet area. The spectral distribution function is computed from a sum of modes that

result from the instability wave theory. Correlated equations for the wave number and convection velocity

are used to enable rapid calculation of the modal summation at each frequency. The summed results are

integrated across bands of frequency to obtain the desired 1/3-octave spectrum.

4.2.4 ANOPP Module ST2JET (Shock)

The shock-associated noise predicted by the ST2JET module is based on an equation that has the same

form as equation (7) but written as

hp

2

i ∝ 1

r

2

Π(β, θc, Mj , M∞) D(θc) F(S

0

, θc) (13)

The acoustic power function depends on a correlation using the shock parameter β and a corrected directivity

angle. The latter also determines the interpolated value for the directivity function D. The spectrum function

F also requires the effective Strouhal number to obtain its interpolated value.

NASA/TM—2010-216328 6
4.2.5 RANS-Based Model

Morris & Miller19 developed a broadband shock-associated noise prediction model that uses a RANS-based

flow solution as input. This enables the prediction of shock-associated noise from one or two stream jets

from nozzles with realistic geometries. Using the inviscid compressible equations of motion, the flow field

variables are separated into four components: the mean value, the perturbations associated with the shock

cell structure, the turbulent fluctuations, and the disturbances generated by the interaction between the

turbulence and the shock cell structure. Linearized inhomogeneous equations for the interaction disturbances

are derived where the sources are products of the shock cell perturbations and the turbulent fluctuations.

An integral solution is derived using the Green’s function approach. After considerable manipulation, the

solution for the far field spectral density is found to have the form

S(x, ω) ∼

ω

2

c

4∞|x|2

Z∞

−∞

1

l

2

ps(y)ps(y + η)R

v

(y, η, τ ) exp iω τ −

x · η

|x|c∞

 dτ dη dy (14)

where l is a characteristic turbulent length scale, ps is the shock cell pressure perturbation, Rvis a twopoint, cross-correlation function of turbulent velocity fluctuations, and the exponential term represents the

far field Green’s function. The Rv(y, η, τ ) term must be modeled in order to obtain a solution. The model

contains turbulent length and time scales that are computed using the RANS turbulent kinetic energy and

viscous dissipation rate data with an additional constant coefficient. The chosen form of the model for Rv

has three constant coefficients. In addition, equation (14) requires a constant to set the proper amplitude of

the spectrum. Once these four constant coefficients are set by fitting predictions to experimental data, all

the other required parameters in the final form of the integral are found from the RANS solution.

5 Results for Jet Noise Component Predictions

The 1/3-octave spectral data shown in Figures 3 to 5 will now be compared to predicted results using the

empirical jet noise prediction models. The comparisons are shown as lossless 1/3-octave spectra in terms

of sound pressure level (dB reference 2 × 10−5 Pa) versus the Strouhal number for the operating conditions

shown in Table 1. The first set of figures compares predictions for the mixing noise component spectra to

velocity-scaled mixing noise spectra determined from data with and without the amplification effects. The

second set of figures makes comparisons between predictions and measured data for the shock-associated

noise component spectra. Finally in this section, the third set of figures compares predictions to both the

total measured jet noise spectra and the shock-associated noise component spectra. For each set of figures,

the predicted spectra are compared to the measured spectral data taken at the directivity angles of 50, 90,

and 120 degrees to the jet inlet.

5.1 Mixing Noise Component Spectra

Figures 6 to 8 compare predictions for the mixing noise from the ANOPP modules SGLJET and ST2JET to

the mixing component of the jet noise spectrum. Starting at the cold jet conditions and the 50 degree inlet

angle, Figures 6(a)–(f) show qualitatively good comparisons between the two predictions and the mixing

noise with amplification at the low frequencies less than the peak frequency for the shock-associated noise.

As the amplification effect becomes more important as the jet speed increases, the predicted spectra tend to

be closer to the amplified mixing noise at low frequencies and close to the normally scaled mixing noise at the

high frequencies. For all these cold jet conditions, the SGLJET predictions, in general, produce spectrum

levels that are slightly higher than those produced by the mixing noise part of the ST2JET predictions.

As the jet total temperature ratio increases with Tt/T∞ ≈ 1.76 in Figures 6(g)–(l), Tt/T∞ ≈ 2.16 in

Figures 6(m)–(r), and Tt/T∞ ≈ 2.65 in Figures 6(s)–(x), the levels of mixing noise increase. This follows

from the scaling of mixing noise with jet velocity which, as shown in Table 1, has increased as the jet

temperature increased in order to approximately maintain a constant fully expanded jet Mach number.

There are few general trends in these comparisons to which there are not exceptions. One general trend is

that the mixing noise predictions are all closer to the mixing noise with amplification spectra. Another is

that the SGLJET predicted levels continue to be generally higher than those from the ST2JET predictions.

NASA/TM—2010-216328 7
When predicted spectra are compared to the mixing noise with amplification spectra, there is qualitative

agreement at the low frequencies and a general trend to predict lower spectral levels than the component

levels at higher frequencies especially at higher jet velocities. The predictions are always higher than the

velocity-scaled mixing noise without the amplification effects included.

At 90 degrees, Figures 7(a)–(f) show comparisons for the cold jet. The predictions are qualitatively as

good as they were at 50 degrees except here the ST2JET predictions are generally slightly higher than the

SGLJET predictions. The mixing component and the mixing with amplification component are close for

these cold jet conditions. However, as the jet total temperature ratio increases, the mixing noise component

spectra with amplification have generally a greater level than just the velocity-scaled mixing noise. This

separation in level becomes larger as the jet Mach number increases. As with the 50 degree comparisons,

the predicted spectra in Figures 7(g)–(x) follow the mixing component with amplification spectra as the

total temperature ratio changes. In general, both prediction modules produce spectral levels that are a little

higher than the mixing component spectra with amplification, with the ST2JET spectra levels being higher

at all the operating conditions.

Figure 8 shows the mixing noise component spectra comparisons at a 120 degree inlet angle. At this

angle, the measured data component separation is showing very little in the way of amplification effects on

the mixing noise. Both predicted spectra are higher than the measured data at just about all frequencies

and operating conditions. The ST2JET spectra are higher than the SGLJET spectra except at the higher

frequencies where the ST2JET spectra drops to a lower level than the SGLJET spectra.

Given that these two jet mixing noise prediction models depend on measured data and that the supersonic

conditions used here are within the original data range used when these models were developed, it is possible

that the original jet spectral data were measured from supersonic jets that had a sufficient amount of screech

that resulted in amplified mixing noise. The comparisons in Figures 6 to 8 show that the mixing noise

predicted spectra are closer to the mixing noise component spectra with amplification. Even then, the

predictions are typically higher in amplitude than measured amplitudes by as much as 9 dB at low to mid

frequencies at 120 degrees. To summarize this, it is noted that the low frequency measured and predicted

mixing noise spectra are similar in shape and often nearly constant in separation, hence the difference between

the predicted level and the measured component level with amplification at a Strouhal number of 0.1 is used

to indicate the quality of the prediction or the prediction error. Figure 9 shows contour plots using those

errors as a function of the jet operating conditions. Within the limitations of interpolating within the set of

data points used in the plots, the plots show that more often than not both models predict higher amplitude

levels of mixing noise than was measured, especially for higher speed and/or higher temperature jets. Both

models have similar behavior for the mixing noise level error. At 50 degrees, the predicted noise levels are

too high for lower speed, higher temperature jets. Basically all the higher temperature jets have predicted

levels too high at 90 degrees. Finally at 120 degrees, all levels are predicted too high with the highest

levels occurring for the higher speed, higher temperature jets. Based on the levels of the extreme values

indicated by the scale on each plot, the mixing noise predictions from the SGLJET module tend to give

more accurate predictions than the mixing noise predictions from the ST2JET module for shock containing

jets. The variations in the SGLJET module predictions are 5.7 dB at 50 degrees, 4.4 dB at 90 degrees, and

3.6 dB at 120 degrees. The ST2JET module predictions have variations of 6.5 dB at 50 degrees, 4.7 dB at 90

degrees, and 7.1 dB at 120 degrees. These results are based on the data at the actual measurement points

and not on any interpolated results.

5.2 Shock-Associated Noise Component Spectra

The broadband shock-associated noise component spectrum for an under-expanded supersonic jet was obtained by subtracting the velocity-scaled mixing noise component spectrum from the total jet noise spectrum.7, 9 As shown in Figures 3 to 5, and discussed previously, the noise amplification phenomenon resulting

from the presence of any screech tones increases the noise levels of the component spectra. In this report,

all of the noise due to amplification is assigned to the mixing noise component. Figures 10 to 12 show the

comparison of the predicted broadband shock-associated noise spectra to the resulting shock-associated noise

component spectra without any amplification.

Figure 10 shows the shock-associated noise component comparisons between measured data and model

predictions at a 50 degree inlet angle. Harper-Bourne & Fisher13 and Tanna20 discuss the variations of

NASA/TM—2010-216328 8
total shock-associated noise intensity with β found in their experimental data. The predictions from the

three empirical models follow these experimental results in terms of the behavior of their computed 1/3-

octave spectra. Each group of jet temperature operating conditions shown in Table 1 have six similar values

for β. At the lowest β, Figures 10(a), (g), (m), and (s) all show that the ST2JET shock-associated noise

component predictions peak at a frequency lower than the other predictions and has a peak level higher than

the other predictions. This is followed by the ‘Simplified’ spectra which have a lower level and a higher peak

frequency. The peak for the TAMSHK predictions have yet a lower level, but about the same or slightly

higher peak frequency than the ‘Simplified’ model. The four plots have similar high frequency behavior for

the predictions. As β increases, the peak levels and frequencies become to have greater agreement with each

other and with the measured data as in Figures 10(d), (j), (p), and (v). The high frequency slope behavior

of the spectra are similar across these four plots, also, though the TAMSHK high frequency levels are lower.

