Clifford A. Brown

Glenn Research Center, Cleveland, Ohio

Developing an Empirical Model for Jet-Surface

Interaction Noise

NASA/TM—2014-218120

June 2014

AIAA–2014–0878
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Clifford A. Brown

Glenn Research Center, Cleveland, Ohio

Developing an Empirical Model for Jet-Surface

Interaction Noise

NASA/TM—2014-218120

June 2014

AIAA–2014–0878

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

SciTech 2014

sponsored by the American Institute of Aeronautics and Astronautics

National Harbor, Maryland, January 13–17, 2014
Acknowledgments

This work was supported by the NASA Fundamental Aeronautics Program, Fixed Wing and High Speed.

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Available electronically at http://www.sti.nasa.gov

Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

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. 
The process of developing an empirical model for jet-surface interaction noise is described

and the resulting model evaluated. Jet-surface interaction noise is generated when the

high-speed engine exhaust from modern tightly integrated or conventional high-bypass

ratio engine aircraft strikes or flows over the airframe surfaces. An empirical model based

on an existing experimental database is developed for use in preliminary design system

level studies where computation speed and range of configurations is valued over absolute

accuracy to select the most promising (or eliminate the worst) possible designs. The model

developed assumes that the jet-surface interaction noise spectra can be separated from

the jet mixing noise and described as a parabolic function with three coefficients: peak

amplitude, spectral width, and peak frequency. These coefficients are fit to functions of

surface length and distance from the jet lipline to form a characteristic spectra which is then

adjusted for changes in jet velocity and/or observer angle using scaling laws from published

theoretical and experimental work. The resulting model is then evaluated for its ability to

reproduce the characteristic spectra and then for reproducing spectra measured at other

jet velocities and observer angles; successes and limitations are discussed considering the

complexity of the jet-surface interaction noise versus the desire for a model that is simple

to implement and quick to execute.

I. Introduction

M

odern aircraft designs may employ complex geometry exhaust systems to maximize efficiency or reduce

noise. Subsonic aircraft, for example, have benefited from the reduced noise and improved fuel efficiency

offered by the current high bypass ratio engines. These larger engines, however, have pushed the exhaust

closer to the airframe surfaces where interactions between the exhaust gases and the hard surfaces may

create a new noise problem: jet-surface interaction noise. Supersonic aircraft, in an effort to minimize sonic

boom, have moved to embedded engine designs which often exhaust gases over aft airframe surfaces creating

a similar noise problem, and while the performance impact of these configurations is fairly well understood,

the noise implications remain difficult to predict.

A system level study incorporating many aircraft components combines predictions of performance,

efficiency, and noise until the optimal design is determined. However, the ability to predict the noise created

or shielded when a high-speed engine exhaust interacts with an airframe surface has been, historically, limited.

Physics based exhaust noise prediction methods, that incorporate nearby surfaces, are not yet a viable for

for optimization design studies over a large parameter space due to either limiting assumptions or long

solution times. Acoustic analogies, for example, rely on Reynolds-Averaged-Navier-Stokes computations,

which themselves are time consuming, for information about the flow generally assume that the jet is in

free-space. More recent predictions using Large Eddy Simulations may include a surface but require far too

much time for a system level study (especially if the surface boundary layer must be resolved). However,

an empirical model based on available experimental data can offer a first-order approximation of the affect

aircraft surfaces near the engine exhaust have on the overall noise levels within the experimental variable

space and with a rapid solution time.

An extensive database of jet-surface interaction noise measurements over several tests conducted at the

NASA Glenn Research Center’s Aero-Acoustic Propulsion Laboratory and supported by both the Fixed

Developing an Empirical Model for Jet-Surface Interaction Noise 

Clifford A. Brown 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

NASA/TM—2014-218120 1
Wing and High Speed Projects under the Fundamental Aeronautics Program. These far-field noise data

form the basis for an empirical model capable of describing the surface trailing edge noise spectra across

a range of surface lengths, distances, and subsonic jet velocities (which apply during airport operations in

both subsonic and supersonic aircraft). A common and simple geometry, a flat plate and a round convergent

nozzle, has been used to create general jet-surface configuration upon which an empirical model can be

developed, modified, and augmented to provide a first-order approximation applicable to many common

aircraft configurations. The jet-surface interaction noise is separated from the jet mixing noise and the

surface shielding (or reflecting) effects to model one component of the larger jet-surface interaction problem.

This separation is important because it provides a basic building block that can be expanded independent

from other considerations; for example, the trailing edge noise may be a function of nozzle aspect ratio1

but the noise shielding might only depend on the surface length and span so the a modification factor

for aspect ratio can be applied to the jet-surface interaction noise model while the noise shielding model

remains unchanged. Once extracted, a series of mathematical functions are fitted onto the far-field jet-surface

interaction noise data to give representation of the complete spectra at for any surface length and distance

within the limits of the original database. The result is consistent with many system level tools that rely on

their ability to quickly run thousands of cases in order to determine a range of the best possible outcomes

for more detailed study with actual geometries and jet exit conditions.

II. Test Setup, Data Acquisition and Processing

Jet-surface interaction tests were conducted using the Small Hot Jet Acoustic Rig (SHJAR) located

in the Aero-Acoustic Propulsion Laboratory (AAPL) at the NASA Glenn Research Center (GRC). The

SHJAR is capable of supplying air at flow rates up to 2.7 kg/s to a single-steam nozzle. A hydrogen burning

combustor is used to simulate core exhaust at temperatures up to 975 ◦K. Flow conditioning and a lineof-sight muffler are used to achieve a clean and quiet flow at jet exit Mach numbers down to Ma = 0.35.

Additional information on the SHJAR, including performance validation data, can be found in.2, 3 The

AAPL is covered with wedges to provide an anechoic environment at frequencies above 200 Hz. To ensure

the correct operating conditions, each operating point, as defined by a Mach number and temperature ratio

(Table 1), was entered into the AAPL facility data acquisition system, which monitored all relevant rig

temperatures and pressures once per second to compute the difference between the current and specified jet

exit conditions (based on an L2-norm). The jet condition was required to be within 0.5% of the specified

value throughout the acquisition for an acoustic point to be accepted. The AAPL data system also acquired

and stored the ambient conditions for later reference and data corrections.

The configuration common to all these experiments was formed using a flat plate near an axisymmetric

De = 2” nozzle (Figure 1). The surface was fabricated using a single plate around the nozzle and a single

trailing edge piece. Inserts were used to extend the surface between 1.3 ≤ xT E/De ≤ 10. Each piece was

created using 1/2” thick aluminum sheet with the trailing edge piece tapered to a 45◦ angle. The plate was

mounted to an automated traverse and allowed to move between 0.5 ≤ h/De ≤ 5 in the radial direction. A

complete list of surface positions used for the empirical model is given in Table 2. Note that far-field noise

data were acquired on both the ’shielded’ (φ = 0◦) and ’reflected’ (φ = 180◦) sides of the surface as identified

in Figure 1.

The far-field noise data were acquired using an array of 24 microphones mounted on an arc (150” radius)

centered on the jet exit. The 1/4” Bruel & Kjaer microphones (type 4939) were placed at 5◦intervals from

approximately 50◦ upstream to 165◦ downstream of the nozzle exit. One additional microphone was mounted

on the opposite side of the jet from the primary arc array at approximately θ = 115◦ during testing with

surfaces xT E/De ≤ 12. Bruel & Kjaer Nexus units provided signal conditioning and amplification. Data

were digitized by a DataMAX Instrumentation Recorded from R. C. Electronics using 200 kHz sample rate

(90 kHz Nyquist filter). Once acquired, the time series data were transformed into the frequency domain

using a 214 point Kaiser window to achieve a 12.21 Hz spectral resolution. The background noise, as measured

at the beginning of each test day, was then subtracted on a frequency by frequency basis; any data point

within 3 dB of the background noise was removed from the spectra to minimize contamination to the jet

noise database. The data were then corrected for the individual frequency response of each microphone using

the current calibration obtained from the manufacturer. Finally, the data were corrected for atmospheric

attenuation, scaled to a distance of 100De assuming spherical spreading of sound, and integrated into 1/12

octave power spectral density bands based on Strouhal frequency scaling.

NASA/TM—2014-218120 2
h

xTE / De

"Reflected" Observer

"Shielded" Observer

Figure 1. Schematic showing the configuration tested with the nomenclature used to describe the

surface and observed locations.

Setpoint NPR Ts,j/Ta Ma Mass Flow

Pj/Pa Ue/ca kg/s

3 1.197 0.968 0.5 0.44

5 1.436 0.902 0.7 0.65

7 1.860 0.835 0.9 0.91

Table 1. Subsonic jet exit conditions common to all the jet-surface interaction noise tests.

h (inches) xT E/De

0.65 1.35 2 4 6 8 10

0.0 x x x x x x x

0.1 x x x x x

0.2 x x x x x

0.3 x x x x x

0.5 x x x x x x x

0.7 x x x x x

1.0 x x x x x x x

1.4 x x x x x

1.5 x x

1.9 x x x x x

2.0 x x

2.5 x x x x x x x

3.0 x x

3.2 x x x x x

3.5 x x

4.0 x x x x x x x

5.0 x x x x x x x

Table 2. Surface lengths (xT E/Dj ) and radial positions (h) used to generate the empirical model.

