Abbas Khavaran

Science Applications International Corporation, Cleveland, Ohio

Jet Surface Interaction Noise in a High 

Aspect Ratio Rectangular Exhaust

NASA/CR—2017-219528

July 2017
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Abbas Khavaran

Science Applications International Corporation, Cleveland, Ohio

Jet Surface Interaction Noise in a High 

Aspect Ratio Rectangular Exhaust

NASA/CR—2017-219528

July 2017

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared under Contract NNC12BA01
Acknowledgments

Support by the acoustics branch at NASA Glenn Research Center, and the Advanced Air Transport Technology (AATT) 

projects under NASA Fundamental Aeronautics Program, is greatly appreciated.

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NASA/CR—2017-219528 iii

Contents

Abstract.........................................................................................................................................................1

1.0 Overview...............................................................................................................................................1

2.0 Mean Flow Computation Details..........................................................................................................2

2.1 File Recommendations.................................................................................................................2

2.2 Normalization Rule ......................................................................................................................4

3.0 Acoustic Simulation..............................................................................................................................5

3.1 Mixing/Scrubbing Noise Component––“JSI-MIX” .....................................................................5

3.1.1 Input Preparation...............................................................................................................6

3.1.2 Primary Input File––“jsi-mix.inp” ....................................................................................8

3.1.3 Primary Output File––“ fort.55” .......................................................................................9

3.1.4 Shielded Side Primary Input File––“jsi-mix.inp” ...........................................................12

3.1.5 Shielded Side Primary Output File––“fort.55” ...............................................................14

3.1.6 File Summary..................................................................................................................15

3.2 Trailing Edge Noise Component––“JSI-TEN” ..........................................................................15

3.2.1 Primary Input File––“jsi-ten.inp” ...................................................................................15

3.2.2 Primary Output File––“fort.55” ......................................................................................16

3.2.3 File Summary..................................................................................................................20

4.0 Code Implementation..........................................................................................................................20

4.1 Obtaining the Source Code.........................................................................................................20

4.2 Creating the Executable..............................................................................................................20

5.0 Sample Computational Results...........................................................................................................21

5.1 Flow Simulations––RANS Solver..............................................................................................21

5.2 Post Processing of the Mean Flow––Interpolation to Acoustic Grid .........................................24

5.3 Acoustic Results.........................................................................................................................24

References...................................................................................................................................................29

NASA/CR—2017-219528 1

Jet Surface Interaction Noise in a High 

Aspect Ratio Rectangular Exhaust

Abbas Khavaran

Science Applications International Corporation

Cleveland, Ohio 44135

Abstract

A physics-based prediction model is employed to simulate jet surface interaction (JSI) noise in a 

transversely sheared jet exhaust. The methodology finds application in jets with a high aspect ratio (AR)

rectangular exhaust in the proximity of a flat surface. Two component spectra are simulated: 

(i) mixing/scrubbing noise; (ii) trailing edge noise––and are superimposed to obtain the far field exhaust 

noise on either side of a nearby surface. This document describes the necessary input parameters 

(including mean flow and turbulence information for the nozzle exhaust of interest) that should be 

prepared in order to initiate the simulation for each noise component. Sample input/output files in 

connection with an 8:1 aspect ratio rectangular exhaust at Mach 0.98 near a rigid surface are described. 

1.0 Overview

A schematic of a transversely sheared mean flow, such as a high aspect ratio (HAR) rectangular jet 

near a solid surface, is shown in Figure 1. The coordinate axes (1, 2, 3) denote the stream-wise, spanwise, and transverse (i.e., normal) directions, respectively. Parameters h and XTE refer to the standoff 

distance (measured from the lower lip of the nozzle to the flat surface), and the stream-wise plate length 

(measured from jet exit plane to the trailing edge of the surface). Polar angle θ is with respect to

downstream jet axis, and azimuthal angle φ is from the span-wise direction x2. For now, we consider the 

surface as infinitely long in the span-wise direction, and the mean flow as locally parallel in both x1 and x2

directions such the flow gradients of significance occur in the normal direction only (a planar flow). Our 

goal is to implement an acoustic analogy approach to simulate the far field jet exhaust noise. 