At the two highest β’s, we see that levels predicted by the ‘Simplified’ model are getting higher compared

to the other predictions and the measured data and the TAMSHK spectra has larger peaks and valleys than

previous. Though the higher frequency behaviors are quite varied between predictions, they are consistent

across the plots with constant β and the peak frequency is predicted quite well by all models.

Similar comments can be made about the 90 degree spectral comparisons in Figure 11 as was made for

the 50 degree comparisons. An obvious exception is that the ST2JET predictions are consistently lower in

level than the other predictions at the higher β’s.

At the 120 degree angle, Figure 12 shows more variability across the predicted shock-associated noise

spectra with constant β. The peak frequency predicted by ST2JET is lowest at low β. As β increases,

the peak frequency from ST2JET comes to agree with the TAMSHK prediction for cold jets. As the jet

temperature increases, the ST2JET prediction for peak frequency is higher than the TAMSHK prediction

at higher β’s. For all higher speed, heated jet cases, the ‘Simplified’ model predicts a higher peak frequency

than the other two models. The spectral levels for the ST2JET predictions are always lowest and lower than

the shock-associated noise component spectra. The TAMSHK predictions for spectral levels agree with the

data from cold jets, but under predicts for heated jets. The high frequency spectral predictions from the

‘Simplified’ model tend to agree with the total noise spectra even though the peak frequencies are predicted

to be higher than that shown in the data for heated jets.

The quality of the shock-associated noise predictions is determined by computing the error in predicting

both the peak level and the peak frequency. For each of the three model predictions shown in Figures 10

to 12, the peak level error is computed by subtracting the measured 1/3-octave peak level from the predicted

1/3-octave peak level. The error in peak frequency is determined relatively by dividing the predicted peak

frequency by the measured peak frequency. Figures 13 to 15 show contour plots of peak level error and peak

frequency error as a function of the jet operating conditions and angle for each of the three shock-associated

noise prediction models. The levels shown on the legends indicate the range of values on the plot. The

largest errors on the peak level error plots are found at either the Mj ≈ 1.05 or the Mj ≈ 1.8 conditions.

Using the results for all jet temperatures between about Mj = 1.2 and Mj = 1.7, the following variations in

peak level error are found for the three broadband shock-associated noise prediction models:

Simplified Model

50 degrees, +3.8 dB, −2.5 dB for a 6.2 dB variation.

90 degrees, +2.3 dB, −3.8 dB for a 6.1 dB variation.

120 degrees, +1.7 dB, −3.9 dB for a 5.6 dB variation.

TAMSHK Module

50 degrees, +4.0 dB, −0.0 dB for a 4.0 dB variation.

90 degrees, +2.1 dB, −2.2 dB for a 4.3 dB variation.

120 degrees, +1.3 dB, −6.2 dB for a 7.5 dB variation.

ST2JET Module

50 degrees, +0.0 dB, −3.8 dB for a 3.8 dB variation.

90 degrees, −0.2 dB, −7.0 dB for a 6.8 dB variation.

120 degrees, +0.0 dB, −8.7 dB for a 8.7 dB variation.

On the basis of the these values shown for the peak level error in the 1.2 . Mj . 1.7 operating range, the

TAMSHK module provides more accurate predictions over the range of directivity angles shown. The peak

frequency error plots all contain large areas of constant error due to the 1/3-octave band accuracy of the

NASA/TM—2010-216328 9
spectra. The peak frequency is only known within a 1/3-octave band which limits the accuracy of the peak

frequency error and provides only an approximate or qualitative indication of the ability to predict the peak

frequency.

5.3 Total Jet Noise Spectra

Jet noise spectral predictions computed by the ST2JET module and the SAESHK module are shown in

Figures 16 to 18. These results are compared to the total measured noise spectra and to the measured

shock-associated noise component spectra. While the ST2JET module was used to compute the total noise

spectrum for these comparisons, it should be recalled that the SAESHK module was designed to predict

broadband shock-associated noise using the HBF model. However, the SAESHK model predictions were

found to compare favorably with measured total noise spectra, especially at upstream angles, for many operating conditions. Hence those results are included in these figures to more clearly highlight the comparisons

with measured data rather than adding another model result for shock-associated noise in Figures 10 to 12.

The ST2JET predictions contain both the mixing and shock-associated noise components of the model.

Given the issues discussed with the separate component comparisons, the ST2JET predicted total noise

spectra compare as follows to the measured spectra at 50 degrees, Figure 16, and 90 degrees, Figure 17:

(1) ST2JET predicts the low frequency mixing noise well, (2) ST2JET predicts the shock-associated noise

peak frequency where shock-associated noise dominates except at lower β’s, (3) ST2JET predicts the shockassociated noise peak level more accurately at 50 degrees than at 90 degrees, (4) ST2JET predicts high

frequency levels consistently lower than the measured data. At the 120 degree inlet angle, the ST2JET

predictions in Figure 18 are dominated by the mixing noise component model and typically has levels much

higher than the measured spectra at low to mid frequencies. At higher frequencies, the presence of shockassociated noise is only clearly seen in the predicted spectra for the cold, lower speed jets, Figure 18(a)–(d).

The predicted spectra from the SAESHK module are also shown in Figures 16 to 18. As mentioned above,

this module contains the HBF model which was designed to predict broadband shock-associated noise. As

can be seen in the comparisons at 50 degrees in Figure 16, the SAESHK module predicts the shock-associated

noise quite well for low-speed, low β jets, especially at β ≈ 0.6. At higher speeds, the predicted spectra

compare favorably with the entire total noise spectra especially at lower frequencies where mixing noise is

dominant, but not quite as well at frequencies higher than the peak frequency where shock-associated noise

dominates. At 90 degrees in Figure 17, the higher frequency predictions for the shock-associated noise are

lower creating a larger difference between predicted and measured spectra. In addition, a low frequency

hump develops in the predicted spectra as β increases above 0.6 that does not exist in the shock noise

component spectra and does not represent the total noise spectral shape, either. This low frequency hump

further develops at 120 degrees, as shown in Figure 18, and comes to dominate the spectra over that of the

shock-associated noise related peak as β and the jet temperature increase. There is little agreement between

the SAESHK module predictions and the measured data at these conditions.

6 Results for Shock-Associated Noise Component Predictions

The comparisons of the RANS-based model predictions with measured spectral data are shown in Figures 19

and 20. The RANS-based model predictions are taken from Morris & Miller19 for a converging nozzle with

Mj = 1.5 and either cold, Tt/T∞ = 1.00, or hot, Tt/T∞ = 2.20, conditions. The measurement conditions

are not identical to those used for the prediction calculations. Table 1 shows the measured conditions that

are closest to those used in the predictions to be Rdg# 2082 for the cold jet and Rdg# 2096 for the hot jet.

Using the prediction value for β of 1.118 and the measurement value of β of 1.109, an estimate of the peak

level difference between these two conditions is found using equation (10). Substituting for the β values and

taking the difference in decibels, with all other parameters assumed equal, results in a ±0.14 dB variation

between the two operating conditions. A similar test for the peak frequency in terms of the Strouhal number

uses equation (9) to ratio the two peak Strouhal numbers resulting in at most a ±1.8% variation in the

peak Strouhal number between the two operating conditions at inlet angles less than 120 degrees. Hence,

the measured spectra for these readings are used for comparison to the predictions performed by Morris &

Miller plotted in Figures 19 and 20. Both figures show power spectral density and 1/3-octave spectra for

each inlet directivity angle from 50 degrees to 120 degrees in 10 degree increments.

NASA/TM—2010-216328 10
The results for the cold jet are shown in Figure 19. For the power spectral density plots, the RANS-based

model and the Tam model are compared to the measured jet noise component spectra. In order to obtain

power spectral density in this case, the Tam model was programmed separately from the TAMSHK module

in ANOPP (which produces only 1/3-octave spectra output.) The peak frequencies and the peak levels are in

good agreement between the two predictions at the upstream angles. At 90 degrees and downstream, the two

predictions deviate with higher peak frequencies predicted by the RANS-based model. When the spectral

data are combined into 1/3-octave levels, the RANS-based model, the Tam model, and the ‘Simplified’ model

are in general agreement in the peak frequency, the peak level, and the higher frequency broadband levels

at all the directivity angles shown in the figure. The ST2JET predictions have the least agreement with the

data at the higher frequencies and under predicts the peak frequencies and levels as the directivity angle

increases downstream.

Figure 20 shows the hot jet results. There are larger differences between the shock-associated noise

models for the hot jet than there were for the cold jet. There is agreement between the peak frequencies and

levels at the upstream angles for the RANS-based model and the Tam model. But at higher frequencies,

both models predict much lower levels than the measured data. At the downstream angles, both models

deviate from each other and neither compare favorably with the data. The 1/3-octave spectra show some

agreement in the peak frequency at the upstream angles, but a wide difference exists in the predictions for

the higher frequency levels. At downstream angles, the predictions have even less agreement. In general for

the nozzle and jet flow conditions in this case, the ‘Simplified’ model predictions give the best agreement

with the measured data.

A summary of these prediction results in terms of the error in peak level and in peak Strouhal number

are given in Figure 21 for the power spectral density results and in Figure 22 for the 1/3-octave band results.

For the cold jet, Figure 21(a) shows that the Tam model has peak level errors varying between ±2 dB and the

RANS-based model ±2.5 dB over the range of directivity angles. The peak Strouhal number error for both

is less than 20%, Figure 21(b). When the jet is hot, both models have large peak amplitude errors in the

downstream direction and the RANS-based model approaches 40% in the peak Strouhal number error. The

errors derived from the 1/3-octave data, Figure 22, show similar results for the peak level errors for these two

models. The ‘Simplified’ model exhibits less peak level error overall compared to the Tam and RANS-based

models. The ST2JET model has much larger errors. The accuracy of using 1/3-octave spectra to determine

the peak Strouhal number error depends on both the position of the peak relative to the 1/3-octave band

cutoff frequencies and the quality of the measured spectra. At 90 degrees, for example, a screech tone exists

near the peak of the broadband shock-associated noise spectrum that lowers the peak Strouhal number in

the 1/3-octave spectrum. This results in a large peak Strouhal number error for the RANS-based predictions

at 90 degrees.