NASA/TM—2014-218120 3
III. Model Development

Jet-surface interaction noise broadly describes an increase in low frequency noise that results when a

hard surface is located near turbulent jet. This increase is generally attributed to two source mechanisms:

flow ’scrubbing’ noise and trailing edge noise. Flow scrubbing noise is formed throughout any region where

the high-speed flow passes directly over a hard surface. Trailing edge noise (as the name suggests) originates

at the edge of the surface where the flow transitions from wall-bounded to a free-shear layer. Both of these

noise sources are dipolar as shown by the mid-1950’s theoretical work of Curle.4 These theories were later

expanded to give scaling as a function of velocity (and surface compliance) and a directivity pattern for the

trailing edge noise source.5, 6 Experimental data has generally supported these theories (e.g.7–9) and, as a

result, they are commonly used. The proposed empirical model leverages these results to greatly simplify

development and implementation while improving accuracy.

The empirical model is based on the idea that a spectra can be determined for each measured surface

length and standoff at a single flow velocity and observer angle then scaled, using general theories on the

behavior of dipole noise sources, to represent other flow conditions and observer angles. These characteristic

spectra are determined by a mathematical fit to the available data with care taken to ensure these functions

behave in a reasonable manner between the data points (e.g. no diverging polynomials, singularities, etc.).

However, the jet-surface interaction noise, must be extracted from total measured noise before a characteristic

spectra can be determined.

III.A. Noise Source Decomposition

The affect of a surface near a jet can be separated into two parts: jet-surface interaction noise source and

the noise shielding/reflecting effect. In addition, the measured far-field noise will include the jet mixing

noise that is not shielded or reflected jet mixing noise. Figure 2(a) shows an example of these components

when the surface is in the jet flow and where jet mixing noise is represented by the isolated (no surface)

jet. Even in this case, there is a problem extracting the jet-surface interaction noise by simple subtraction;

the extent of the shielding or reflection relative to the jet-surface interaction noise and isolated jet is not

fully known. As the surface moves out of the flow, it passes through a region where the flow velocity over

the surface is relatively small it is still subject to the hydrodynamic pressure fluctuations present near a

high-speed turbulent jet which still create jet-surface interaction noise but at a lower level closer to the jet

mixing noise making it much more difficult to extract by simple subtraction (Figure 2(b)). Furthermore,

because the jet-surface noise decreases more slowly than the jet mixing noise (U

6

e versus U

8

e

), jet-surface noise

that is masked by the mixing noise at some frequencies will become exposed as the jet velocity decreases.

This signal (jet-surface interaction noise) to noise (jet mixing noise) ratio problem where robust model must

extend across a frequency range that will sometimes be hidden by the jet mixing noise; extracting an accurate

jet-surface interaction noise spectra from measured noise is critical to building a quality empirical model.

The low signal to noise ratio problem is minimized in two ways: the jet-surface interaction spectra is

extracted from data acquired at the lowest jet Mach number (Ma = 0.5) to form the characteristic spectra

and the relatively high coherence of the surface dipole source. Previous studies have shown that the jetsurface interaction noise produced using a flat surface in similar configurations is dominated by the trailing

edge source.9, 10 Thus, the jet-surface interaction noise should be coherent and 180◦ out of phase if measured

on both sides of the surface simultaneously. Figure 3 shows representative coherence and phase relationship

for a jet-surface configuration as measured simultaneously on opposite sides of the surface. The jet mixing

noise, represented by the isolated jet, is highly incoherent between these measurement locations as opposed

to the trailing edge noise which is coherent and, as expected of a dipole, 180◦ out of phase. Similar coherence

data can be extracted for each surface configuration and flow condition. These data can then be used to

extract the percentage of coherent (dipole) noise from each measured spectra providing an estimate of the

sound energy associated with the jet-surface interaction noise (or mathematically, Pd = Pt ∗ γ

2

xy where Pt

and Pd are in sound power not dB). Figure 4 shows the results of this source decomposition procedure one

case with dominant jet-surface interaction noise and one case when the trailing edge noise source is relatively

weak. In each case the decomposition is verified by adding the extracted energy to the sound measured from

an isolated jet (equivalent Mach number) to reconstruct the original measured jet-surface spectra (note that

noise shielding is not included in the reconstruction the spectra at higher frequencies follows the isolated

jet rather than the shielded jet). Notice in the second configuration (Figure 4(b)) where the dipole spectra

changes slope around StDe = 0.35. This is the point where the coherence has devolved to levels similar to

NASA/TM—2014-218120 4
the isolated jet (i.e. the jet-surface dipole has no energy) which are low but not quite zero. These frequencies

need to removed from the jet-surface spectra prior to the mathematical fitting process either by setting a

threshold below which the coherence is set to zero or by limiting the frequency range allowed in by the

fit procedure or the modeled jet-surface spectra will be far too broad in many cases (using the fit method

described below). However, comparing back to Figure 4(a), this point will be different for each surface

position so the coherence method is generally preferred.

The data available at most surface positions could be decomposed using the coherence method with a

microphone on each side of the surface. However, the longest two surfaces (xT E/De ≥ 8 in Table 2) were

only tested in one entry and did not include this opposite side microphone. These lengths were considered

important to the model because their inclusion would ensure the model includes at least some surface that

extend downstream past the end of the jet’s potential core for most subsonic exit conditions. The jet-surface

noise was extracted from the spectra at these configurations using the coherence between two microphones

on the same side but at different polar angles (θ = 90◦ and θ = 120◦). The jet mixing noise is relatively

incoherent across these angles while the dipole coherence remains strong. Source separation based on these

polar angles was generally successful but does introduce more uncertainty at these locations compared to

the other points (particularly when the surface is away from the flow).

(a) xT E/De = 15, h = 1

StDj

PSD (dB)

10-2 10-1 100 101

70

80

90

100

110

0.5

1.0

2.0

3.0

Isolated

C09

11745

11747

11751

11753

12842

h/Dj

(b) xT E/De = 6

Figure 2. Jet-surface interaction noise, jet mixing noise (Isolated), noise shielding, and reflected noise

labeled for a typical jet-surface arrangement where the flow is directly over the trailing edge (left)

and changes in the jet-surface noise as the surface moves away from the jet (right).

III.B. Jet-Surface Noise Model

The jet-surface interaction noise spectra, extracted from the total measured noise, can be modeled in many

different ways which all have the same goal: to describe the behavior within some parameter space in the

simplest possible form given the accuracy requirements for the given problem. One common method is to

define a series of basis functions and use a singular value decomposition fit to determine coefficients for each

function at each frequency and/or angle. This may result in a high number of coefficients but computers are

remarkably good at dealing with these. This was the first method tried on the jet-surface interaction data

but several problems were encountered. The most significant of these was that the relatively low signal to

noise ratio created a situation where not all configurations yielded valid data at each frequency and, as a

result, the model was biased toward the configurations with higher jet-surface interaction noise. And while

it is possible to extrapolate based on the available data to restore some of the missing data, this process

introduces its own modeling assumptions. It was, therefore, decided to use the assumptions at this point to

apply a different modeling method.

The jet surface interaction noise spectra depends on several variables: surface length, surface distance, jet

velocity (or Mach number), jet temperature, and observer angle. Of these variables, theory and experimental

evidence gives guidance to changes in jet velocity and observer angle and jet temperature is not yet considered

in the current data set. That leaves the surface length and distance as the two remaining fit variables. If

a model provided a characteristic spectra within the range of available surface positions then that spectra

NASA/TM—2014-218120 5
Strouhal Frequency (StDe)

Coherence

10-2 10-1 100 101

0

0.2

0.4

0.6

0.8

1

Jet-Surface

Isolated

Background

Source (a) Coherence

Strouhal Frequency (StDe)

Phase Angle (radians)

10-2 10-1 100 101

-2

0

2

4

6

8

10

Jet-Surface

Source

(b) Phase

Figure 3. Coherence of a jet with a surface relative to an isolated jet and the AAPL background

noise (left) and the phase relationship measured between two microphones on opposite sides of the

jet-surface configuration (right). The horizontal dashed line locates the 180◦(π) phase angle.

Strouhal Frequency (StDe)

1/12 Octave PSD (dB)

10-1 100 101

20

40

60

80

100

Measured

Dipole

Isolated

(Dipole+Isolated)

Source

Ma = 0.5

xTE/De = 4, h=0.3

 = 90°

(a) xT E/De = 4, h = 0.3

Strouhal Frequency (StDe)

1/12 Octave PSD (dB)

10-1 100 101

20

40

60

80

100

Measured

Dipole

Isolated

(Dipole+Isolated)

Source

Ma = 0.5

xTE/De = 4, h=3.2

 = 90°

(b) xT E/De = 4, h = 3.2

Figure 4. Source decomposition and reconstruction using the coherence based method at two surface

positions and a jet Mach number Ma = 0.5. Note that the reconstructed spectra collapse to the isolated

jet spectra rather than the measured spectra because the noise shielding effect is not included in the

model.