The analysis, as detailed in (Refs. 1, 2, and 3), considers the exhaust noise as a superposition of two 

component spectra: 

(i) Combined turbulent mixing noise and scrubbing noise in the presence of a nearby surface 

(referred to as mixing noise, MIX)

(ii) Trailing edge noise (TEN)

Noise component (i) is governed by the inhomogeneous Rayleigh equation and its source is the 

generalized Reynolds stress (includes product of fluctuating temperature and velocity in addition to 

velocity and velocity). This broadband noise component covers a full three octave spectrum and

dominates the latter two octaves of the total spectrum. Noise component (ii) is governed by the 

inhomogeneous adjoint Rayleigh equation. Its source, as formulated in the context of Rapid Distortion 

Theory (RDT), is described as an arbitrary convective quantity (Ref. 4) that, among other factors, relates

to the transverse momentum perturbations upstream of the trailing edge (TE)—and its power spectrum 

dominates the low frequency end of the total spectrum. 

Each noise component is evaluated as a convolution product of a source and an appropriate Green’s 

function (GF) integrated over a specified jet region. 
NASA/CR—2017-219528 2

Figure 1.—Geometry—a high aspect ratio rectangular exhaust 

near a solid surface.

In the following, we describe computational tools that use the above acoustic analogy approach to 

accurately predict the far-field sound pressure level due to jet surface interaction (JSI) in a transversely 

sheared jet exhaust. Two Fortran-90 computer codes designated as “JSI-MIX” and “JSI-TEN”, and

designed to output tables of spectral density for the mixing/scrubbing noise and the trailing edge noise,

will be discussed. The Alpha version of the JSI codes implies that prediction model should be viewed as 

an on-going research effort open to future improvements in compliance with flow and noise 

measurements.

Code input must include the mean flow solution from a Reynolds-Averaged Navier Stoke (RANS) 

solver. Turbulence kinetic energy and its dissipation rate from a k–ε or a k–ω turbulence model must also 

be provided. Recommendations will be made concerning the topology of the structured grids, which could 

simplify the process of preparing the input for each code. It is understood that it may not always be 

feasible to meet these recommendations within a particular RANS solver. Subsequently, flow solutions 

obtained on unstructured grids must be mapped onto a structured grid suitable for such noise calculations. 

This is done externally and with appropriate interpolation routines.

2.0 Mean Flow Computation Details

It is recognized that significant effort may be devoted to mean flow simulation prior to acoustic 

predictions. As is commonplace in most physics-based acoustic analogy applications, three files are 

supplied pursuant to the RANS calculations for the nozzle flow of interest: a grid file, a solution file, and 

a turbulence file.

2.1 File Recommendations

Simulation of jet surface interaction noise in planar flows is best achieved through an H-grid topology. 

The assumption that the mean flow be locally parallel in stream- and span-wise directions requires a 

summation of the convolution product over elementary jet volume slices in x1 and x2 directions. Ideally 

separate blocks may be deployed to identify plume segments upstream and downstream of the TE when a 

nearby surface is present. Sample file structure consisting of two blocks is shown in Figure 2. Only the jet

segment downstream of the jet exit plane enters noise simulation. The GF applicable to the 

mixing/scrubbing noise component deploys a local boundary condition, i.e., initial conditions at the 

surface upstream of the TE (block 1); and the radiation condition at x3 = –∞ if we suppose the observer is 

positioned at x3 = +∞ (block 2).
NASA/CR—2017-219528 3

Figure 2.—Example of block structure—rectangular jet exhaust near a flat surface.

RANS files follow the usual Plot3D standards (i.e., multi-block, whole-format):

!!!!!!!!!!!!!

!