7 Summary

An assessment has been completed of the predictive capability of jet mixing noise and jet broadband shockassociated noise prediction codes using an acoustic database created from the far-field noise measurements

of single-stream, round, shock-containing jets operated at 24 under-expanded conditions covering a matrix

of jet velocities and temperatures. The following is a summary for the five semi-empirical models that

produced 1/3-octave spectra for comparison to the measured spectra from all the jet operating conditions.

A summary of the assessment for the newer RANS-based model using two cases is given at the end of the

previous section.

ANOPP Module SGLJET – The SGLJET module predicted the radiated jet mixing noise from supersonic jets issuing from a round, convergent nozzle at frequencies less than the peak frequency for

shock-associated noise. The levels of predicted mixing noise were found to be in closer agreement to

measured mixing noise component levels when the amplification effects were included in the mixing

noise. Over the range of operating conditions for which measurements were taken, the SGLJET module

predicted mixing noise levels within an accuracy variation of 5.7 dB or less for directivity angles of 50

to 120 degrees.

ANOPP Module ST2JET – The ST2JET module predicted the jet noise for both the mixing noise

NASA/TM—2010-216328 11
and the shock-associated noise components radiated from a supersonic, shock-containing jet. The

predicted mixing noise component was found to be in closer agreement to measured mixing noise levels

with amplification with accuracy variations of 7.1 dB or less over the range of operating conditions for

directivity angles of 50 to 120 degrees. The ST2JET module predicted the shock-associated noise peak

level more accurately at 50 degrees, within a 3.8 dB variation, than at 90 degrees, a 6.8 dB variation.

The high frequency levels for shock-associated noise were predicted consistently lower that the measured

data. At 120 degrees, the ST2JET predictions were dominated by the mixing noise component of the

model.

ANOPP Module SAESHK – The SAESHK module predicted the broadband shock-associated noise using the HBF model. The model gave reasonable predictions for shock-associated noise for lower speed

jets and predicted the total jet noise spectra for higher speed jets including low frequency mixing

noise at the 50 degree direction. The predictions at 90 degrees were still qualitatively good for peak

shock-associated noise levels at lower jet temperatures but becoming less accurate with increasing

jet temperature. At 120 degrees, there was little agreement between the SAESHK module predicted

spectra and the measured spectra.

ANOPP Module TAMSHK – The broadband shock-associated noise model of Tam is based on the

theory that large-scale turbulent structures generated in the supersonic jet mixing layer interact with

the periodic-like shock cell structure that exists in imperfectly expanded jets. The TAMSHK module

predicted the shock-associated noise peak levels with similar accuracy at 50 and 90 degrees, within

4.0 dB and 4.3 dB variations, respectively. The model predicted high frequency levels lower than

measured levels especially as the jet speed increased. At 120 degrees, the model performed well for

cold jets, but consistently predicted much lower spectral levels compared to measured levels for heated

jets.

Simplified Shock-Associated Noise Model – The ‘Simplified’ model is an empirical correlation for the

spectrum of shock-associated noise based on two straight lines that join at the peak of the spectrum.

Between the extremes of tested jet velocities, this model gave consistent peak level predictions within

about a 6 dB variation at all angles. There was a trend to predict higher levels than measured for

higher temperature jets. The peak frequencies were predicted well except at 120 degrees where the

peak frequencies were predicted to be higher than measured for higher speed jets.

References

[1] Dahl, M. D., “A Process for Assessing NASA’s Capability in Aircraft Noise Prediction Technology,”

AIAA Paper No. 2008-2813, 2008.

[2] Bridges, J. E., Khavaran, A., and Hunter, C., “Assessment of Current Jet Noise Prediction Capabilities,”

AIAA Paper No. 2008-2933, 2008.

[3] Bridges, J. and Brown, C. A., “Validation of the Small Hot Jet Acoustic Rig for Aeroacoustic Research,”

AIAA Paper No. 2005-2846, 2005.

[4] Bridges, J. and Wernet, M. P., “Measurements of the Aeroacoustic Sound Sources in Hot Jets,” AIAA

Paper No. 2003-3130, 2003.

[5] Brown, C. A. and Bridges, J., “Small Hot Jet Acoustic Rig Validation,” NASA TM-2006-214234, 2006.

[6] Bridges, J. and Wernet, M. P., “Effect of Temperature on Jet Velocity Spectra,” AIAA Paper No.

2007-3628, 2007.

[7] Khavaran, A. and Bridges, J., “SHJAR Jet Noise Data and Power Spectral Laws,” NASA TM-2009-

215608, 2009.

[8] NACA Ames Research Staff, “Equations, Tables, and Charts for Compressible Flow,” NACA Report

1135, 1953.

NASA/TM—2010-216328 12
[9] Khavaran, A. and Bridges, J., “Development of Jet Noise Power Spectral Laws Using SHJAR Data,”

AIAA Paper No. 2009-3378, 2009.

[10] Deneuville, P. and Jacques, J., “Jet Noise Amplification: A Practically Important Problem,” AIAA

Paper No. 77-1368, 1977.

[11] Zorumski, W. E., “Aircraft Noise Prediction Program Theoretical Manual, Parts 1 & 2, (Revised),”

NASA TM-83199, February 1982.

[12] SAE, “Gas Turbine Jet Exhaust Noise Prediction,” ARP876 Rev. E, SAE International, 2006.

[13] Harper-Bourne, M. and Fisher, M. J., “The Noise from Shock Waves in Supersonic Jets,” Noise Mechanisms, AGARD-CP-131, 1974, pp. 11.1–11.13.

[14] Deneuville, P., “Simplified Prediction Method of Shock Cell Noise of Supersonic Jets from Conical Nozzles,” SNECMA YKA No. 5982/76, Societe Nationale d’Edute et de Construction de Moteurs d’Avion,

France, 1976.

[15] Balsa, T. F., Gliebe, P. R., Kantola, R. A., Mani, R., Stringes, E. J., and Wang, J. F. C., “High Velocity

Jet Noise Source Location and Reduction. Task 2. Theoretical Developments and Basic Experiments;

Final Report,” FAA-RD-76-79-2, FAA, 1978.

[16] Tam, C. K. W., “Forward Flight Effects on Broadband Shock Associated Noise of Supersonic Jets,”

AIAA Paper No. 89-1088, 1989.

[17] Tam, C. K. W., “Broadband Shock-Associated Noise of Moderately Imperfectly Expanded Supersonic

Jets,” J. Sound Vib., Vol. 140, No. 1, 1990, pp. 55–71.

[18] Gliebe, P. R., Motsinger, R. E., and Sieckman, A., “High Velocity Jet Noise Source Location and Reduction. Task 6. Supplement. Computer Programs: Engineering Correlation (MS) Jet Noise Prediction

Method and Unified Aeroacoustic Prediction Model (M*G*B) for Nozzles of Arbitrary Shape; Final

Report,” FAA-RD-76-79-6A, FAA, 1979.

[19] Morris, P. J. and Miller, S. A. E., “The Prediction of Broadband Shock-Associated Noise Using RANS

CFD,” AIAA Paper No. 2009-3315, 2009.

[20] Tanna, H. K., “An Experimental Study of Jet Noise, Part II: Shock Associated Noise,” J. Sound Vib.,

Vol. 50, 1977, pp. 429–444.

NASA/TM—2010-216328 13
Rdg Tt/T∞ NPR Mj Vj/c∞ β γj T∞(K) p∞(Pa) c∞(m/s)

2079 1.01 2.005 1.049 0.954 0.315 1.4000 279.4 97789 335.04

2080 1.01 2.358 1.178 1.047 0.623 1.4000 279.2 97783 334.92

2081 1.01 3.147 1.392 1.186 0.969 1.4000 279.2 97788 334.93

2082 1.01 3.636 1.493 1.245 1.109 1.4000 279.2 97790 334.93

2083 1.01 4.647 1.660 1.338 1.325 1.4000 279.2 97796 334.89

2085 1.01 5.708 1.796 1.406 1.491 1.4000 279.1 97794 334.87

2088 1.77 2.004 1.050 1.264 0.319 1.3951 280.1 97814 335.44

2089 1.77 2.365 1.182 1.388 0.630 1.3963 280.2 97817 335.52

2090 1.76 3.143 1.392 1.568 0.968 1.3978 280.2 97826 335.49

2091 1.76 3.627 1.492 1.647 1.108 1.3983 280.2 97831 335.50

2092 1.77 4.644 1.660 1.775 1.325 1.3990 280.0 97826 335.37

2093 1.76 5.674 1.792 1.858 1.487 1.3994 279.8 97814 335.30

2100 2.16 1.989 1.045 1.390 0.305 1.3872 279.9 97851 335.34

2098 2.16 2.356 1.181 1.533 0.628 1.3896 279.9 97842 335.34

2097 2.16 3.130 1.390 1.734 0.966 1.3929 279.8 97837 335.25

2096 2.16 3.629 1.494 1.828 1.109 1.3942 279.6 97839 335.18

2095 2.16 4.638 1.659 1.959 1.324 1.3961 279.6 97825 335.16

2094 2.16 5.685 1.794 2.056 1.489 1.3973 279.7 97830 335.23

2102 2.66 1.987 1.048 1.542 0.314 1.3736 280.2 97865 335.54

2103 2.65 2.327 1.175 1.691 0.617 1.3769 280.3 97857 335.58

2104 2.66 3.120 1.391 1.926 0.967 1.3823 280.3 97859 335.59

2105 2.65 3.597 1.490 2.020 1.105 1.3849 280.4 97864 335.61

2106 2.64 4.630 1.660 2.168 1.325 1.3889 280.4 97857 335.61

2107 2.65 5.638 1.789 2.276 1.484 1.3913 280.3 97854 335.58

Table 1: Test conditions for a convergent nozzle designated smc021 grouped according to total temperature.