NASA/TM—2014-218120 6
could be scaled through the range of the other parameters. Looking at the jet-surface interaction spectra

(e.g. Figure 4), a parabolic model was selected for the characteristic spectra giving the model:

Pd = A + B log10(f /Fpeak)

2

(1)

where A gives the peak amplitude, B describes the spectral width, and Fpeak locates the spectral peak. The

advantage of this model is that the three coefficients (A, B, and Fpeak) can be determined using a minimum

number of frequencies and then extended to cover the entire frequency space as desired in effect extrapolating

based on the ”best” data available. Furthermore, the experimental data show that the jet-surface interaction

noise spectra generally has a single peak and decreases to a level significantly below the jet mixing noise

before changing slope (a point which is likely to be the measurement noise floor as opposed to a physical

characteristic of the jet-surface interaction noise). So allowing a parabolic model to decrease to some very

low levels at high and very low frequencies will not affect the overall predicted spectra.

A least-squares fit was used to identify the model coefficients for each individual spectra. Although the

model equation is not linear with respect to the peak frequency term (Fpeak), it is linear in the amplitude

(A) and spectral width terms (B) so a range of peak frequencies (0.01 ≤ StDe ≤ 5) was used. The leastsquares fit was then repeated at increments of 0.025 within this range to determine A and B as well as

the fit residual. The value of Fpeak, A, and B that yielded the lowest fit residual were then stored as the

fit parameters for that jet Mach number, surface length, and surface distance. This process allows a fairly

straightforward fit method to get the model parameters at each configuration but leads to a situation where

the accuracy of the coefficients is dependent on the number of frequencies available to the fit but (1) the fits

with more uncertainty are likely to have fewer points exerting less influence on the spectra particularly at

the frequencies where data is missing and (2) the parabolic model equation will force a decreasing amplitude

away from the peak frequency as observed in the coherence plots (e.g. Figure ??) as long as B < 0 (this

should be checked as B may become positive when the velocity over the trailing edge is low because of a

long surface or a low Ue). This fit would provide the extrapolation to the missing frequencies and, therefore,

could be put back into another fit method (like the previously mentioned frequency by frequency singular

value decomposition for example). Alternatively, if all these fit spectra are considered together, Equation

(1) can be written as:

Pd(xT E/De, h) = A(xT E/De, h) + B(xT E/De, h) log10[f /Fpeak(xT E/De, h)]2(2)

In this form each coefficient is considered its own function of surface length and position. Each coefficient

can be modeled or fit to the output data from the previous least-squares fit and, when combined, give a

characteristic spectra for each surface position in the domain. Once determined for each surface length and

position, the characteristic spectra can be adjusted for jet velocity and observer angle using known scaling

laws for dipole sources. Expanded Pd to include these variables would give the equation:

Pd(xT E/De, h, Ma, θ) = [A + B log10(f /Fpeak)

2 + 60 log10(Ma/Mf it)][1 − cos2

(θ)] (3)

where Mf it is the Mach number used to generate the A, B, and Fpeak and θ is polar angle. Furthermore,

future modifications and additions may be applied to the model by introducing new terms to the coefficient

equations; for example, jet exit temperature may be included by introducing a new function to the amplitude

coefficient (A) so that it becomes A(xT E/De, h)∗Td(Ttr) (where Td is a function giving the amplitude change

of the dipole noise as a function of total temperature ratio, Ttr). Similar modifications could be applied to the

other coefficients (B and/or F peak). Other parameters, such as nozzle aspect ratio, might also be included

in this way.

III.B.1. Defining A(xT E/De, h)

The model given by Equation 2 requires three coefficients that are each a function of surface length and

position. The first of these, A, gives the characteristic model spectra its peak amplitude. To develop a

mathematical fit, the values of A determined using the least-squares parabolic fit are plotted as a function

of h for each measured xT E/De given in Table 2. These plots are shown in Figure 5. The initial expectation

based on previous test data was that the peak amplitude would decrease logarithmically as h increased and,

in fact, a logarithmic function could be used if the model began in the 0.5 ≤ h ≤ 1 region. However, as the

surface moves closer to the jet A peak in the 0.3 ≤ h ≤ 0.5 range and then decreases again as h goes to zero.

NASA/TM—2014-218120 7
One hypothesis for this behavior is that a surface very near the jet will suppress the turbulence over the

trailing edge (possibly by limiting entrainment air) which reduces the peak trailing edge noise. In this case,

the peak amplitude would occur at a position just off the nozzle and then decrease as the surface proceeds

out of the flow. Therefore, a cubic polynomial function is used to fit the A coefficient as a function of h at

each fixed value of xT E in an effort to capture this behavior. Note that the fit is quite poor (based onR2) for

the shortest surfaces because the surface moves out of the flow very quickly. However, the values of A when

the surface is at xT E/De = 0.65 are quite close together (notice the scale in Figure 5(a)) so the impact of the

difference on the overall spectra is relatively small while the rapid fall off with distance at xT E/De = 1.35

leads to maximum 2 dB difference at the peak. Also, as the surface gets longer the maximum value of A

occurs when the surface in slightly farther away from the jet. Finally, both the values from Equation (2) and

the corresponding polynomial fit are not as smooth and predictable as when the surface is shorter because

(1) there are fewer data points at these surface lengths to fit and (2) the jet-surface interaction noise was

extracted using the coherence at two polar angles rather than the coherence on opposite sides of the surface.

The individual cubic polynomial fits shown in Figure 5 can provide the peak amplitude coefficient (A) to

Equation (2) for the discrete values of xT E/De measured. The desired model, however, needs to provide an

estimated jet-surface interaction noise spectra for any value of xT E/De. Thus, the coefficients of individual

polynomial fits are considered as data points for another fit across all surface lengths so that each coefficient

(Axn ) becomes is a function of xT E/De. Mathematically, the A coefficient to Equation (2) is now written

as:

A(xT E/De, h) = Ax3 (xT E/De)h

3 + Ax2 (xT E/De)h2 + Ax1 (xT E/De)h1 + Ax0 (xT E/De) (4)

Separating the coefficients so that a set based on one variable provides the second set allows the model

to cover a 2-dimensional parameter space while using only 1-dimensional fit methods. In exchange, each

coefficient (Ax3 , Ax2 , etc.) requires a different fit creating another separate set of coefficients.

The behavior of A as a function of h was reasonably described by a third-order polynomial at the

individual surface lengths (xT E/De) where data were acquired. The coefficients of that polynomial, however,

are not as easily described by simple functions of xT E/De. Figure 6 shows the fit results to the the Axn

coefficients in Equation 4. A general polynomial equation was used for each fit with a few restrictions

applied. First, no polynomials above 3rd order were allowed. Higher order polynomials were found to fit

the data points but these functions were unpredictable between the data points. Second, regions with sharp

changes (e.g. xT E/De ≈ 2 in Figure 6(b)) or where fourth order polynomials (or higher) were needed were

sub-divided into multiple regions with different functions/coefficients to best represent the nearby data. Each

division increases the complexity of the overall model but allows for a more predictable result between data

points. Finally, the trend the lower and upper limits of the data was considered in an effort to avoid any

non-physical divergence immediately outside of the fit range (note that this was more successful on the lower

end of surface lengths). Figure 6 shows the fit results compared to the data points for the 4 coefficients in

Equation 4 (regions, functions, and coefficients can be found in Appendix A). It is important to remember

here that the results of these fits proved the coefficients to another equation and, therefore, are two steps

removed from the actual physics (with the exception of Ax0 , Figure 6(d), which represents the behavior of

A(xT E/De, h = 0)). The fit data and results for the Axn coefficients is shown to illustrate the process of

fitting equations to the coefficients of another equation to get a usable model. It is how these coefficients

combine in Equation 4 that provides the characteristic spectra with its peak amplitude.

The coefficients Axn (xT E/De) are obtained through a fit to the coefficients of a third-order polynomial

(in h, Figure 5) across all values of surface length (xT E/De). These coefficients are used with Equation 4 to

get the peak amplitude term (A(xT E/De, h)) in the jet-surface interaction noise model (Equation 2). Figure

7 shows how the peak amplitude varies in the jet-surface interaction noise model for six surface distances

(h) and all surface length within the limits of the original data (Table 2). When the surface is on the

nozzle lipline (h = 0) there is flow across the surface trailing edge for any length of surface. As a result,

the amplitude of the jet-surface interaction noise varies smoothly increases as the surface length increases

(possibly) because the boundary layer on the surface has more time to develop and, thus, the turbulence

intensity is greater at the trailing edge (and, presumably, if a surface were long enough the amplitude would

decrease because the flow passing over the trailing edge would not have enough energy to create as much

sound). When the surface is at h = 1, the shortest surfaces are no longer subject to the flow directly as

reflected in the lower amplitudes. A transition occurs between 2 ≤ xT E/De ≤ 5 where the flow first strikes

the surface and develops a turbulent boundary layer. When this occurs, the peak amplitude matches the

NASA/TM—2014-218120 8
level at A(xT E/De, h = 1). Beyond h = 1 the surface appears to be in a lower velocity/turbulence region

as it passes through the hydrodynamic field of the jet (2 ≤ h ≤ 3), dropping in amplitude as h increases.

Finally, the A(xT E/De, h) settles to about the same level/profile which may be indication that the jet-surface

noise decomposition has reached the signal to noise ratio limit. In this region (4 ≤ h ≤ 5) the surface is far

enough away to significantly weaken the trailing edge dipole source making the surface more a shield for the

jet mixing noise than a noise source itself and the peak value collapses to some background noise level. That

it does not continue to decrease does not generally appear to be an issue because the jet mixing noise will

be sufficiently above this level at least for jet Mach numbers greater than Ma = 0.5.