Write (LUNG) NBLK ! Grid File

Write (LUNG) (JMAX(I), KMAX(I), LMAX(I), I = 1, NBLK)

DO I = 1, NBLK

J_MAX = JMAX(I) ! stream-wise x1

K_MAX = KMAX(I) ! transverse (normal) x3

L_MAX = LMAX(I) ! span-wise x2

! fill work-space with Block I grid coordinates

Write (LUNG) (((( XYZ(J,K,L,n),J=1,J_MAX),K=1,K_MAX),L=1,L_MAX), n=1,3)

ENDDO

!

Write (LUNQ) NBLK ! Q File

Write (LUNQ) (JMAX(I), KMAX(I), LMAX(I), I = 1, NBLK)

DO I = 1, NBLK

J_MAX = JMAX(I) ! stream-wise

K_MAX = KMAX(I) ! transverse (normal)

L_MAX = LMAX(I) ! span-wise

! fill work-space with Block I solution variables

Write (LUNQ) FSMACH, ALPHA, RE, TIME ! condition at Block I

Write (LUNQ) (((( QQ((J,K,L,n),J=1,J_MAX),K=1,K_MAX),L=1,L_MAX), n=1,5)

ENDDO

!

Write (LUNT) NBLK ! T File

Write (LUNT) (JMAX(I), KMAX(I), LMAX(I), I = 1, NBLK)

DO I = 1, NBLK

J_MAX = JMAX(I) ! stream-wise

K_MAX = KMAX(I) ! transverse (normal)

L_MAX = LMAX(I) ! span-wise

! fill work-space with Block I solution variables

Write (LUNT) FSMACH, ALPHA, RE, TIME ! condition at Block I

Write (LUNT) ((((QT(J,K,L,n),J=1,J_MAX),K=1,K_MAX),L=1,L_MAX), n=1,2)

ENDDO

!

!!!!!!!!!!!!!
NASA/CR—2017-219528 4

2.2 Normalization Rule

Parameters stored in the grid file (XYZ), Q file (QQ), and turbulence file (QT) are expected to follow 

the normalization standards in Table I.

When the ideal gas law holds, and with γ as the specific heat ratio and R as the gas constant, 

specified reference values for length, temperature, and pressure – (Lr, Tr, pr) = Lref(ft), 

Tinf(R), Pinf(psf), are deployed to define normalization parameters listed in Table I 

2 , r rr r

r

p a T

T =γ ρ = RR (1)

Parameters Tr and pr are usually selected as the ambient temperature and pressure, and ar is the reference 

sound speed. 

Cartesian coordinates (x1, x2, x3) are normalized relative to reference length Lr. Grid size within each 

block, in the order of x1, x3, and x2 directions, is (JMAX,KMAX,LMAX ). Ideally grid construction slated

for noise work should be an assortment of parallel slices stacked in the stream-wise direction. 

Figure 3 shows an H-grid construct in the span-wise plane within Block 2. Projection of the 

rectangular nozzle (blue) and the surface TE (dark) are also highlighted (Deq denotes the area-equivalent 

diameter for the rectangular nozzle 2 4 Area). π = Deq Cartesian coordinates x

 and y

 are used 

interchangeably to denote dependent and source coordinates. Within Block 1 the grid geometry excludes 

nodes shown below the surface (i.e., shielded side). 

The mean flow variables stored in file (QQ) are density, momentum components, and internal energy 

per unit volume (, , , , ) ρρ ρ ρ u v wE , normalized as

1

2

3

4

5

/

/( )

/( )

/( )

/( ),

r

r r

r r

r r

r

Q

Qua

Qva

Qwa

QEp

=ρ ρ

=ρ ρ

=ρ ρ

=ρ ρ

= γ

(2)

and the mean static pressure p is evaluated as

222

234

5

1

1 ( 1) r 2

p QQQ Q p Q

  + +

= γ− −  

γ  

(3)

TABLE I.—NORMALIZING FACTORS

Property Notation Normalizing parameter JSI variable

Coordinates X, Y, Z Lr (ft) Lref

Temperature T Tr (R) Tinf

Velocity component u, v, w ar (ft/s2) Aref

Pressure p γ pr (lbf/ ft2) Gamma*Pinf

Density ρ ρr (Slug/ft3) Rhoref

Time t Lr /ar (sec)

Total internal energy/unit volume E ρr 2 ar (lbf/ft2)

Turbulent kinetic energy k -

Turbulent dissipation rate ε -

Omega ω -
NASA/CR—2017-219528 5

Figure 3.—Acoustic grid in a span-wise plane.