Figure 1: Diagram of the smc000 nozzle.

NASA/TM—2010-216328 14
Figure 2: Nozzles: smc000 on the left, smc021 on the right.

NASA/TM—2010-216328 15
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2079

(a) Mj = 1.049, NPR = 2.005, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2080

(b) Mj = 1.178, NPR = 2.358, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2081

(c) Mj = 1.392, NPR = 3.147, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2082

(d) Mj = 1.493, NPR = 3.636, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2083

(e) Mj = 1.660, NPR = 4.647, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2085

(f) Mj = 1.796, NPR = 5.708, Tt/T∞ = 1.01

Figure 3: 1/3-Octave measured total jet noise spectra and derived jet noise component spectra from jets

with shocks at a 50 degree inlet angle and distance 100D.

NASA/TM—2010-216328 16
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2088

(g) Mj = 1.050, NPR = 2.004, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2089

(h) Mj = 1.182, NPR = 2.365, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2090

(i) Mj = 1.392, NPR = 3.143, Tt/T∞ = 1.76

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2091

(j) Mj = 1.492, NPR = 3.627, Tt/T∞ = 1.76

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2092

(k) Mj = 1.660, NPR = 4.644, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2093

(l) Mj = 1.792, NPR = 5.674, Tt/T∞ = 1.76

Figure 3: (50 Deg., Cont.)

NASA/TM—2010-216328 17
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2100

(m) Mj = 1.045, NPR = 1.989, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2098

(n) Mj = 1.181, NPR = 2.356, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2097

(o) Mj = 1.390, NPR = 3.130, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2096

(p) Mj = 1.494, NPR = 3.629, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2095

(q) Mj = 1.660, NPR = 4.638, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2094

(r) Mj = 1.794, NPR = 5.685, Tt/T∞ = 2.16

Figure 3: (50 Deg., Cont.)

NASA/TM—2010-216328 18
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2102

(s) Mj = 1.048, NPR = 1.987, Tt/T∞ = 2.66

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2103

(t) Mj = 1.175, NPR = 2.327, Tt/T∞ = 2.65

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2104

(u) Mj = 1.391, NPR = 3.120, Tt/T∞ = 2.66

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2105

(v) Mj = 1.490, NPR = 3.597, Tt/T∞ = 2.65

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2106

(w) Mj = 1.660, NPR = 4.630, Tt/T∞ = 2.64

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2107

(x) Mj = 1.789, NPR = 5.638, Tt/T∞ = 2.65

Figure 3: (50 Deg., Cont.)

NASA/TM—2010-216328 19
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2079

(a) Mj = 1.049, NPR = 2.005, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2080

(b) Mj = 1.178, NPR = 2.358, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2081

(c) Mj = 1.392, NPR = 3.147, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2082

(d) Mj = 1.493, NPR = 3.636, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2083

(e) Mj = 1.660, NPR = 4.647, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2085

(f) Mj = 1.796, NPR = 5.708, Tt/T∞ = 1.01

Figure 4: 1/3-Octave measured total jet noise spectra and derived jet noise component spectra from jets

with shocks at a 90 degree inlet angle and distance 100D.

NASA/TM—2010-216328 20
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2088

(g) Mj = 1.049, NPR = 2.004, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2089

(h) Mj = 1.182, NPR = 2.365, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2090

(i) Mj = 1.392, NPR = 3.143, Tt/T∞ = 1.76

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2091

(j) Mj = 1.492, NPR = 3.627, Tt/T∞ = 1.76

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2092

(k) Mj = 1.660, NPR = 4.644, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2093

(l) Mj = 1.792, NPR = 5.674, Tt/T∞ = 1.76

Figure 4: (90 Deg., Cont.)

NASA/TM—2010-216328 21
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2100

(m) Mj = 1.045, NPR = 1.989, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2098

(n) Mj = 1.181, NPR = 2.356, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2097

(o) Mj = 1.390, NPR = 3.130, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2096

(p) Mj = 1.494, NPR = 3.629, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2095

(q) Mj = 1.660, NPR = 4.638, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2094

(r) Mj = 1.794, NPR = 5.685, Tt/T∞ = 2.16

Figure 4: (90 Deg., Cont.)

NASA/TM—2010-216328 22
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2102

(s) Mj = 1.048, NPR = 1.987, Tt/T∞ = 2.66

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2103

(t) Mj = 1.175, NPR = 2.327, Tt/T∞ = 2.65

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2104

(u) Mj = 1.391, NPR = 3.120, Tt/T∞ = 2.66

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2105

(v) Mj = 1.490, NPR = 3.597, Tt/T∞ = 2.65

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2106

(w) Mj = 1.660, NPR = 4.630, Tt/T∞ = 2.64

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2107

(x) Mj = 1.789, NPR = 5.638, Tt/T∞ = 2.65

Figure 4: (90 Deg., Cont.)

NASA/TM—2010-216328 23
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2079

(a) Mj = 1.049, NPR = 2.005, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2080

(b) Mj = 1.178, NPR = 2.358, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2081

(c) Mj = 1.392, NPR = 3.147, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2082

(d) Mj = 1.493, NPR = 3.636, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2083

(e) Mj = 1.660, NPR = 4.647, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2085

(f) Mj = 1.796, NPR = 5.708, Tt/T∞ = 1.01

Figure 5: 1/3-Octave measured total jet noise spectra and derived jet noise component spectra from jets

with shocks at a 120 degree inlet angle and distance 100D.

NASA/TM—2010-216328 24
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2088

(g) Mj = 1.049, NPR = 2.004, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2089

(h) Mj = 1.182, NPR = 2.365, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2090

(i) Mj = 1.392, NPR = 3.143, Tt/T∞ = 1.76

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2091

(j) Mj = 1.492, NPR = 3.627, Tt/T∞ = 1.76

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2092

(k) Mj = 1.660, NPR = 4.644, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2093

(l) Mj = 1.792, NPR = 5.674, Tt/T∞ = 1.76

Figure 5: (120 Deg., Cont.)

NASA/TM—2010-216328 25
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2100

(m) Mj = 1.045, NPR = 1.989, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2098

(n) Mj = 1.181, NPR = 2.356, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2097

(o) Mj = 1.390, NPR = 3.130, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2096

(p) Mj = 1.494, NPR = 3.629, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2095

(q) Mj = 1.660, NPR = 4.638, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2094

(r) Mj = 1.794, NPR = 5.685, Tt/T∞ = 2.16

Figure 5: (120 Deg., Cont.)

NASA/TM—2010-216328 26
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2102

(s) Mj = 1.048, NPR = 1.987, Tt/T∞ = 2.66

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2103

(t) Mj = 1.175, NPR = 2.327, Tt/T∞ = 2.65

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2104

(u) Mj = 1.391, NPR = 3.120, Tt/T∞ = 2.66

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2105

(v) Mj = 1.490, NPR = 3.597, Tt/T∞ = 2.65

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2106

(w) Mj = 1.660, NPR = 4.630, Tt/T∞ = 2.64

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Mixing w/Amp.

Shock w/Amp.

Mixing

Nozzle: smc021, Rdg #: 2107

(x) Mj = 1.789, NPR = 5.638, Tt/T∞ = 2.65

Figure 5: (120 Deg., Cont.)

NASA/TM—2010-216328 27
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2079

(a) Mj = 1.049, NPR = 2.005, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2080

(b) Mj = 1.178, NPR = 2.358, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2081

(c) Mj = 1.392, NPR = 3.147, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2082

(d) Mj = 1.493, NPR = 3.636, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2083

(e) Mj = 1.660, NPR = 4.647, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2085

(f) Mj = 1.796, NPR = 5.708, Tt/T∞ = 1.01

Figure 6: 1/3-Octave spectra comparisons of jet mixing noise prediction models to the mixing noise component spectra for measured data from jets with shocks at a 50 degree inlet angle and distance 100D.

NASA/TM—2010-216328 28
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2088

(g) Mj = 1.050, NPR = 2.004, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2089

(h) Mj = 1.182, NPR = 2.365, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2090

(i) Mj = 1.392, NPR = 3.143, Tt/T∞ = 1.76

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2091

(j) Mj = 1.492, NPR = 3.627, Tt/T∞ = 1.76

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2092

(k) Mj = 1.660, NPR = 4.644, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2093

(l) Mj = 1.792, NPR = 5.674, Tt/T∞ = 1.76

Figure 6: (50 Deg., Cont.)

NASA/TM—2010-216328 29
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2100

(m) Mj = 1.045, NPR = 1.989, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2098

(n) Mj = 1.181, NPR = 2.356, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2097

(o) Mj = 1.390, NPR = 3.130, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2096

(p) Mj = 1.494, NPR = 3.629, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2095

(q) Mj = 1.660, NPR = 4.638, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2094

(r) Mj = 1.794, NPR = 5.685, Tt/T∞ = 2.16

Figure 6: (50 Deg., Cont.)

NASA/TM—2010-216328 30
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2102

(s) Mj = 1.048, NPR = 1.987, Tt/T∞ = 2.66

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2103

(t) Mj = 1.175, NPR = 2.327, Tt/T∞ = 2.65

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2104

(u) Mj = 1.391, NPR = 3.120, Tt/T∞ = 2.66

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2105

(v) Mj = 1.490, NPR = 3.597, Tt/T∞ = 2.65

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2106

(w) Mj = 1.660, NPR = 4.630, Tt/T∞ = 2.64

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2107

(x) Mj = 1.789, NPR = 5.638, Tt/T∞ = 2.65

Figure 6: (50 Deg., Cont.)

NASA/TM—2010-216328 31
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2079

(a) Mj = 1.049, NPR = 2.005, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2080

(b) Mj = 1.178, NPR = 2.358, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2081

(c) Mj = 1.392, NPR = 3.147, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2082

(d) Mj = 1.493, NPR = 3.636, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2083

(e) Mj = 1.660, NPR = 4.647, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2085

(f) Mj = 1.796, NPR = 5.708, Tt/T∞ = 1.01

Figure 7: 1/3-Octave spectra comparisons of jet mixing noise prediction models to the mixing noise component spectra for measured data from jets with shocks at a 90 degree inlet angle and distance 100D.