Finally, a note about the behavior of A(xT E/De, h) in the 8 ≤ xT E/De ≤ 10 should be added here as

the character of the curves changes significantly in this region. The source data in this region included fewer

h and the source decomposition of these data points used two polar angles rather than to points on opposite

sides of the surface. So while the coefficient fit in this region showed a similar accuracy to other areas (often

due to a separate set of fit equations, see Figure 6), these issues with the source data permeate the model

and appear in the output. Therefore, improving the data quality in this region should improve (and possibly

simplify) the model.

h

A(xTE/D

e=0.65,h)

0 1 2 3 4 5 6 66.5

67

67.5

68

68.5

69

69.5

70

70.5

71

71.5

72

72.5

A (Equation (2))

A (polynominal fit*)

*

poly(xTE/De=0.65,h) = 0.0837h3

+-0.6958*h2+1.5373*h+68.205

(R2

 = 0.082)

(a) xT E/De = 0.65

h

A(xTE/D

e=1.35,h)

0 1 2 3 4 5 6 68

69

70

71

72

73

74

75

76

77

A (Equation (2))

A (polynominal fit*)

*

poly(xTE/De=1.35,h) = -0.2268h3

+2.2619*h2+-6.97*h+75.543

(R2

 = 0.858)

(b) xT E/De = 1.35

h

A(xTE/D

e=2,h)

0 1 2 3 4 5 6

68

70

72

74

76

78

80

A (Equation (2))

A (polynominal fit*)

*

poly(xTE/De=2,h) = -0.1334h3

+1.8419*h2+-8.2779*h+80.582

(R2

 = 0.948)

(c) xT E/De = 2.0

h

A(xTE/D

e=4,h)

0 1 2 3 4 5 6 68

70

72

74

76

78

80

82

84

86

88

A (Equation (2))

A (polynominal fit*)

*

poly(xTE/De=4,h) = 0.2904h3

+-2.1553*h2+0.3202*h+86.182

(R2

 = 0.991)

(d) xT E/De = 4.0

h

A(xTE/D

e=6,h)

0 1 2 3 4 5 6 74

76

78

80

82

84

86

88

90

92

A (Equation (2))

A (polynominal fit*)

*

poly(xTE/De=6,h) = 0.282h3

+-2.343*h2+2.0589*h+89.019

(R2

 = 0.999)

(e) xT E/De = 6.0

h

A(xTE/D

e=8,h)

0 1 2 3 4 5 6 80

82

84

86

88

90

92

94

A (Equation (2))

A (polynominal fit*)

*

poly(xTE/De=8,h) = 0.2997h3

+-2.0802*h2+1.615*h+90.461

(R2

 = 0.996)

(f) xT E/De = 8.0

h

A(xTE/D

e=10,h)

0 1 2 3 4 5 6 84

86

88

90

92

94

96

98

100

A (Equation (2))

A (polynominal fit*)

*

poly(xTE/De=10,h) = -0.234h3

+1.8207*h2+-4.8417*h+95.612

(R2

 = 0.807)

(g) xT E/De = 10.0

Figure 5. Values of A(xT E/De, h) determined by the fit process using Equation (1) and the cubic

polynomial fit to A(xT E/De, h) determined at each xT E/De. Note the scale change on the y-axis of each

plot.

NASA/TM—2014-218120 9
xTE/De

Ax3

0 2 4 6 8 10 12 -2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

(a) Ax3

xTE/De

Ax2

0 2 4 6 8 10 12 -15

-10

-5

0

5

10

15

(b) Ax2

xTE/De

Ax1

0 2 4 6 8 10 12 -20

-15

-10

-5

0

5

10

(c) Ax1

xTE/De

Ax0

0 2 4 6 8 10 12 60

65

70

75

80

85

90

95

100

(d) Ax0

Figure 6. Fit results (line) with input data points (squares) for each coefficient to Equation 4. Fit

equations, coefficients, and ranges of applicability are given in Appendix A.

III.B.2. Defining B(xT E/De, h)

The characteristic spectra for the jet-surface interaction model is defined by a parabolic equation peak

amplitude, spectra width, and peak frequency terms. The peak amplitude was defined by an empirical fit to

the available data in Section III.B.1. The spectral width (B(xT E/De, h)) is determined using the same general

procedure. First, the values of B(xT E/De, h) determined by a parabolic fit to the jet-surface interaction

noise spectra as measured at each surface position. A third-order polynomial function of h is then fit to

these values at each surface length (e.g. B(xT E/De = 0.65, h), B(xT E/De = 1.35, h), B(xT E/De = 2.0, h),

etc.). The term by term coefficients of these polynomials are then used as source data to fit another series

of first- to third-order polynomial functions of xT E/De. The coefficient B(xT E/De, h) is then obtained by

working back through this process; xT E/De is used to find the coefficients to the cubic polynomial function

of h which is in turn used to calculate the spectral width. Mathematically, the equation for B(xT E/De, h)

written:

B(xT E/De, h) = Bx3 (xT E/De)h

3 + Bx2 (xT E/De)h2 + Bx1 (xT E/De)h1 + Bx0 (xT E/De) (5)

which has the same form used in Equation 4 for A(xT E/De, h). The difference arises in the fit equations (with

applicable regions) and coefficients used to determine the values Bx3 , Bx2 , Bx1 , and Bx0 . The process itself,

however, is identical to that used to determine A(xT E/De, h) in Section III.B.1 and so will not be repeated

here in such detail. The results for several surface distances (h) are shown in Figure 8 while the fit coefficients

and equations can be found in Appendix B. Note that the B parameter required more sub-regions than A

primarily to keep the polynomial fit equations from giving positive values. Still there are a few instances

where positive values can occur (e.g extrapolating to xT E/De < 0.65, h = 0 or at xT E/De > 6, h = 5) and,

therefore, a limiter is recommended to keep B ≤ −10.

NASA/TM—2014-218120 10
xTE/De

A(xTE/D

e,h)

0 5 10 55

60

65

70

75

80

85

90

95

100

A(h=0)

A(h=1)

A(h=2)

A(h=3)

A(h=4)

A(h=5)

Figure 7. A(xT E/De, h) obtained using the fit results shown in Figure 6 for 6 values of h.

The parabolic model requires that B(xT E/De, h) remain less than zero to maintain its convex shape.

Smaller values of B(xT E/De, h) will give the jet-surface interaction noise spectra a narrow peak while values

approaching zero gives a spectra covering a broad range of frequencies. However, the mechanisms behind

the trends in spectra width is not easily identified. Jet mixing noise theory holds that high frequency

noise originates from the small-scale turbulence in the thin shear layer near the jet while lower frequencies

are generated by the large-scale turbulence structures farther downstream in the fully developed jet. The

combination of these source (with the intermediate turbulence scales in between) gives the jet mixing noise

spectra its characteristic broadband shape. If this relationship between turbulence scale and noise were

applied to the jet-surface interaction noise spectra, then shorter surfaces should have a relatively narrow

peak (smaller B) because of the relatively few small range of turbulence scales in the flow at the surface

trailing edge. Similarly, as the surface moves away from the jet (h increasing) the spectral width should

decrease because only the large-scale turbulent structures have sufficient energy to exert influence outside of

the jet column. Figure 8 shows the spectral width parameter (B) as a function of surface length. When the

surface is on the nozzle lipline (h = 0) the jet-surface interaction noise spectra has a near constant width

for xT E/De > 4 (which may correspond to the length required to develop a fully turbulent boundary layer

on the surface). A similar trend, although at a lower overall level, is found at h = 1 but for xT E/De > 6

presumably because a longer surface is need for the jet to spread to the surface then develop a boundary

layer. This trend continues out the h ≈ 3. The spectral width for shorter surfaces or surfaces farther away is

generally not easily explained in fluid dynamic terms (e.g. the low point at xT E/De = 5 or the broadening

at h = 5). Rather it is likely that the fit in these regions is heavily influenced by the spectral decomposition

and the related signal to noise ratio issues discussed in Section III.A. Fortunately the spectral width plays a

secondary role to the peak amplitude in these regions; as long as the peak amplitude decreases as predicted,

the extra wide parts of the predicted spectra will be masked by the jet mixing noise.

III.B.3. Defining Fpeak(xT E/De, h)

The final parameter to model the jet-surface interaction noise spectra is the peak frequency (Fpeak) in the

parabolic model. The procedure used to obtain a usable fit for Fpeak(xT E/De, h) is identical to that used

to determine values for A and B in the previous two sections (so a detailed description will not be repeated

here) with the exception that a second-order polynomial was suitable to describe Fpeak as a function of h.

Thus, the equation for Fpeak(xT E/De, h) is:

NASA/TM—2014-218120 11
xTE/De

B(xTE,h)

0 5 10 -160

-140

-120

-100

-80

-60

-40

-20

0

B(h=0)

B(h=1)

B(h=2)

B(h=3)

B(h=4)

B(h=5)

Figure 8. B(xT E/De, h) obtained using the fit results in Appendix B for 6 values of h. A dashed horizontal

line is shown at B(xT E/De, h) = 0 as the convex shape of the parabolic jet-surface noise model requires

B(xT E/De, h) < 0.