The turbulence file (QT) consists of two variables. An input FLAG “TurbModel” identifies each 

variable as either (k and ε) or (k and ω). For convenience, the turbulence variables are provided in

dimensional form: k (ft2

/s2), ε (ft2/s3), and ω (1/s). Conversion from ω to ε is carried out according to

ε= × ×ω 0.90 . k (4)

Normalization of turbulence variables for the purpose of evaluating turbulence scales is carried out 

internally as ( ) ( ) 2 3 , , ka L a r rr ε and (ωL a r r ) . 

3.0 Acoustic Simulation

Two jet-surface interaction codes, “JSI-MIX” and “JSI-TEN”, evaluate mixing/scrubbing (MIX) and 

trailing edge noise (TEN), respectively. A superposition of two component spectra provides the total 

noise spectrum in a planar jet exhaust near a surface.

3.1 Mixing/Scrubbing Noise Component––“JSI-MIX”

This noise component requires an integration of the source/GF product over jet volume elements (or 

source correlation volumes) that radiate to a far-field observer. A criterion based on the line-of-sight 

argument determines the extent of volume integration. For an observer on the reflected side of a nearby 

surface, jet slice integration starts following the exit plane and marches downstream. As an example, both 

blocks are included in the simulation for such an observer when using block structure in Figure 2. On the 

other hand, we consider source correlation elements above the surface, i.e., block 1, as masked relative to 

an observer on the shielded side of the surface (although this argument may not be quite accurate if the 

observer angle is close to the downstream axis). Subsequently, slice integration starts immediately 

following the TE (block 2 in Figure 2). Details of the GF calculation and the numerical solution to a 

second-order ODE contributing to this GF are provided in (Ref. 1). While initial values for solving the

ODE are specified on the surface upstream of the TE, such near-field boundary is missing in block-2, and 

the initial values are stated at x3 = ∞ depending on observer location at x3 = ±∞ . 
NASA/CR—2017-219528 6

A pseudo-code outline of the “JSI-MIX” computation is given below, followed by more detailed 

information about each step:

For each observer location

For each frequency

 For each grid element

 1) calculate the source intensity

 2) calculate the propagator (GF) assuming a locally parallel mean flow

 3) calculate the SPL (source/GF convolution integral)

 Repeat each grid element

 Repeat each frequency

Repeat each observer location

Jet exit conditions are evaluated at a user-specified location along the jet. This information is used to 

evaluate a nominal exhaust velocity Uj that is employed to calculate source convection velocity 

Uc = αUj + βU where (α,β) are a pair of empirical constants and U is the local mean axial velocity. The

Strouhal frequency is St = f Dj/Uj where length Dj may be selected as the minor side of the rectangular 

nozzle. 

Sound pressure level (SPL) is evaluated in either narrow-band or 1/3-octave band. The narrow-band 

calculations are performed per Strouhal number at each center frequency f (Hz) in a third-octave band

( ) 1 2 2 10log10 UD p p J o J

− (5)

and the 1/3-octave predictions are 

( ) 2 2 10log10 BW p p × o (6)

where the bandwidth at frequency f is 

1/6 1/6 BW f (2 2 ) − =× − (7)

and the band number is defined as Band = 10log10 ( f ). Parameter 2 p in (5) and (6) refers to the meansquare acoustic pressure at an observer location, and po = 0.0002 μbar = 4.17×10–7 psf is the standard

acoustic reference pressure. In either case, the Overall Sound Pressure Level (OASPL) is calculated by

integrating the SPL on a 1/3-octave basis. 