NASA/TM—2010-216328 32
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2088

(g) Mj = 1.049, NPR = 2.004, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2089

(h) Mj = 1.182, NPR = 2.365, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2090

(i) Mj = 1.392, NPR = 3.143, Tt/T∞ = 1.76

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2091

(j) Mj = 1.492, NPR = 3.627, Tt/T∞ = 1.76

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2092

(k) Mj = 1.660, NPR = 4.644, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2093

(l) Mj = 1.792, NPR = 5.674, Tt/T∞ = 1.76

Figure 7: (90 Deg., Cont.)

NASA/TM—2010-216328 33
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2100

(m) Mj = 1.045, NPR = 1.989, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2098

(n) Mj = 1.181, NPR = 2.356, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2097

(o) Mj = 1.390, NPR = 3.130, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2096

(p) Mj = 1.494, NPR = 3.629, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2095

(q) Mj = 1.660, NPR = 4.638, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2094

(r) Mj = 1.794, NPR = 5.685, Tt/T∞ = 2.16

Figure 7: (90 Deg., Cont.)

NASA/TM—2010-216328 34
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2102

(s) Mj = 1.048, NPR = 1.987, Tt/T∞ = 2.66

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2103

(t) Mj = 1.175, NPR = 2.327, Tt/T∞ = 2.65

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2104

(u) Mj = 1.391, NPR = 3.120, Tt/T∞ = 2.66

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2105

(v) Mj = 1.490, NPR = 3.597, Tt/T∞ = 2.65

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2106

(w) Mj = 1.660, NPR = 4.630, Tt/T∞ = 2.64

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2107

(x) Mj = 1.789, NPR = 5.638, Tt/T∞ = 2.65

Figure 7: (90 Deg., Cont.)

NASA/TM—2010-216328 35
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2079

(a) Mj = 1.049, NPR = 2.005, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2080

(b) Mj = 1.178, NPR = 2.358, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2081

(c) Mj = 1.392, NPR = 3.147, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2082

(d) Mj = 1.493, NPR = 3.636, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2083

(e) Mj = 1.660, NPR = 4.647, Tt/T∞ = 1.01

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2085

(f) Mj = 1.796, NPR = 5.708, Tt/T∞ = 1.01

Figure 8: 1/3-Octave spectra comparisons of jet mixing noise prediction models to the mixing noise component spectra for measured data from jets with shocks at a 120 degree inlet angle and distance 100D.

NASA/TM—2010-216328 36
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2088

(g) Mj = 1.049, NPR = 2.004, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2089

(h) Mj = 1.182, NPR = 2.365, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2090

(i) Mj = 1.392, NPR = 3.143, Tt/T∞ = 1.76

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2091

(j) Mj = 1.492, NPR = 3.627, Tt/T∞ = 1.76

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2092

(k) Mj = 1.660, NPR = 4.644, Tt/T∞ = 1.77

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2093

(l) Mj = 1.792, NPR = 5.674, Tt/T∞ = 1.76

Figure 8: (120 Deg., Cont.)

NASA/TM—2010-216328 37
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2100

(m) Mj = 1.045, NPR = 1.989, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2098

(n) Mj = 1.181, NPR = 2.356, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2097

(o) Mj = 1.390, NPR = 3.130, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2096

(p) Mj = 1.494, NPR = 3.629, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2095

(q) Mj = 1.660, NPR = 4.638, Tt/T∞ = 2.16

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2094

(r) Mj = 1.794, NPR = 5.685, Tt/T∞ = 2.16

Figure 8: (120 Deg., Cont.)

NASA/TM—2010-216328 38
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2102

(s) Mj = 1.048, NPR = 1.987, Tt/T∞ = 2.66

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2103

(t) Mj = 1.175, NPR = 2.327, Tt/T∞ = 2.65

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2104

(u) Mj = 1.391, NPR = 3.120, Tt/T∞ = 2.66

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2105

(v) Mj = 1.490, NPR = 3.597, Tt/T∞ = 2.65

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2106

(w) Mj = 1.660, NPR = 4.630, Tt/T∞ = 2.64

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Mixing

Mixing w/Amp.

Mixing (SGLJET)

Mixing (ST2JET)

Nozzle: smc021, Rdg #: 2107

(x) Mj = 1.789, NPR = 5.638, Tt/T∞ = 2.65

Figure 8: (120 Deg., Cont.)

NASA/TM—2010-216328 39
! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

"2.1

3.6

(a) SGLJET Module, 50 degrees.

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

"1.3

3.1

(b) SGLJET Module, 90 degrees.

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

1.4

5.0

(c) SGLJET Module, 120 degrees. ! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

"4.0

2.5

(d) ST2JET Module, 50 degrees.

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

"0.8

3.9

(e) ST2JET Module, 90 degrees.

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

2.1

9.2

(f) ST2JET Module, 120 degrees.

Figure 9: Error in mixing noise level (dB(predicted) - dB(measured)) with amplification at the 1/3-octave

band nearest the Strouhal number 0.1. Black line = 0 dB. Data located at positions of black dots.

NASA/TM—2010-216328 40
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2079

(a) Mj = 1.049, NPR = 2.005, Tt/T∞ = 1.01, β = 0.315

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2080

(b) Mj = 1.178, NPR = 2.358, Tt/T∞ = 1.01, β = 0.623

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2081

(c) Mj = 1.392, NPR = 3.147, Tt/T∞ = 1.01, β = 0.969

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2082

(d) Mj = 1.493, NPR = 3.636, Tt/T∞ = 1.01, β = 1.109

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2083

(e) Mj = 1.660, NPR = 4.647, Tt/T∞ = 1.01, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2085

(f) Mj = 1.796, NPR = 5.708, Tt/T∞ = 1.01, β = 1.491

Figure 10: 1/3-Octave spectra comparisons of jet shock-associated noise prediction models to the shockassociated noise component spectra for measured data from jets with shocks at a 50 degree inlet angle and

distance 100D.

NASA/TM—2010-216328 41
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2088

(g) Mj = 1.050, NPR = 2.004, Tt/T∞ = 1.77, β = 0.319

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2089

(h) Mj = 1.182, NPR = 2.365, Tt/T∞ = 1.77, β = 0.630

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2090

(i) Mj = 1.392, NPR = 3.143, Tt/T∞ = 1.76, β = 0.968

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2091

(j) Mj = 1.492, NPR = 3.627, Tt/T∞ = 1.76, β = 1.108

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2092

(k) Mj = 1.660, NPR = 4.644, Tt/T∞ = 1.77, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2093

(l) Mj = 1.792, NPR = 5.674, Tt/T∞ = 1.76, β = 1.487

Figure 10: (50 Deg., Cont.)

NASA/TM—2010-216328 42
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2100

(m) Mj = 1.045, NPR = 1.989, Tt/T∞ = 2.16, β = 0.305

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2098

(n) Mj = 1.181, NPR = 2.356, Tt/T∞ = 2.16, β = 0.628

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2097

(o) Mj = 1.390, NPR = 3.130, Tt/T∞ = 2.16, β = 0.966

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2096

(p) Mj = 1.494, NPR = 3.629, Tt/T∞ = 2.16, β = 1.109

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2095

(q) Mj = 1.660, NPR = 4.638, Tt/T∞ = 2.16, β = 1.324

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2094

(r) Mj = 1.794, NPR = 5.685, Tt/T∞ = 2.16, β = 1.489

Figure 10: (50 Deg., Cont.)

NASA/TM—2010-216328 43
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2102

(s) Mj = 1.048, NPR = 1.987, Tt/T∞ = 2.66, β = 0.314

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2103

(t) Mj = 1.175, NPR = 2.327, Tt/T∞ = 2.65, β = 0.617

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2104

(u) Mj = 1.391, NPR = 3.120, Tt/T∞ = 2.66, β = 0.967

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2105

(v) Mj = 1.490, NPR = 3.597, Tt/T∞ = 2.65, β = 1.105

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2106

(w) Mj = 1.660, NPR = 4.630, Tt/T∞ = 2.64, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2107

(x) Mj = 1.789, NPR = 5.638, Tt/T∞ = 2.65, β = 1.484

Figure 10: (50 Deg., Cont.)

NASA/TM—2010-216328 44
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2079

(a) Mj = 1.049, NPR = 2.005, Tt/T∞ = 1.01, β = 0.315

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2080

(b) Mj = 1.178, NPR = 2.358, Tt/T∞ = 1.01, β = 0.623

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2081

(c) Mj = 1.392, NPR = 3.147, Tt/T∞ = 1.01, β = 0.969

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2082

(d) Mj = 1.493, NPR = 3.636, Tt/T∞ = 1.01, β = 1.109

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2083

(e) Mj = 1.660, NPR = 4.647, Tt/T∞ = 1.01, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2085

(f) Mj = 1.796, NPR = 5.708, Tt/T∞ = 1.01, β = 1.491

Figure 11: 1/3-Octave spectra comparisons of jet shock-associated noise prediction models to the shockassociated noise component spectra for measured data from jets with shocks at a 90 degree inlet angle and

distance 100D.

NASA/TM—2010-216328 45
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2088

(g) Mj = 1.049, NPR = 2.004, Tt/T∞ = 1.77, β = 0.319

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2089

(h) Mj = 1.182, NPR = 2.365, Tt/T∞ = 1.77, β = 0.630

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2090

(i) Mj = 1.392, NPR = 3.143, Tt/T∞ = 1.76, β = 0.968

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2091

(j) Mj = 1.492, NPR = 3.627, Tt/T∞ = 1.76, β = 1.108

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2092

(k) Mj = 1.660, NPR = 4.644, Tt/T∞ = 1.77, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2093

(l) Mj = 1.792, NPR = 5.674, Tt/T∞ = 1.76, β = 1.487

Figure 11: (90 Deg., Cont.)