Fpeak(xT E/De, h) = Fx2 (xT E/De)h

2 + Fx1 (xT E/De)h

1 + Fx0 (xT E/De) (6)

where the coefficients Fxn are functions of xT E/De and provided by the fit equations and coefficients shown

in Appendix C. Figure 9 shows how the peak frequency of the jet-surface interaction noise spectra predicted

by the model changes as a function of xT E/De at several surface distances (h). Like the spectral width,

the peak frequency could be related to the turbulence in the flow at the trailing edge. In this hypothesis,

surfaces close to the jet (e.g. h = 0) would have a higher peak frequency than found in spectra measured with

surfaces farther away which would be more affected by the large-scale turbulence. As Figure 9 shows this

trend generally holds for the peak frequencies plotted. The second part of this hypothesis, concerning surface

length, would suggest that the peak frequency would decrease as the surface length increases because the

dominate flow structures would be larger. Again, Figure 9 shows that after an initial increase (presumably

while the boundary layer develops on the surface), this trend at all surface distances. Note that this is not

sufficient evidence to prove this flow to noise link but to point out interesting trends that may be observed

by modeling the data in this way and discuss how those may relate to the fluid dynamics for future theory,

experiments, or modeling efforts.

The peak frequency term of the characteristic spectra model was the easiest of the three variables to fit.

Each term required only two regions and most of these were sufficiently described by quadratic polynomials.

However, the fitted peak frequency shown in Figure 9 shows a couple of issues related to the fit. First, there

is a rapid jump around xT E/De = 2 which develops when the surface is around h = 4. While not ideal, this

was not considered a major issue because the jet-surface interaction noise is generally low relative to the jet

mixing noise with surfaces that are short and far from the jet so that the affect on the reconstructed spectra

is small. Second, the peak frequency trends to negative values for longer surfaces (xT E/De > 8) that are

far from the jet (h > 4). The peak frequency identified by the original parabolic fit to Equation 2 for the

points in this region was the minimum allowed in the fit routine. Therefore, a limiter was placed on Fpeak

so that the predicted value will not go below the range specified in the original fit (note that the A and B

values fit correspond this minimum peak frequency so allowing it to go outside of the original range may

have unintended consequences). Finally, the peak frequency is somewhat unpredictable when extrapolated

to surfaces shorter xT E/Dj = 0.65. Cutting the model off at xT E/De = 0.5 (as in A and B) limits the

spread in this region so it may or may not be a problem; there is no validation data in this region so this

behavior should be noted at this point for future evaluation.

NASA/TM—2014-218120 12
xTE/De

Fpeak(xTE/D

e

)

0 5 10 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Fpeak(h=0)

Fpeak(h=1)

Fpeak(h=2)

Fpeak(h=3)

Fpeak(h=4)

Fpeak(h=5)

Figure 9. Fpeak(xT E/De, h) obtained using the fit results in Appendix C for 6 values of h. Note the limiter

that engages for longer surfaces at the farthest two surface positions to ensure a positive frequency.

IV. Model Evaluation and Performance

An empirical model has been developed based on the idea that a characteristic jet-surface interaction

noise spectra can be generated across a range of surface lengths and positions using a parabolic equation with

coefficients selected to fit experimental data at one jet velocity and one observer angle. The characteristic

spectra, according to the model, can then be scaled to other jet Mach numbers and/or observed angles using

the theoretical rules for a dipole noise source. Furthermore, the scaled jet-surface interaction noise spectra

can be added to a modeled jet mixing noise spectra to recreate the complete noise source spectra (note

that shielding or reflection of the jet mixing noise is not included in the reconstruction). The jet-surface

interaction noise model is evaluated on these three performance metrics: (1) matching the characteristic

spectra to the experimental data, (2) scaling the characteristic spectra to account for changes in jet exit

velocity, and (3) scaling the characteristic spectra to predict the noise at other observer angles. An empirical

jet mixing noise prediction model11, 12 is combined with the jet-surface interaction noise model for these

comparisons.

IV.A. Characteristic Spectra

The first test of any empirical model is how well it reproduces the source data used to develop it. The volume

of data, however, makes it difficult to present comparisons for every data point. Therefore, the model is

compared back to the source data to show a comparison in trends as h increases and a comparison of trend

as xT E/De increases with special attention to areas where discrepancies appear. Figure 10(f) shows the

decrease in jet-surface interaction noise as a mid-length xT E/De = 6 surface moves from h = 0 to h = 5.

The agreement is good with the model capturing the decrease in peak amplitude and frequency as h increases.

The noise from the equivalent isolated (no surface) jet is also included in Figure 10(f); the spectral width of

the jet-surface interaction noise is shown by the frequency where the jet-surface interaction noise cross the

isolated jet (above this frequency the model returns the isolated jet spectra because a noise shielding model

has not been included). The model accurately predicts the cross over frequency and spectral width across

the full range of h.

One issue not addressed by Figure 10(f) but worthy of special attention is the spectral changes between

NASA/TM—2014-218120 13
h = 0 and h = 0.5 where the data motivated the use of a cubic polynomial to fit the peak amplitude coefficient

in Section III.B.1 rather than the logarithmic relationship initially expected. Figure 11 shows predicted and

measured spectra for surface lengths xT E/De = 2 and xT E/De = 4 for each measured 0 ≤ h ≤ 0.5. First, at

xT E/De = 4 (Figure 11(b)), where the amplitude coefficient (A) as a function of h followed a more parabolic

trend that was almost flat around the peak between 0 ≤ h ≤ 0.5 (Figure 5(d)), the model produces a

reconstructed spectra with a peak at Fpeak ≈ 0.2 that does not vary significantly in amplitude. The peak in

the measured spectra, however, occurs as a spectral hump peaking around StDe = 0.17 and decreasing as h

increases. This does not, however, appear to be a problem fitting the peak amplitude but rather a limitation

of the parabolic model used to define the characteristic spectra; the actual peak of the measured data is an

extra hump on top of the underlying parabolic jet-surface noise interaction spectra. Similarly, the measured

spectra contains several tonal spikes (particularly for h = 0.2 − 0.3) that can not be captured by a strictly

parabolic model but, along with the extraneous peak, influence the spectra width resulting in the spread

across the predicted noise between 0.4 ≤ StDe ≤ 1.0 where the jet mixing noise supports the unshielded

spectral reconstruction. At xT E/De = 2 (Figure 11(b)) the jet-surface interaction peak is not as far above

the underlying parabolic form but the mid-frequency tonal content is significantly stronger and occurs to

some extent for all 0 ≤ h ≤ 0.5. These resonances have been documented in rectangular nozzle/surface

configurations and data indicates that have fluid dynamic origins (i.e. structural or plate vibrations).1, 13

Furthermore, these resonances appear through a relatively small combination of flow velocity and surface

length/distance making them difficult to capture in any predictive model. As stated above, the current

parabolic jet-surface interaction noise model is functionally incapable of warping to these tonal peaks but

these could be modeled separately and implemented as a addition to the parabolic characteristic spectra aAs

a side note, attempts to model these spectral features on a frequency by frequency basis spanning surface

positions and flow velocities required functions that made the model somewhat unstable at other positions..

Thus, this tonal content is less of a concern than the model under-predicting the lower frequency peak at

these surface positions because of the underlying parabolic spectra assumption.

The influence of these tones on the predicted jet-surface interaction noise spectra is not limited to changes

in surface distance. Figure 12 shows predictions and measure data for each surface length tested at h = 0.5

(the first point acquired for all surface lengths off the nozzle lipline). The shortest surface (xT E/De = 0.65)

is already out of the jet flow by h = 0.5 and the model correctly shows very little jet-surface interaction

noise (Figure 12(a)). Extending the surface to xT E/De = 1.35 gives a small low frequency augmentation

that is not reflected by the model but also shows the onset of a resonance in the mid-frequency range (Figure

12(b). These tones are amplified at xT E/De = 2 (Figure 12(c)) along with the low frequency jet-surface

interaction noise and the model settles above the isolated jet noise but on the lower end of the jet-surface

noise. The model improves for the longer surface at xT E/De = 4 but still misses at frequencies below the

peak jet-surface interaction noise peak (Figure 12(d)). At first it appears the the peak amplitude coefficient

determined by the model is just low but a closer examination shows that the measured spectra is not well

defined as a symmetric parabola (look at the growing difference as frequency decreases) and the optimal

model coefficients fit the higher frequencies better (although the peak amplitude may still be 1 − 2 dB

low). This configuration presents a case for adding a linear term to the original parabolic model to provide

finer control over the spectral shape (in exchange for another term, associated fits, coefficients, and general

complexity). The model performs well at xT E/De = 6 (Figure 10(b)). The prediction at xT E/De = 8 shows

a trend reversal from the shorter surfaces by slightly over estimating the peak amplitude as the measured

spectra becomes very flat in the peak frequency region (Figure 12(e)). Finally, the predicted spectra at

xT E/De = 10 gets close to the measured peak amplitude (Figure 12(f)) but with a wider spectral width

(note lack of a defined peak at this position). It is important to remember that the jet-surface interaction

noise across this range of surface lengths alone varies by approximately 20 dB (more when variations in h are

included) so while this model may lack the absolute accuracy often desired it does appear to fairly represent

the trends in highly varying parameter space.