3.1.1 Input Preparation

An example of an input file “jsi-mix.inp” assigned to an 8:1 aspect ratio rectangular exhaust (N8Z) 

with dimensions (5.3- by 0.67-in.) near a solid surface “h19_xte12” (h = 1.9-in., XTE = 12-in.) is provided 

in Section 3.1.2. Solution files generated by a typical RANS solver have been post-processed 

(interpolated) to a new grid that consists of two blocks—the first block (51 by 65 by 137) consists of 51 

axial planes (measured from nozzle exit), 65 points in transverse direction (above the surface), and 137 

points in the span-wise (x2) direction. Block 2 covers the remaining jet volume following the TE of the 

nearby surface—it extends below the surface (–x3 direction) with dimensions (77 by 93 by 137) as seen in 

Figure 4 and Figure 5.
NASA/CR—2017-219528 7

Figure 4.—Input parameters—stream-wise plane.

Figure 5.—Input parameters—span-wise plane.

A short description of variables appearing in “Namelist” is also provided in comment statements that

follow. The CaseTitle and RANS files information are subsequently followed, under header “JET_DATA”,

by parameters that define a nominal exit plane and source-volume integration range (stream- and span-wise 

directions). For clarity, some of the parameters are highlighted in Figure 4 and Figure 5. In this example, 

exit conditions are evaluated at the third slice within block 2 (Exit_block = 2, Jexit =3), and 

integration starts in block 1 and ends in block 2 (Start_block =1, End_block =2) at slice 

numbers identified through j_start and j_end, respectively. Required source integration range in the 

span-wise direction is defined for half of the jet volume from L_start (near the jet boundary) to L_END

(at the x1x3 plane of symmetry). As expected, careful selection of parameters in the input file is required for 

best results. For example, jet exit velocity Uj (when evaluated from nozzle upstream conditions) may not 

exactly develop at the nozzle exit plane—as the mean flow could accelerate and reach this velocity at some

distance further downstream. This is known to influence the source convection velocity, which in turn has 

an impact on the SPL levels particularly at observer angles closer to the jet axis. 

A restart file (fort.54) is written (or updated) following the treatment of each axial slice as source/GF 

volume integration proceeds (see File Summary, Section 3.1.6). This file needs to be copied to a new file 
NASA/CR—2017-219528 8

(fort.53) if stream-wise slice integration is to be continued from a previous terminal point. This type of 

output is useful if one is interested in inspecting the contributions to the jet noise from various segments 

in a plume. Ambient values for pressure and temperature are usually assigned to reference values (Pinf, 

Tinf), and Lref is the reference length. Other parameters of interest utilized in presentation of the 

output are Strouhal number range (St_min, St_max), observer locations (distance and angles), and 

output type (third-octave vs. narrow-band sound spectral density). Polar angles are provided relative to 

the downstream x1 axis, and a single azimuthal angle is also specified. Tables of predicted spectra are 

presented as lossless as well as with atmospheric loss (attenuation) at ambient temperature (Tinf) and 

relative humidity (h_r). 

Since any physics-based prediction model may be viewed as an on-going research effort in its utility

range and compliance with measurements, a host of other parameters are accessible in the input 

“Namelist” that are currently commented out within the source code, and could be modified from their 

preset default values.

The primary output file “fort.55” is listed in Section 3.1.3. It presents a reflection of the input 

parameters, RANS files, their blocks and grid sizes, mean flow parameters such as (U, ρ, T, a, M) at the

designated exit plane, frequency and Strouhal number range, and finally tables of far field sound spectral 

density at angles of choice.

Sample listing for the two main input/output files is provided below, followed by a file summary in 

Section 3.1.6.