NASA/TM—2010-216328 46
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2100

(m) Mj = 1.045, NPR = 1.989, Tt/T∞ = 2.16, β = 0.305

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2098

(n) Mj = 1.181, NPR = 2.356, Tt/T∞ = 2.16, β = 0.628

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2097

(o) Mj = 1.390, NPR = 3.130, Tt/T∞ = 2.16, β = 0.966

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2096

(p) Mj = 1.494, NPR = 3.629, Tt/T∞ = 2.16, β = 1.109

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2095

(q) Mj = 1.660, NPR = 4.638, Tt/T∞ = 2.16, β = 1.324

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2094

(r) Mj = 1.794, NPR = 5.685, Tt/T∞ = 2.16, β = 1.489

Figure 11: (90 Deg., Cont.)

NASA/TM—2010-216328 47
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2102

(s) Mj = 1.048, NPR = 1.987, Tt/T∞ = 2.66, β = 0.314

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2103

(t) Mj = 1.175, NPR = 2.327, Tt/T∞ = 2.65, β = 0.617

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2104

(u) Mj = 1.391, NPR = 3.120, Tt/T∞ = 2.66, β = 0.967

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2105

(v) Mj = 1.490, NPR = 3.597, Tt/T∞ = 2.65, β = 1.105

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2106

(w) Mj = 1.660, NPR = 4.630, Tt/T∞ = 2.64, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2107

(x) Mj = 1.789, NPR = 5.638, Tt/T∞ = 2.65, β = 1.484

Figure 11: (90 Deg., Cont.)

NASA/TM—2010-216328 48
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2079

(a) Mj = 1.049, NPR = 2.005, Tt/T∞ = 1.01, β = 0.315

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2080

(b) Mj = 1.178, NPR = 2.358, Tt/T∞ = 1.01, β = 0.623

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2081

(c) Mj = 1.392, NPR = 3.147, Tt/T∞ = 1.01, β = 0.969

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2082

(d) Mj = 1.493, NPR = 3.636, Tt/T∞ = 1.01, β = 1.109

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2083

(e) Mj = 1.660, NPR = 4.647, Tt/T∞ = 1.01, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2085

(f) Mj = 1.796, NPR = 5.708, Tt/T∞ = 1.01, β = 1.491

Figure 12: 1/3-Octave spectra comparisons of jet shock-associated noise prediction models to the shockassociated noise component spectra for measured data from jets with shocks at a 120 degree inlet angle and

distance 100D.

NASA/TM—2010-216328 49
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2088

(g) Mj = 1.049, NPR = 2.004, Tt/T∞ = 1.77, β = 0.319

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2089

(h) Mj = 1.182, NPR = 2.365, Tt/T∞ = 1.77, β = 0.630

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2090

(i) Mj = 1.392, NPR = 3.143, Tt/T∞ = 1.76, β = 0.968

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2091

(j) Mj = 1.492, NPR = 3.627, Tt/T∞ = 1.76, β = 1.108

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2092

(k) Mj = 1.660, NPR = 4.644, Tt/T∞ = 1.77, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2093

(l) Mj = 1.792, NPR = 5.674, Tt/T∞ = 1.76, β = 1.487

Figure 12: (120 Deg., Cont.)

NASA/TM—2010-216328 50
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2100

(m) Mj = 1.045, NPR = 1.989, Tt/T∞ = 2.16, β = 0.305

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2098

(n) Mj = 1.181, NPR = 2.356, Tt/T∞ = 2.16, β = 0.628

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2097

(o) Mj = 1.390, NPR = 3.130, Tt/T∞ = 2.16, β = 0.966

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2096

(p) Mj = 1.494, NPR = 3.629, Tt/T∞ = 2.16, β = 1.109

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2095

(q) Mj = 1.660, NPR = 4.638, Tt/T∞ = 2.16, β = 1.324

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2094

(r) Mj = 1.794, NPR = 5.685, Tt/T∞ = 2.16, β = 1.489

Figure 12: (120 Deg., Cont.)

NASA/TM—2010-216328 51
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2102

(s) Mj = 1.048, NPR = 1.987, Tt/T∞ = 2.66, β = 0.314

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2103

(t) Mj = 1.175, NPR = 2.327, Tt/T∞ = 2.65, β = 0.617

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2104

(u) Mj = 1.391, NPR = 3.120, Tt/T∞ = 2.66, β = 0.967

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2105

(v) Mj = 1.490, NPR = 3.597, Tt/T∞ = 2.65, β = 1.105

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2106

(w) Mj = 1.660, NPR = 4.630, Tt/T∞ = 2.64, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (Simplified)

Shock (TAMSHK)

Shock (ST2JET)

Nozzle: smc021, Rdg #: 2107

(x) Mj = 1.789, NPR = 5.638, Tt/T∞ = 2.65, β = 1.484

Figure 12: (120 Deg., Cont.)

NASA/TM—2010-216328 52
! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

"2.4

9.2

(a) Peak level error, 50 degrees.

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

"3.9

9.8

(b) Peak level error, 90 degrees.

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

"7.8

6.6

(c) Peak level error, 120 degrees. ! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

0.8

7.8

(d) Peak frequency error, 50 degrees.

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

0.8

4.0

(e) Peak frequency error, 90 degrees.

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

0.8

3.1

(f) Peak frequency error, 120 degrees.

Figure 13: Simplified Model. (a-c) Error in broadband shock-associated noise 1/3-octave band peak

level (dB(predicted) - dB(measured)). Black line = 0 dB. (d-f) Relative 1/3-octave band peak frequency

fp(predicted)/fp(measured). Black line = 1. Data located at positions of black dots.

NASA/TM—2010-216328 53
! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

"1.6

7.4

(a) Peak level error, 50 degrees.

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

"2.2

7.4

(b) Peak level error, 90 degrees.

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

"12.4

1.8

(c) Peak level error, 120 degrees. ! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

0.02

8.0

(d) Peak frequency error, 50 degrees.

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

0.8

4.0

(e) Peak frequency error, 90 degrees.

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

0.8

2.5

(f) Peak frequency error, 120 degrees.

Figure 14: TAMSHK Module. (a-c) Error in broadband shock-associated noise 1/3-octave band peak

level (dB(predicted) - dB(measured)). Black line = 0 dB. (d-f) Relative 1/3-octave band peak frequency

fp(predicted)/fp(measured). Black line = 1. Data located at positions of black dots.

NASA/TM—2010-216328 54
! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

"3.8

13.5

(a) Peak level error, 50 degrees.

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

"7.0

12.2

(b) Peak level error, 90 degrees.

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

"14.7

0.0

(c) Peak level error, 120 degrees. ! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

0.6

6.3

(d) Peak frequency error, 50 degrees.

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

0.6

2.5

(e) Peak frequency error, 90 degrees.

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

! ! ! ! ! !

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1.0

1.5

2.0

2.5

Mj

Tt

!

T!

0.5

2.0

(f) Peak frequency error, 120 degrees.

Figure 15: ST2JET Module. (a-c) Error in broadband shock-associated noise 1/3-octave band peak

level (dB(predicted) - dB(measured)). Black line = 0 dB. (d-f) Relative 1/3-octave band peak frequency

fp(predicted)/fp(measured). Black line = 1. Data located at positions of black dots.

NASA/TM—2010-216328 55
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2079

(a) Mj = 1.049, NPR = 2.005, Tt/T∞ = 1.01, β = 0.315

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2080

(b) Mj = 1.178, NPR = 2.358, Tt/T∞ = 1.01, β = 0.623

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2081

(c) Mj = 1.392, NPR = 3.147, Tt/T∞ = 1.01, β = 0.969

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2082

(d) Mj = 1.493, NPR = 3.636, Tt/T∞ = 1.01, β = 1.109

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2083

(e) Mj = 1.660, NPR = 4.647, Tt/T∞ = 1.01, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2085

(f) Mj = 1.796, NPR = 5.708, Tt/T∞ = 1.01, β = 1.491

Figure 16: 1/3-Octave spectra comparisons of jet noise prediction models to the total and shock component

noise spectra for measured data from jets with shocks at a 50 degree inlet angle and distance 100D.

NASA/TM—2010-216328 56
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2088

(g) Mj = 1.050, NPR = 2.004, Tt/T∞ = 1.77, β = 0.319

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2089

(h) Mj = 1.182, NPR = 2.365, Tt/T∞ = 1.77, β = 0.630

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2090

(i) Mj = 1.392, NPR = 3.143, Tt/T∞ = 1.76, β = 0.968

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2091

(j) Mj = 1.492, NPR = 3.627, Tt/T∞ = 1.76, β = 1.108

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2092

(k) Mj = 1.660, NPR = 4.644, Tt/T∞ = 1.77, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2093

(l) Mj = 1.792, NPR = 5.674, Tt/T∞ = 1.76, β = 1.487

Figure 16: (50 Deg., Cont.)

NASA/TM—2010-216328 57
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2100

(m) Mj = 1.045, NPR = 1.989, Tt/T∞ = 2.16, β = 0.305

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2098

(n) Mj = 1.181, NPR = 2.356, Tt/T∞ = 2.16, β = 0.628

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2097

(o) Mj = 1.390, NPR = 3.130, Tt/T∞ = 2.16, β = 0.966

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2096

(p) Mj = 1.494, NPR = 3.629, Tt/T∞ = 2.16, β = 1.109

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2095

(q) Mj = 1.660, NPR = 4.638, Tt/T∞ = 2.16, β = 1.324

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2094

(r) Mj = 1.794, NPR = 5.685, Tt/T∞ = 2.16, β = 1.489

Figure 16: (50 Deg., Cont.)