IV.B. Velocity Scaling

An empirical model for jet-surface interaction noise has been developed based on the idea that a characteristic

spectra can be found for a range of surface positions at a single jet condition and then scaled to account for

changes in jet velocity. Previous experimental and theoretical work has shown that jet-surface interaction

noise is dipolar in nature and scales with velocity like U

5

e

to U

6

e depending on primarily surface rigidity

(e.g.4, 5, 7–9). The current jet-surface noise model has been implemented with U

6

e velocity scaling. Figure 13

NASA/TM—2014-218120 14
Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

100

Modeled

Measured

Isolated

16975

16975

18692

18692

(a) h = 0.0

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

100

Modeled

Measured

Isolated

16979

16979

18692

18692

(b) h = 0.5

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

100

Modeled

Measured

Isolated

16981

16981

18692

18692

(c) h = 1.0

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

100

Modeled

Measured

Isolated

16983

16983

18692

18692

(d) h = 1.9

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

Modeled

Measured

Isolated

16985

16985

18692

18692

(e) h = 3.2

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

Modeled

Measured

Isolated

16987

16987

18692

18692

(f) h = 5.0

Figure 10. Modeled spectra (dashed lines) compared to measured data (solid lines) for xT E/De = 6 with

an unheated Ma = 0.5 jet (setpoint 3).

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

100

h=0

h=0.1

h=0.2

h=0.3

h=0.5

(a) xT E/De = 2

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

100

h=0

h=0.1

h=0.2

h=0.3

h=0.5

(b) xT E/De = 4

Figure 11. Comparison between modeled spectra (dashed lines) and measured data (solid lines) for an

unheated Ma = 0.5 unheated jet (setpoint 3) at surface positions close to the jet (0 ≤ h ≤ 0.5).

NASA/TM—2014-218120 15
Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

Modeled

Measured

Isolated

18353

18353

18692

18692

(a) xT E/De = 0.65

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

Modeled

Measured

Isolated

18308

18308

18692

18692

(b) xT E/De = 1.35

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

Modeled

Measured

Isolated

17068

17068

18692

18692

(c) xT E/De = 2.0

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

100

Modeled

Measured

Isolated

17025

17025

18692

18692

(d) xT E/De = 4.0

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

100

Modeled

Measured

Isolated

11846

11846

18692

18692

(e) xT E/De = 8.0

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

30

40

50

60

70

80

90

Modeled

Measured

Isolated

11919

11919

18692

18692

(f) xT E/De = 10.0

Figure 12. Modeled spectra (dashed lines) compared to measured data (solid lines) for 0.65 ≤ xT E/De =

10 at h = 0.5 and an unheated Ma = 0.5 jet (setpoint 3). Note that the comparison at xT E/De = 6 can

be found in Figure 10(b) and so is not repeated here.

shows measured and modeled spectra for jet exit velocities Ma = 0.5, Ma = 0.7 and Ma = 0.9 at h = 0.3

(near the peak for jet-surface interaction noise at most surface lengths tested) and 0.65 ≤ xT E/De ≤ 6.

When xT E/De ≤ 2, scaling the modeled characteristic spectra with U

6

e fits the measured data well and, in

fact, the fit improves as the resonance behavior found at Ma = 0.5 disappears (or is masked by the jet mixing

noise). At xT E/De = 4 and 6, however, this velocity scaling breaks down around the jet-surface interaction

noise peak frequency where the peak of the measured data at Ma = 0.7 and 0.9 is flatter than at Ma = 0.5.

This change in spectral shape can not be accounted for by any velocity scaling rule without considering

the scaling on a frequency by frequency basis; even then there may be issues as the simple scaling appears

to hold for shorter surfaces requiring scaling based on frequency and surface length. Using the U

6

e

scaling

introduces error up to 5 dB at M9

a and xT E/De = 6.

IV.C. Directivity Scaling

The empirical model developed to predict jet-surface interaction noise provides a characteristic spectra that

can be scaled to account for changes in jet velocity or observer angle. Scaling the model spectra assuming

that the jet-surface interaction noise source behaves like a pure dipole on a rigid plate was discussed in

Section IV.B. These same assumption about the noise are now applied to describe changes in observer angle

bNote that only polar angle, θ, is considered here because the underlying dataset only includes measurements

at one azimuthal angle. An extension to include dependence on azimuthal angle based on a recently acquired

dataset is planned. Mathematically the dipole source at the trailing edge of the surface should change with

observer angle (θ) appears as:

Pd(xT E/De, h, Ma, θ) = Pd(xT E/De, h, Ma, 90◦)[1 − cos2(θ)] (7)

where Pd is the modeled jet-surface interaction noise as a function of surface length (xT E/De), surface

distance (h), and Mach number (Ma). The empirical model defines the characteristic spectra at θ = 90◦

where Pd has its maximum value based on angle (i.e. 1−cos2(θ) = 1) so moving the observer angle upstream

NASA/TM—2014-218120 16
Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

100

0.5

0.7

0.9

Ma

18352

18352

18366

18366

18380

18380

(a) xT E/De = 0.65

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

100

110

0.5

0.7

0.9

Ma

18307

18307

18322

18322

18336

18336

(b) xT E/De = 1.35

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

100

110

0.5

0.7

0.9

Ma

17067

17067

17083

17083

17097

17097

(c) xT E/De = 2.0

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

100

110

0.5

0.7

0.9

Ma

17024

17024

17038

17038

17052

17052

(d) xT E/De = 4.0

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

100

110

120

0.5

0.7

0.9

Ma

16978

16978

16992

16992

17006

17006

(e) xT E/De = 6.0

Figure 13. Modeled spectra (dashed lines) compared to measured data (solid lines) for 0.65 ≤ xT E/De =

10 at h = 0.3 and an unheated Ma = 0.5, Ma = 0.7, and Ma = 0.9 jets. Note that the deviations above

StDe ≈ 1 for the longer surfaces are due to the shielding of jet-mixing noise which is not included in

the noise modeling.

NASA/TM—2014-218120 17
or downstream will reduce the predicted amplitude.

Two surface lengths will used to investigate the directivity of the reconstructed spectra. First, Figure 14

shows the shape of the reconstructed spectra, with contours representing the difference from the measured

spectra, across all angles for the xT E/De = 6 surface and a range of h locations. As shown in Section IV.A,

the model performed fairly well compared to the experimental data at this surface length (see Figure 10)

making it a good staring point for discussion of directivity scaling. At each surface distance (h) in Figure

14 the spectra is dominated by a high ridge extending at relatively low frequency that is the jet-surface

interaction noise. This ridge extends across most angles when the surface is close to the jet h = 0 − 0.5

but fades into the jet mixing noise around θ ≈ 120◦ with the jet mixing noise dominating at downstream

angles when the surface is far from the jet (e.g. Figure 14(f)). The largest errors appear in this cross-over

region between 110 ≤ θ ≤ 130 with the worst case at h = 0.5 and approximately θ = 120◦. Figure 15 shows

a comparison between the modeled, measured, and isolated for this surface positions at θ = 60◦, 90◦, 120◦.

At θ = 60◦the jet-surface interaction noise peak is lower and flatter than predicted by the model (although

it should be noted that this may partially be due to noise shielding at this angle) while there is good

agreement at the characteristic spectra at θ = 90◦. However, at θ = 120◦some additional noise appears past

the jet-surface interaction noise peak that appears similar in character to the resonant noise observed in the

characteristic spectra with shorter surfaces (Section IV.A). While it is not clear from these data if the noise

at θ = 120◦(and to a lesser extent at θ = 150◦) is generated by the same underlying mechanisms, it does

account for most of the difference found Figure 14(f). Otherwise, this directivity scaling appears to track

the peak amplitude of the jet-surface interaction noise fairly well.

The largest difference between the measured and modeled spectra for xT E/De = 6 appears has spectral

characteristics that differ from the classic low frequency augmentation description of jet-surface interaction

noise but are more like the resonant tones found in interaction noise created by a rectangular nozzle near

a surface.1, 13 Therefore, the xT E/De = 2 surface, which showed a significant amount of this type noise

(Section IV.A), will be used as a second case to evaluate the directivity of the empirical model. Figure 16

compares the modeled and measured spectra at all angles for the xT E/De = 2 surface at several distances

(h). These data show a trend similar to that observed for xT E/De = 6; the peak differences are in the

mid-angles (100 ≤ θ ≤ 130) at frequencies just above the peak frequency and are maximum at h = 0.5. The

absolute value of these difference is larger which would be consistent with the stronger resonance present in

spectra from the shorter surface previously noted. Again extracting the spectra at θ = 60◦, 90◦, 120◦, and

150◦for a more detailed comparison, Figure 17 compares the modeled, measured, and isolated spectra for

xT E/De = 2 and h = 0.5. The model predicts the directivity change at θ = 60◦fairly well. At θ = 90◦

and θ = 120◦, however, the differences are larger. In fact, the directivity model predicts that the jet-surface

interaction noise should decrease between θ = 90◦ and 120◦ but the peak spikes in the measured data are

actually higher at θ = 120◦(while the modeled spectra has decreased and is closer to the isolated spectra at

θ = 120◦than at θ = 90◦). These peaks appear to have a similar amplitudes at θ = 90◦ and θ = 150◦ but the

model appears function better at the downstream angle largely because the increased jet mixing noise is more

dominant. Thus, this aspect of the jet-surface interaction seems to follow a different directivity pattern than

the more traditional low frequency augmentation and, combined with changes in this noise due to velocity

noted in Section IV.B, would add considerable complexity to a relatively simple model. Alternatively, a

more robust approach may be to build a second model dedicated only to tracking this more tonal noise and

add it to the characteristic spectra, scaled for velocity and observer angle, produced by the parabolic model

presented here.