3.1.2 Primary Input File––“jsi-mix.inp”

The following input file is used when the far-field observer is positioned on the reflected side of a 

nearby surface. The RANS files, designated as “N8Z_sp07_h19_xte12”, are prepared for an 

8:1 aspect ratio rectangular exhaust with nozzle upstream conditions of: pressure ratio NPR = 1.86, 

and temperature ratio NTR = 1.0 (i.e., Set Point sp07). The nearby surface is positioned at standoff 

h = 1.90-in. with length XTE = 12.0-in. Input file applicable to the shielded side is slightly different and 

will be discussed in Section 3.1.4.

$TITLE

 CaseTitle = ' JSI-MIX 8:1 Rectangular Jet, N8Z(H19, XTE12, SP07) '

&END

&CFD_FILES

GFILE = './N8Z_sp07_h19_xte12_jsi.x' ! Grid file 

QFILE = './N8Z_sp07_h19_xte12_jsi.q' ! Q file

TFILE = './N8Z_sp07_h19_xte12_jsi.t' ! Turb file

&END 

&JET_DATA

Exit_block = 1 ! Block# for evaluating jet exit conditions

Jexit = 4 ! Axial index for exit plane conditions within "Exit_block"

Dj = 0.0558 ! Nozzle minor-axis (ft)

Start_block = 1 ! Slice integration starts at "Start_block"

End_block = 2 ! Slice integration ends at "End_block"

 ! (for complete integration, set "End_block" larger than 

! total No. of blocks; this will also over-ride "j_end")

I_Wall= 1 ! Block# less than or equal to I_wall interact with the surface

I_Side = 1 ! Integer Flag 

 ! (1:Reflected side; 0: Shielded side)

j_start= 4 ! Axial slice# to start slice integration within "Start_block"

 ! (All following blocks start at j_start =1)

j_end =77 ! Ends slice integration at "j_end" within "End_block" 

 ! (blocks prior to End_block are integrated completely)

! (set "j_end" larger than the Max of slices in 
NASA/CR—2017-219528 9

 ! "End_block" for complete integration)

j_inc= 1 ! Axial increment for slice integration - applicable 

 ! to all blocks

L_start = 14 ! starting slice in x2-direction

L_END = 69 ! ending slice in x2-direction

L_inc= 1 ! increment for sector integration in Z-direction

Pinf = 2102.4 ! Reference pressure - psf

Tinf = 529.0 ! Reference temperature - R

h_r = 70.0 ! Percentage ambient relative humidity 

Rgas=1716.0 ! Gas constant - ft^2/(s^2 * R)

Gamma=1.4 ! Specific heats ratio

Lref=1.0 ! Reference length (ft) in grid file

Noz_scale=1.0 ! A factor to scale to a new nozzle diameter

 ! Use 1.0 if desired nozzle diameter is not different 

 ! from that in RANS solution 

N_Arc=1 ! Integer (1: Arc; 2: sideline)

Robs = 17.81 ! Distance (ft) at 90-deg

St_min =1.0d-2 ! Strouhal limits; (St= f Dj/Uj), Dj is nozzle minor-axis

 ! in x3 direction

St_max= 10.0 ! 

I_restart = 0 ! Integer Flag ( 0: no restart file;

 ! 1: solution uses restart file fort.53)

I_band=3 ! Integer Flag (0 : narrow-band spectra; 3: 3rd-octave spectra) 

TurbModel= 1 ! Integer Flag to identify Turbulence Model;

 ! (1 : k-e; 2: k-Omega )

Zimp_r = 0.0 ! Real and imaginary parts of Normalized Surface Impedance

Zimp_i = 0.0 ! default values (0.0, 0.0) indicate a rigid surface.

 

&END

&Polar

Nang = 4 ! No. of observer angles

Thetd = 40.0, 60.0, ! Polar Angles (deg) wrt downstream axis X1.

 90.0, 120.0 

&END

&Azimuthal

Azimuth = 90.0 ! A single Azimuthal angle (deg) wrt X2 axis. 