NASA/TM—2010-216328 58
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2102

(s) Mj = 1.048, NPR = 1.987, Tt/T∞ = 2.66, β = 0.314

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2103

(t) Mj = 1.175, NPR = 2.327, Tt/T∞ = 2.65, β = 0.617

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2104

(u) Mj = 1.391, NPR = 3.120, Tt/T∞ = 2.66, β = 0.967

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2105

(v) Mj = 1.490, NPR = 3.597, Tt/T∞ = 2.65, β = 1.105

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2106

(w) Mj = 1.660, NPR = 4.630, Tt/T∞ = 2.64, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2107

(x) Mj = 1.789, NPR = 5.638, Tt/T∞ = 2.65, β = 1.484

Figure 16: (50 Deg., Cont.)

NASA/TM—2010-216328 59
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2079

(a) Mj = 1.049, NPR = 2.005, Tt/T∞ = 1.01, β = 0.315

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2080

(b) Mj = 1.178, NPR = 2.358, Tt/T∞ = 1.01, β = 0.623

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2081

(c) Mj = 1.392, NPR = 3.147, Tt/T∞ = 1.01, β = 0.969

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2082

(d) Mj = 1.493, NPR = 3.636, Tt/T∞ = 1.01, β = 1.109

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2083

(e) Mj = 1.660, NPR = 4.647, Tt/T∞ = 1.01, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2085

(f) Mj = 1.796, NPR = 5.708, Tt/T∞ = 1.01, β = 1.491

Figure 17: 1/3-Octave spectra comparisons of jet noise prediction models to the total and shock component

noise spectra for measured data from jets with shocks at a 90 degree inlet angle and distance 100D.

NASA/TM—2010-216328 60
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2088

(g) Mj = 1.049, NPR = 2.004, Tt/T∞ = 1.77, β = 0.319

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2089

(h) Mj = 1.182, NPR = 2.365, Tt/T∞ = 1.77, β = 0.630

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2090

(i) Mj = 1.392, NPR = 3.143, Tt/T∞ = 1.76, β = 0.968

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2091

(j) Mj = 1.492, NPR = 3.627, Tt/T∞ = 1.76, β = 1.108

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2092

(k) Mj = 1.660, NPR = 4.644, Tt/T∞ = 1.77, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2093

(l) Mj = 1.792, NPR = 5.674, Tt/T∞ = 1.76, β = 1.487

Figure 17: (90 Deg., Cont.)

NASA/TM—2010-216328 61
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2100

(m) Mj = 1.045, NPR = 1.989, Tt/T∞ = 2.16, β = 0.305

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2098

(n) Mj = 1.181, NPR = 2.356, Tt/T∞ = 2.16, β = 0.628

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2097

(o) Mj = 1.390, NPR = 3.130, Tt/T∞ = 2.16, β = 0.966

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2096

(p) Mj = 1.494, NPR = 3.629, Tt/T∞ = 2.16, β = 1.109

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2095

(q) Mj = 1.660, NPR = 4.638, Tt/T∞ = 2.16, β = 1.324

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2094

(r) Mj = 1.794, NPR = 5.685, Tt/T∞ = 2.16, β = 1.489

Figure 17: (90 Deg., Cont.)

NASA/TM—2010-216328 62
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2102

(s) Mj = 1.048, NPR = 1.987, Tt/T∞ = 2.66, β = 0.314

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2103

(t) Mj = 1.175, NPR = 2.327, Tt/T∞ = 2.65, β = 0.617

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2104

(u) Mj = 1.391, NPR = 3.120, Tt/T∞ = 2.66, β = 0.967

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2105

(v) Mj = 1.490, NPR = 3.597, Tt/T∞ = 2.65, β = 1.105

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2106

(w) Mj = 1.660, NPR = 4.630, Tt/T∞ = 2.64, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2107

(x) Mj = 1.789, NPR = 5.638, Tt/T∞ = 2.65, β = 1.484

Figure 17: (90 Deg., Cont.)

NASA/TM—2010-216328 63
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2079

(a) Mj = 1.049, NPR = 2.005, Tt/T∞ = 1.01, β = 0.315

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2080

(b) Mj = 1.178, NPR = 2.358, Tt/T∞ = 1.01, β = 0.623

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2081

(c) Mj = 1.392, NPR = 3.147, Tt/T∞ = 1.01, β = 0.969

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2082

(d) Mj = 1.493, NPR = 3.636, Tt/T∞ = 1.01, β = 1.109

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2083

(e) Mj = 1.660, NPR = 4.647, Tt/T∞ = 1.01, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2085

(f) Mj = 1.796, NPR = 5.708, Tt/T∞ = 1.01, β = 1.491

Figure 18: 1/3-Octave spectra comparisons of jet noise prediction models to the total and shock component

noise spectra for measured data from jets with shocks at a 120 degree inlet angle and distance 100D.

NASA/TM—2010-216328 64
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2088

(g) Mj = 1.049, NPR = 2.004, Tt/T∞ = 1.77, β = 0.319

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2089

(h) Mj = 1.182, NPR = 2.365, Tt/T∞ = 1.77, β = 0.630

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2090

(i) Mj = 1.392, NPR = 3.143, Tt/T∞ = 1.76, β = 0.968

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2091

(j) Mj = 1.492, NPR = 3.627, Tt/T∞ = 1.76, β = 1.108

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2092

(k) Mj = 1.660, NPR = 4.644, Tt/T∞ = 1.77, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2093

(l) Mj = 1.792, NPR = 5.674, Tt/T∞ = 1.76, β = 1.487

Figure 18: (120 Deg., Cont.)

NASA/TM—2010-216328 65
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2100

(m) Mj = 1.045, NPR = 1.989, Tt/T∞ = 2.16, β = 0.305

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2098

(n) Mj = 1.181, NPR = 2.356, Tt/T∞ = 2.16, β = 0.628

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2097

(o) Mj = 1.390, NPR = 3.130, Tt/T∞ = 2.16, β = 0.966

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2096

(p) Mj = 1.494, NPR = 3.629, Tt/T∞ = 2.16, β = 1.109

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2095

(q) Mj = 1.660, NPR = 4.638, Tt/T∞ = 2.16, β = 1.324

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2094

(r) Mj = 1.794, NPR = 5.685, Tt/T∞ = 2.16, β = 1.489

Figure 18: (120 Deg., Cont.)

NASA/TM—2010-216328 66
10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2102

(s) Mj = 1.048, NPR = 1.987, Tt/T∞ = 2.66, β = 0.314

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2103

(t) Mj = 1.175, NPR = 2.327, Tt/T∞ = 2.65, β = 0.617

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2104

(u) Mj = 1.391, NPR = 3.120, Tt/T∞ = 2.66, β = 0.967

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2105

(v) Mj = 1.490, NPR = 3.597, Tt/T∞ = 2.65, β = 1.105

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2106

(w) Mj = 1.660, NPR = 4.630, Tt/T∞ = 2.64, β = 1.325

10-2 10-1 100 101

Strouhal Number

20

40

60

80

100

120

1/3rd-Octave SPL (dB) - Lossless

Total

Shock

Shock (SAESHK)

Total (ST2JET)

Nozzle: smc021, Rdg #: 2107

(x) Mj = 1.789, NPR = 5.638, Tt/T∞ = 2.65, β = 1.484

Figure 18: (120 Deg., Cont.)

NASA/TM—2010-216328 67
10-1 100 101

Strouhal Number

90

100

110

120

130

140

SPL (dB) per unit St

Total

Shock

Mixing w/Amp.

Shock (Tam)

Shock (RANS-based)

(a) Power Spectral Density at 50 degrees.

10-1 100 101

Strouhal Number

40

60

80

100

120

1/3rd-Octave SPL (dB)

Shock

Shock (Simplified)

Shock (Tam)

Shock (ST2JET)

Shock (RANS-based)

(b) 1/3-Octave Spectra at 50 degrees.

10-1 100 101

Strouhal Number

90

100

110

120

130

140

SPL (dB) per unit St

Total

Shock

Mixing w/Amp.

Shock (Tam)

Shock (RANS-based)

(c) Power Spectral Density at 60 degrees.

10-1 100 101

Strouhal Number

40

60

80

100

120

1/3rd-Octave SPL (dB)

Shock

Shock (Simplified)

Shock (Tam)

Shock (ST2JET)

Shock (RANS-based)

(d) 1/3-Octave Spectra at 60 degrees.

10-1 100 101

Strouhal Number

90

100

110

120

130

140

SPL (dB) per unit St

Total

Shock

Mixing w/Amp.

Shock (Tam)

Shock (RANS-based)

(e) Power Spectral Density at 70 degrees.

10-1 100 101

Strouhal Number

40

60

80

100

120

1/3rd-Octave SPL (dB)

Shock

Shock (Simplified)

Shock (Tam)

Shock (ST2JET)

Shock (RANS-based)

(f) 1/3-Octave Spectra at 70 degrees.

Figure 19: Spectral comparisons of jet shock associated noise prediction models to the jet noise component

spectra for measured data from jets with shocks at a distance 100D; Mj = 1.493, NPR = 3.636, Tt/T∞ = 1.01.

NASA/TM—2010-216328 68
10-1 100 101

Strouhal Number

90

100

110

120

130

140

SPL (dB) per unit St

Total

Shock

Mixing w/Amp.

Shock (Tam)

Shock (RANS-based)

(g) Power Spectral Density at 80 degrees.

10-1 100 101

Strouhal Number

40

60

80

100

120

1/3rd-Octave SPL (dB)

Shock

Shock (Simplified)

Shock (Tam)

Shock (ST2JET)

Shock (RANS-based)

(h) 1/3-Octave Spectra at 80 degrees.

10-1 100 101

Strouhal Number

90

100

110

120

130

140

SPL (dB) per unit St

Total

Shock

Mixing w/Amp.

Shock (Tam)

Shock (RANS-based)

(i) Power Spectral Density at 90 degrees.

10-1 100 101

Strouhal Number

40

60

80

100

120

1/3rd-Octave SPL (dB)

Shock

Shock (Simplified)

Shock (Tam)

Shock (ST2JET)

Shock (RANS-based)

(j) 1/3-Octave Spectra at 90 degrees.

10-1 100 101

Strouhal Number

90

100

110

120

130

140

SPL (dB) per unit St

Total

Shock

Mixing w/Amp.