NASA/TM—2014-218120 18
Log10(StDe)

-2

-1

0

1

Polar Angle ( deg.)

50

100

150

1/3

O

c

t

a

v

e

P

S

D

(

d

B

)

20

40

60

80

100

dPSD (dB)

5

4

3

2

1

0

-1

-2

-3

-4

-5

16975

16975

18692

(a) h = 0.0

Log10(StDe)

-2

-1

0

1

Polar Angle ( deg.)

50

100

150

1/3

O

c

t

a

v

e

P

S

D

(

d

B

)

20

40

60

80

100

dPSD (dB)

5

4

3

2

1

0

-1

-2

-3

-4

-5

16977

16977

18692

(b) h = 0.2

Log10(StDe)

-2

-1

0

1

Polar Angle ( deg.)

50

100

150

1/3

O

c

t

a

v

e

P

S

D

(

d

B

)

20

40

60

80

100

dPSD (dB)

5

4

3

2

1

0

-1

-2

-3

-4

-5

16979

16979

18692

(c) h = 0.5

Log10(StDe)

-2

-1

0

1

Polar Angle ( deg.)

50

100

150

1/3

O

c

t

a

v

e

P

S

D

(

d

B

)

20

40

60

80

100

dPSD (dB)

5

4

3

2

1

0

-1

-2

-3

-4

-5

16981

16981

18692

(d) h = 1.0

Log10(StDe)

-2

-1

0

1

Polar Angle ( deg.)

50

100

150

1/3

O

c

t

a

v

e

P

S

D

(

d

B

)

20

40

60

80

100

dPSD (dB)

5

4

3

2

1

0

-1

-2

-3

-4

-5

16983

16983

18692

(e) h = 1.9

Log10(StDe)

-2

-1

0

1

Polar Angle ( deg.)

50

100

150

1/3

O

c

t

a

v

e

P

S

D

(

d

B

)

20

40

60

80

100

dPSD (dB)

5

4

3

2

1

0

-1

-2

-3

-4

-5

16985

16985

18692

(f) h = 3.2

Figure 14. Modeled spectra at all angles and frequencies with color contours showing dP SD =

P SDmodeled − P SDmeasured for xT E/De = 6 and Ma = 0.5. Note that the dark blue region starting

at upstream angles and high frequencies and extending out as the h increases is caused by the surface

shielding the jet mixing noise in the experimental data.

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

30

40

50

60

70

80

90

100

Modeled

Measured

Isolated

16979

16979

18692

18692

(a) θ = 60◦

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

100

Modeled

Measured

Isolated

16979

16979

18692

18692

(b) θ = 90◦

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

100

Modeled

Measured

Isolated

16979

16979

18692

18692

(c) θ = 120◦

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

100

Modeled

Measured

Isolated

16979

16979

18692

18692

(d) θ = 150◦

Figure 15. Modeled, measured and isolated spectra at four polar angles for a xT E/De = 6 surface at

h = 0.5 and jet velocity Ma = 0.5.

NASA/TM—2014-218120 19
Log10(StDe)

-2

-1

0

1

Polar Angle ( deg.)

50

100

150

1/3

O

c

t

a

v

e

P

S

D

(

d

B

)

20

40

60

80

100

dPSD (dB)

5

4

3

2

1

0

-1

-2

-3

-4

-5

17064

17064

18692

(a) h = 0.0

Log10(StDe)

-2

-1

0

1

Polar Angle ( deg.)

50

100

150

1/3

O

c

t

a

v

e

P

S

D

(

d

B

)

20

40

60

80

100

dPSD (dB)

5

4

3

2

1

0

-1

-2

-3

-4

-5

17066

17066

18692

(b) h = 0.2

Log10(StDe)

-2

-1

0

1

Polar Angle ( deg.)

50

100

150

1/3

O

c

t

a

v

e

P

S

D

(

d

B

)

20

40

60

80

100

dPSD (dB)

5

4

3

2

1

0

-1

-2

-3

-4

-5

17068

17068

18692

(c) h = 0.5

Log10(StDe)

-2

-1

0

1

Polar Angle ( deg.)

50

100

150

1/3

O

c

t

a

v

e

P

S

D

(

d

B

)

20

40

60

80

100

dPSD (dB)

5

4

3

2

1

0

-1

-2

-3

-4

-5

17070

17070

18692

(d) h = 1.0

Log10(StDe)

-2

-1

0

1

Polar Angle ( deg.)

50

100

150

1/3

O

c

t

a

v

e

P

S

D

(

d

B

)

20

40

60

80

100

dPSD (dB)

5

4

3

2

1

0

-1

-2

-3

-4

-5

17072

17072

18692

(e) h = 1.9

Log10(StDe)

-2

-1

0

1

Polar Angle ( deg.)

50

100

150

1/3

O

c

t

a

v

e

P

S

D

(

d

B

)

20

40

60

80

100

dPSD (dB)

5

4

3

2

1

0

-1

-2

-3

-4

-5

17074

17074

18692

(f) h = 3.2

Figure 16. Modeled spectra at all angles and frequencies with color contours showing dP SD =

P SDmodeled − P SDmeasured for xT E/De = 2 and Ma = 0.5.

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

Modeled

Measured

Isolated

17068

17068

18692

18692

(a) θ = 60◦

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

Modeled

Measured

Isolated

17068

17068

18692

18692

(b) θ = 90◦

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

Modeled

Measured

Isolated

17068

17068

18692

18692

(c) θ = 120◦

Strouhal Freqeuncy (StDe)

1/12 Octave PSD (dB)

10-1 100 101

40

50

60

70

80

90

Modeled

Measured

Isolated

17068

17068

18692

18692

(d) θ = 150◦

Figure 17. Modeled, measured and isolated spectra at four polar angles for a xT E/De = 2 surface at

h = 0.5 and jet velocity Ma = 0.5.

NASA/TM—2014-218120 20
V. Conclusions

The process of developing an empirical model to predict noise created by a jet near a surface has been

described and the resulting model presented. This model attempts to represent the complete jet-surface

interaction noise spectra by capturing trends in peak amplitude, spectral width, and peak frequency as

functions of surface length and distance to produce a parabolic characteristic spectra which can then be

scaled to represent different jet Mach numbers and observer angles. The model is relatively simple in

design which allows for the addition of other models to increase the range of applicability (e.g. heated jets,

rectangular nozzles) or improve the accuracy by incorporating spectral details not easily modeled as part

of the larger system (e.g. jet-surface resonances). An comparison between the model results and measured

data showed several areas where the model could be improved if some additional complexity were added such

as including a linear term in the parabolic model to account for non-symmetric spectra. In its current form

this empirical model is best suited for preliminary system level design studies where computation speed is

valued over absolute accuracy and the goal is to select potential configurations for more detailed study.

Subsonic and supersonic aircraft designs are moving to more integrated engine/airframe configurations

in response to for greater efficiency and lower noise. Aircraft noise prediction tools are currently lacking to

ability to quickly produce noise estimates for these tightly integrated configurations. The model presented

represents a first step toward developing a more advanced capability in this area that can be used to evaluate

future aircraft designs.

References

1Bridges, J., ”Noise from Aft Deck Exhaust Nozzles - Differences in Experimental Embodiments”, to be presented at the

2014 AIAA SciTech Conference, 13-17 January, 2014, National Harbor, MD, AIAA 2014-????.

2Brown, C. and Bridges, J., ”Small Hot Jet Acoustic Rig Validation”, NASA/TM-2006-214324, 2006.

3Bridges, J. and Brown, C., ”Validation of the Small Hot Jet Acoustic Rig for Jet Noise Research”, AIAA 2005-2846,

2005.

4Curle, N., ”The influence of solid boundaries upon aerodynamic sound”, Proc. Roy. Soc. of London, 231A, pp. 505-514,

1955.

5Ffowcs-Williams, J.E. and Hall, L.H., ”Aerodynamic sound generation by turbulent flow in the vicinity of a scattering

half plane”, J. Fluid Mech., 40(4), pp. 657-670, 1970.

6Crighton, D.G. and Leppington, F.G., ”Scattering of aerodynamic noise by a semi-infinite compliant plate”, J. Fluid

Mech., 43(4), pp. 721-736, 1970.

7Head, R.W. and Fisher, M.J., ”Jet/Surface Interaction Noise: Analysis Of Farfield Low Frequency Augmentation of Jet

Noise Due To The Presence Of A Solid Surface”, AIAA 1976-502, 1976.

8Lawrence, J.L.T., Azarpeyvand, M., and Self, R.H., ”Interaction between a Flat Plate and a Circular Jet”, AIAA 2011-

2745, 2011.

9Brown, C.A. , ”Jet-Surface Interaction Test: Far-Field Noise Results”, J. Eng. Gas Turbines Power, 135(7), Jun. 2013.

10Podboy, G., ”Jet-Surface Interaction Test: Phased Array Noise Source Localization Results”, ASME GT2012-69801,

2012.

11Khavaran, A. and Bridges, J., ”Development of jet noise power spectral laws using SHJAR data”, AIAA 209-3378, 2009.

12Khavaran, A. and Bridges, J., ”SHJAR jet noise data and power spectral laws”, NASA/TM 2009-215608, 2009.