&END

3.1.3 Primary Output File––“ fort.55”

**********************************************

* JSI-MIX.f90 (Alpha Version) * 

**********************************************

------------------------ input --------------------

 Title= JSI 8:1 Rectangular Jet, N8Z(H19, XTE12, SP07) 

Grid file: 

./N8Z_sp07_h19_xte12_jsi.x 

 

Q file: 

./N8Z_sp07_h19_xte12_jsi.q 

 

Tke file: 

./N8Z_sp07_h19_xte12_jsi.t 

 

Exit_block = 2

Start_block = 1

 End_block = 2

 I_Wall = 1

 I_Side = 1

 Dj = 0.55800E-01
NASA/CR—2017-219528 10

 Jexit = 4

 j_start = 4

 j_inc = 1

 j_end = 77

 L_start = 14

 L_inc = 1

 L_end = 69

 Pinf = 2102.40

 Tinf = 529.00

 h_r = 70.00

 Rgas = 1716.00

 Gamma = 1.40

 Lref = 1.000000

 Noz_Scale = 1.000000

 Robs = 17.81

 N_Arc = 1

 St_min = 0.01

 St_max = 10.00

 I_restart = 0

 I_band = 3

 TurbModel = 1

* Nearby surface is considered as rigid *

Nang = 4

 Polar Angles (deg. from X1) =

 40.0 60.0 90.0 120.0

 Azimuthal Angle (deg. from X2) = 90.0

------------------------------------ 

 GFILE was opened successfully.

 QFILE was opened successfully.

 TFILE was opened successfully.

 

RANS input consists of 2 Blocks

Grid pts in order of StreamWise(X1), Transverse(normal-X3), SpanWise(X2):

Block# 1 Grid: 51 65 137

Block# 2 Grid: 77 93 137

Aref= 0.11273E+04fps, Rhoref= 0.23160E-02 slug/cft

 

Exit/Ambient conditions are evaluated at Block# 1 as:

Max Velocity at J= 4 (K,L)=( 17 67) is Uexit= 1027.87 fps

 ------------------------------------

 Calculated AMBIENT values (from CFD) 

 

 Velocity = 0.752202657172966 fps

 Density = 2.336729508750347E-003 slug/cft

 Pressure = 2116.22673422241 psf

 Static Temp = 527.759998742854 R

 Sound Speed = 1126.00649242348 fps

Ambient Mach(Mamb)= 6.680269272284703E-004

 ------------------------------------

 Exit values are evaluated within Block# 1 at Jexit = 4

 Exit Plane is at X_exit = 0.318382E+00 ft

 Diameter = 5.580000000000000E-002 ft

 ---

 At X_exit, at the point of Max Velocity (j,k)= ( 4, 17) :

 Uexit = 1027.87177083866 fps

 Density = 2.700998103378933E-003 slug/cft

 Pressure = 2120.08356161499 psf

 Static Temp = 457.416067588307 R

 Sound Speed = 1048.28257677696 fps

 Mach No. = 0.980529290107004 

 Jet Thickness = 5.580000000000000E-002 ft

 Stag Temp. Ratio = 1.03094797155550 
NASA/CR—2017-219528 11

 

Umax = 1027.87 is used for Convection velocity and Strouhal Freq.

Uexit/Ainf = 0.91

Texit/Tinf = 0.86 Static Temp Ratio

 Deallocation (Evaluate_At_Exit) in Block# 1 was successful

 

 Strouhal number (f a/U) calculated based on:

 o Freq Range (f) = 160 100000 (Hz) 

 o Nozzle Minor Side(a) = 0.5580E-01 (ft) 

 o Exit Velocity (U) = 0.1028E+04 (fps)

 o Strouhal Range = 0.8686E-02 0.5429E+01

 

 o X_exit = 0.318382E+00 (ft) 

 * ************************************************ *

 * RANS Turb. file was read as a k-epsilon solution *

 * ************************************************ *

 

Block# 1 Grid: 51 65 137 & Q file were successfully processed

Integrating Block# 1 from J= 4 to J= 51 with j_inc= 1

Block# 1 J_loc= 5

FIRST SLICE WAS CALLED AT (J_loc, L_azimuth) = 5 14

 ...