Shock (Tam)

Shock (RANS-based)

(k) Power Spectral Density at 100 degrees.

10-1 100 101

Strouhal Number

40

60

80

100

120

1/3rd-Octave SPL (dB)

Shock

Shock (Simplified)

Shock (Tam)

Shock (ST2JET)

Shock (RANS-based)

(l) 1/3-Octave Spectra at 100 degrees.

Figure 19: (Tt/T∞ = 1.01, Cont.)

NASA/TM—2010-216328 69
10-1 100 101

Strouhal Number

90

100

110

120

130

140

SPL (dB) per unit St

Total

Shock

Mixing w/Amp.

Shock (Tam)

Shock (RANS-based)

(m) Power Spectral Density at 110 degrees.

10-1 100 101

Strouhal Number

40

60

80

100

120

1/3rd-Octave SPL (dB)

Shock

Shock (Simplified)

Shock (Tam)

Shock (ST2JET)

Shock (RANS-based)

(n) 1/3-Octave Spectra at 110 degrees.

10-1 100 101

Strouhal Number

90

100

110

120

130

140

SPL (dB) per unit St

Total

Shock

Mixing w/Amp.

Shock (Tam)

Shock (RANS-based)

(o) Power Spectral Density at 120 degrees.

10-1 100 101

Strouhal Number

40

60

80

100

120

1/3rd-Octave SPL (dB)

Shock

Shock (Simplified)

Shock (Tam)

Shock (ST2JET)

Shock (RANS-based)

(p) 1/3-Octave Spectra at 120 degrees.

Figure 19: (Tt/T∞ = 1.01, Cont.)

NASA/TM—2010-216328 70
10-1 100 101

Strouhal Number

90

100

110

120

130

140

SPL (dB) per unit St

Total

Shock

Mixing w/Amp.

Shock (Tam)

Shock (RANS-based)

(a) Power Spectral Density at 50 degrees.

10-1 100 101

Strouhal Number

40

60

80

100

120

1/3rd-Octave SPL (dB)

Shock

Shock (Simplified)

Shock (Tam)

Shock (ST2JET)

Shock (RANS-based)

(b) 1/3-Octave Spectra at 50 degrees.

10-1 100 101

Strouhal Number

90

100

110

120

130

140

SPL (dB) per unit St

Total

Shock

Mixing w/Amp.

Shock (Tam)

Shock (RANS-based)

(c) Power Spectral Density at 60 degrees.

10-1 100 101

Strouhal Number

40

60

80

100

120

1/3rd-Octave SPL (dB)

Shock

Shock (Simplified)

Shock (Tam)

Shock (ST2JET)

Shock (RANS-based)

(d) 1/3-Octave Spectra at 60 degrees.

10-1 100 101

Strouhal Number

90

100

110

120

130

140

SPL (dB) per unit St

Total

Shock

Mixing w/Amp.

Shock (Tam)

Shock (RANS-based)

(e) Power Spectral Density at 70 degrees.

10-1 100 101

Strouhal Number

40

60

80

100

120

1/3rd-Octave SPL (dB)

Shock

Shock (Simplified)

Shock (Tam)

Shock (ST2JET)

Shock (RANS-based)

(f) 1/3-Octave Spectra at 70 degrees.

Figure 20: Spectral comparisons of jet shock associated noise prediction models to the jet noise component

spectra for measured data from jets with shocks at a distance 100D; Mj = 1.494, NPR = 3.629, Tt/T∞ = 2.16.

NASA/TM—2010-216328 71
10-1 100 101

Strouhal Number

90

100

110

120

130

140

SPL (dB) per unit St

Total

Shock

Mixing w/Amp.

Shock (Tam)

Shock (RANS-based)

(g) Power Spectral Density at 80 degrees.

10-1 100 101

Strouhal Number

40

60

80

100

120

1/3rd-Octave SPL (dB)

Shock

Shock (Simplified)

Shock (Tam)

Shock (ST2JET)

Shock (RANS-based)

(h) 1/3-Octave Spectra at 80 degrees.

10-1 100 101

Strouhal Number

90

100

110

120

130

140

SPL (dB) per unit St

Total

Shock

Mixing w/Amp.

Shock (Tam)

Shock (RANS-based)

(i) Power Spectral Density at 90 degrees.

10-1 100 101

Strouhal Number

40

60

80

100

120

1/3rd-Octave SPL (dB)

Shock

Shock (Simplified)

Shock (Tam)

Shock (ST2JET)

Shock (RANS-based)

(j) 1/3-Octave Spectra at 90 degrees.

10-1 100 101

Strouhal Number

90

100

110

120

130

140

SPL (dB) per unit St

Total

Shock

Mixing w/Amp.

Shock (Tam)

Shock (RANS-based)

(k) Power Spectral Density at 100 degrees.

10-1 100 101

Strouhal Number

40

60

80

100

120

1/3rd-Octave SPL (dB)

Shock

Shock (Simplified)

Shock (Tam)

Shock (ST2JET)

Shock (RANS-based)

(l) 1/3-Octave Spectra at 100 degrees.

Figure 20: (Tt/T∞ = 2.16, Cont.)

NASA/TM—2010-216328 72
10-1 100 101

Strouhal Number

90

100

110

120

130

140

SPL (dB) per unit St

Total

Shock

Mixing w/Amp.

Shock (Tam)

Shock (RANS-based)

(m) Power Spectral Density at 110 degrees.

10-1 100 101

Strouhal Number

40

60

80

100

120

1/3rd-Octave SPL (dB)

Shock

Shock (Simplified)

Shock (Tam)

Shock (ST2JET)

Shock (RANS-based)

(n) 1/3-Octave Spectra at 110 degrees.

10-1 100 101

Strouhal Number

90

100

110

120

130

140

SPL (dB) per unit St

Total

Shock

Mixing w/Amp.

Shock (Tam)

Shock (RANS-based)

(o) Power Spectral Density at 120 degrees.

10-1 100 101

Strouhal Number

40

60

80

100

120

1/3rd-Octave SPL (dB)

Shock

Shock (Simplified)

Shock (Tam)

Shock (ST2JET)

Shock (RANS-based)

(p) 1/3-Octave Spectra at 120 degrees.

Figure 20: (Tt/T∞ = 2.16, Cont.)

NASA/TM—2010-216328 73
40 50 60 70 80 90 100 110 120 130

Inlet Angle (Degrees)

-6

-5

-4

-3

-2

-1

0

1

2

3

Peak Error dB(Pred) - dB(Meas)

Tt/T

!=1.01, Tam

Tt/T

!=1.01, RANS-based

Tt/T

!=2.16, Tam

Tt/T

!=2.16, RANS-based

(a) PSD Peak Level Error.

40 50 60 70 80 90 100 110 120 130

Inlet Angle (Degrees)

0.6

0.8

1

1.2

1.4

1.6

Strouhal No. Error St

p(Pred)/St

p(Meas)

Tt/T

!=1.01, Tam

Tt/T

!=1.01, RANS-based

Tt/T

!=2.16, Tam

Tt/T

!=2.16, RANS-based

(b) PSD Peak Strouhal No. Error.

Figure 21: Errors in peak level and Strouhal number between predicted and measured shock-associated noise

values from the power spectral density (PSD) data in Figures 19 and 20.

40 50 60 70 80 90 100 110 120 130

Inlet Angle (Degrees)

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

Peak Error dB(Pred) - dB(Meas)

Simplified

Tam

ST2JET

RANS-based

(a) 1/3-Octave Peak Level Error, Tt/T∞ = 1.01.

40 50 60 70 80 90 100 110 120 130

Inlet Angle (Degrees)

-8

-7

-6

-5

-4

-3

-2

-1

0

1

Peak Error dB(Pred) - dB(Meas)

Simplified

Tam

ST2JET

RANS-based

(b) 1/3-Octave Peak Level Error, Tt/T∞ = 2.16.

40 50 60 70 80 90 100 110 120 130

Inlet Angle (Degrees)

0.6

0.8

1

1.2

1.4

1.6

Strouhal No. Error St

p(Pred)/St

p(Meas)

Simplified

Tam

ST2JET

RANS-based

(c) 1/3-Octave Peak Strouhal No. Error, Tt/T∞ = 1.01.

40 50 60 70 80 90 100 110 120 130

Inlet Angle (Degrees)

0.6

0.8

1

1.2

1.4

1.6

Strouhal No. Error St

p(Pred)/St

p(Meas)

Simplified

Tam

ST2JET

RANS-based

(d) 1/3-Octave Peak Strouhal No. Error, Tt/T∞ = 2.16.

Figure 22: Errors in peak level and Strouhal number between predicted and measured shock-associated noise

values from the 1/3-octave spectral data in Figures 19 and 20.

NASA/TM—2010-216328 74
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4. TITLE AND SUBTITLE

Predictions of Supersonic Jet Mixing and Shock-Associated Noise Compared with Measured 

Far-Field Data 

5a. CONTRACT NUMBER

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6. AUTHOR(S)

Dahl, Milo, D. 

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WBS 984754.02.07.03.17.02 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

Codes for predicting supersonic jet mixing and broadband shock-associated noise were assessed using a database containing noise

measurements of a jet issuing from a convergent nozzle. Two types of codes were used to make predictions. Fast running codes containing 

empirical models were used to compute both the mixing noise component and the shock-associated noise component of the jet noise

spectrum. One Reynolds-averaged, Navier-Stokes-based code was used to compute only the shock-associated noise. To enable the 

comparisons of the predicted component spectra with data, the measured total jet noise spectra were separated into mixing noise and shockassociated noise components. Comparisons were made for 1/3-octave spectra and some power spectral densities using data from jets 

operating at 24 conditions covering essentially 6 fully expanded Mach numbers with 4 total temperature ratios. 

15. SUBJECT TERMS

Jet noise; Noise prediction; Propulsion noise; Flow noise; Noise; Shocks; Supersonic jets; Accuracy 

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