13Zaman, K.B.M.Q., Fagan, A.F., Clem, M.M., and Brown, C.A., ”Resonant Interaction of a Rectangular Jet with a Flatplate”, to be presented at the 2014 AIAA SciTech Conference, 13-17 January, 2014, National Harbor, MD., AIAA 2014-????.

Appendix A. Equations and Coefficients for A(xT E/De, h) Fit

The variable A(xT E/De, h) in the dipole noise source model (Section III.B, Equation 1) is given by the

equation:

A(xT E/De, h) = Ax3 (xT E/De)h

3 + Ax2 (xT E/De)h2 + Ax1 (xT E/De)h1 + Ax0 (xT E/De) (8)

where the values of Ax3 (xT E/De), Ax2 (xT E/De), Ax1 (xT E/De), and Ax0 (xT E/De) are given by the results

of the fit process described in Section III.B.1. Ax3 , Ax2 and Ax1 were fit using the cubic polynomial:

NASA/TM—2014-218120 21
Axn (xT E/De) = (x

3

)(xT E/De)

3 + (x2

)(xT E/De)

2 + (x1

)(xT E/De)

1 + (x0

)(xT E/De)

0

(9)

where values of (x

n) are provided in Tables 3, 4, and 5 (with the appropriate range of applicability). The

value of Ax0 is obtained from a logarithmic equation:

Ax0 (xT E/De) = 9.3392 ln(xT E/De) + 72.821 (10)

which is valid across the range 1 ≤ xT E/De ≤ 10.

Range x

3 x2 x1 x0

0.5 ≤ xT E/De < 1.35 0 0 -0.4436 0.372

1.35 ≤ xT E/De < 4 -0.001648 -0.00348 0.231256 -0.538605

4 ≤ xT E/De ≤ 10 -0.012032 0.219824 -1.288074 2.6955

Table 3. Coefficients for computing the value of Ax3 (xT E/De) in Equation 8 (based on a cubic polynomial). Note that the unusually large number of significant figures in the coefficients are needed here

because of the potential large values of (xT E/De)

3

.

Range x

3 x2 x1 x0

0.5 ≤ xT E/De ≤ 1.35 0 -3.6084 11.4422 -6.6087

1.35 < xT E/De < 8 0 0 -1.9986 5.8391

8 ≤ xT E/De ≤ 10 0.066408 -1.139036 6.249492 -13.1788

Table 4. Coefficients for computing the value of Ax2 (xT E/De) in Equation 8 (based on a cubic polynomial).

Range x

3 x2 x1 x0

0.5 ≤ xT E/De < 2 0 7.512 -27.178 16.029

2 ≤ xT E/De < 8 0.097432 -2.026624 13.730666 -28.4122

8 ≤ xT E/De ≤ 10 0 0 -3.2284 27.442

Table 5. Coefficients for computing the value of Ax1 (xT E/De) in Equation 8 (based on a cubic polynomial).

Appendix B. Equations and Coefficients for B(xT E/De, h) Fit

The variable B(xT E/De, h) in the dipole noise source model (Section III.B, Equation 1) is given by the

equation:

B(xT E/De, h) = Bx3 (xT E/De)h

3 + Bx2 (xT E/De)h

2 + Bx1 (xT E/De)h

1 + Bx0 (xT E/De) (11)

where the values of Bx3 , Bx2 , Bx1 , and Bx0 are given by the results of the fit process described in Section

III.B.2. Bx3 , Bx2 , Bx1 , and Bx0 were fit using the cubic polynomial:

Bxn (xT E/De) = (x

3

)(xT E/De)

3 + (x2

)(xT E/De)

2 + (x1

)(xT E/De)

1 + (x0

)(xT E/De)

0

(12)

where (x

3

), (x

2

), (x

1

), and (x

0

) are the coefficients corresponding to the cubic, quadratic, linear, and constant

terms respectively. These coefficients (with the appropriate range of applicability) are provided in Tables 6,

7, 8, and 9.

NASA/TM—2014-218120 22
Range x

3 x2 x1 x0

0.5 ≤ xT E/De < 2 0 0.2992 0.4038 −2.4129

2 ≤ xT E/De < 4 0 0.142324 −0.80865 0.6394

4 ≤ xT E/De < 10 0.074472 −1.687588 11.83085 −25.406

Table 6. Coefficients for computing the value of Bx3 (xT E/De) in Equation 11 (based on a cubic polynomial).

Range x

3 x2 x1 x0

0.5 ≤ xT E/De < 2 0 2.3888 −14.0346 26.689

2 ≤ xT E/De < 4 0 −1.871788 12.816652 −9.9713

4 ≤ xT E/De < 6 −0.65556 14.626664 −102.345184 228.657

6 ≤ xT E/De < 10 0 −1.106788 20.900176 −86.012

Table 7. Coefficients for computing the value of Bx2 (xT E/De) in Equation 11 (based on a cubic polynomial).

Range x

3 x2 x1 x0

0.5 ≤ xT E/De < 2 0 −19.26284 63.522824 −82.938286

2 ≤ xT E/De < 6 0 5.4808 −43.334 31.801

6 ≤ xT E/De < 10 0 1.252 −18.9752 37.882

Table 8. Coefficients for computing the value of Bx1 (xT E/De) in Equation 11 (based on a cubic polynomial).

Range x

3 x2 x1 x0

0.5 ≤ xT E/De < 4 0 6.3312 −34.4 14.926

4 ≤ xT E/De < 10 0 0.4356 −3.965 −12.804

0 ≤ xT E/De < 0 0 0 0 0

Table 9. Coefficients for computing the value of Bx0 (xT E/De) in Equation 11 (based on a cubic polynomial).

NASA/TM—2014-218120 23
Appendix C. Equations and Coefficients for Fpeak(xT E/De, h) Fit

The variable Fpeak(xT E/De, h) in the dipole noise source model (Section III.B, Equation 1) is given by

the equation:

Fpeak(xT E/De, h) = Fx2 (xT E/De)h

2 + Fx1 (xT E/De)h1 + Fx0 (xT E/De) (13)

where the values of Fx3 , Fx2 , Fx1 , and Fx0 are given by the results of the fit process described in Section

III.B.3. Fx3 , Fx2 , Fx1 , and Fx0 were fit using the cubic polynomial:

Fxn (xT E/De) = (x

3

)(xT E/De)

3 + (x2

)(xT E/De)

2 + (x1

)(xT E/De)

1 + (x0

)(xT E/De)

0

(14)

where (x

3

), (x

2

), (x

1

), and (x

0

) are the coefficients corresponding to the cubic, quadratic, linear, and constant

terms respectively. These coefficients (with the appropriate range of applicability) are provided in Tables

10, 11, and 12.

Range x

3 x2 x1 x0

0.5 ≤ xT E/De < 2 0 −0.024 0.08 −0.045

2 ≤ xT E/De < 10 −0.00020833336 0.0037 −0.02356666 0.0525

Table 10. Coefficients for the cubic polynomial used to compute the value of Fx2 (xT E/De) in Equation

13.

Range x

3 x2 x1 x0

0.5 ≤ xT E/De < 2 0 0.1432 −0.4952 0.2824

2 ≤ xT E/De < 10 0.000944 −0.01882 0.132992 −0.33358

Table 11. Coefficients for the cubic polynomial used to compute the value of Fx1 (xT E/De) in Equation

13.

Range x

3 x2 x1 x0

0.5 ≤ xT E/De < 2 0 −0.1412 0.5734 −0.2321

2 ≤ xT E/De < 10 0 0.0023 −0.0652 0.46176

Table 12. Coefficients for the cubic polynomial used to compute the value of Fx0 (xT E/De) in Equation

13.

NASA/TM—2014-218120 24

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4. TITLE AND SUBTITLE

Developing an Empirical Model for Jet-Surface Interaction Noise

5a. CONTRACT NUMBER

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6. AUTHOR(S)

Brown, Clifford, A.

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WBS 473452.02.03.07.06.01.02

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National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland, Ohio 44135-3191

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E-18862

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Washington, DC 20546-0001

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14. ABSTRACT

The process of developing an empirical model for jet-surface interaction noise is described and the resulting model evaluated. Jet-surface

interaction noise is generated when the high-speed engine exhaust from modern tightly integrated or conventional high-bypass ratio engine

aircraft strikes or flows over the airframe surfaces. An empirical model based on an existing experimental database is developed for use in

preliminary design system level studies where computation speed and range of configurations is valued over absolute accuracy to select the

most promising (or eliminate the worst) possible designs. The model developed assumes that the jet-surface interaction noise spectra can be

separated from the jet mixing noise and described as a parabolic function with three coefficients: peak amplitude, spectral width, and peak

frequency. These coefficients are fit to functions of surface length and distance from the jet lipline to form a characteristic spectra which is

then adjusted for changes in jet velocity and/or observer angle using scaling laws from published theoretical and experimental work. The

resulting model is then evaluated for its ability to reproduce the characteristic spectra and then for reproducing spectra measured at other jet

velocities and observer angles; successes and limitations are discussed considering the complexity of the jet-surface interaction noise versus

the desire for a model that is simple to implement and quick to execute.

15. SUBJECT TERMS

Aerodynamic noise; (airframe generated); Aerodynamic noise (general); Aerodynamic noise (propulsion systems); Jet engines; Engine noise

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