 ...

LAST SLICE WAS CALLED AT (J_loc, L_azimuth) = 5 69

.

.

.

Block# 2 J_loc= 76

FIRST SLICE WAS CALLED AT (J_loc, L_azimuth) = 76 14

 ...

 ...

LAST SLICE WAS CALLED AT (J_loc, L_azimuth) = 76 69

 Deallocating block# 2 in Main Prog.

 Deallocation (Main program) completed in Block# 2 istat= 0

 -- Azimuthal Angle FI = 90.0DEG. --

Prior 1 Block(s) are integrated within requested slices

Within Block# 2, additional jet slices j= 1 to 77 with j_inc= 1 are complete.

Spectral density is calculated in 3rd-Octave Band

 *** Mixing/Scrubbing Noise ***

 17.81 FT. ARC

 Unattenuated spectra / Angle from down-stream axis

 Freq Band St 40 60 90 120

 160 22 0.009 67.94 67.36 65.94 64.69

 200 23 0.011 71.20 70.52 68.99 67.62

 250 24 0.014 74.27 73.47 71.79 70.28

 315 25 0.017 77.21 76.25 74.39 72.73

 400 26 0.022 79.99 78.82 76.76 74.93

 500 27 0.027 82.33 80.92 78.68 76.68

 630 28 0.034 84.50 82.82 80.39 78.25

 800 29 0.043 86.49 84.51 81.91 79.63

 1000 30 0.054 88.15 85.88 83.14 80.74

 1250 31 0.068 89.66 87.08 84.22 81.74

 1600 32 0.087 91.14 88.24 85.31 82.70

 2000 33 0.109 92.27 89.17 86.19 83.46

 2500 34 0.136 93.24 90.02 86.95 84.10
NASA/CR—2017-219528 12

 3150 35 0.171 94.07 90.85 87.53 84.59

 4000 36 0.217 94.64 91.51 88.16 85.20

 5000 37 0.271 94.55 91.77 88.33 85.02

 6300 38 0.342 94.47 92.11 88.24 84.93

 8000 39 0.434 94.29 91.97 88.14 84.67

10000 40 0.543 93.92 91.99 87.90 84.13

12500 41 0.679 93.37 91.32 87.40 83.74

16000 42 0.869 92.52 90.93 86.77 82.99

20000 43 1.086 91.66 90.41 86.15 82.26

25000 44 1.357 90.74 89.93 85.62 81.42

31500 45 1.710 89.68 89.10 84.65 80.60

40000 46 2.171 88.50 88.32 83.59 79.85

50000 47 2.714 87.44 87.58 81.70 78.91

63000 48 3.420 86.25 86.69 82.19 77.97

80000 49 4.343 85.05 85.85 81.17 77.01

100000 50 5.429 83.96 84.88 80.43 76.07

OASPL DIRECTIVITY 105.29 103.22 99.48 96.22

 *** Mixing/Scrubbing Noise ***

 17.81 FT. ARC

 Attenuated spectra at 70.0000000000000 % Rel. Humidity and

 529.000000000000 deg. R

 Angle from down-stream axis

 Freq Band St 40 60 90 120

 160 22 0.009 67.92 67.34 65.93 64.68

 200 23 0.011 71.18 70.51 68.97 67.60

 250 24 0.014 74.25 73.45 71.77 70.26

 315 25 0.017 77.19 76.23 74.37 72.71

 400 26 0.022 79.96 78.79 76.73 74.90

 500 27 0.027 82.29 80.88 78.64 76.65

 630 28 0.034 84.44 82.76 80.33 78.19

 800 29 0.043 86.41 84.43 81.83 79.55

 1000 30 0.054 88.03 85.76 83.01 80.62

 1250 31 0.068 89.48 86.90 84.04 81.55

 1600 32 0.087 90.85 87.95 85.02 82.41

 2000 33 0.109 91.82 88.72 85.74 83.01

 2500 34 0.136 92.55 89.32 86.25 83.41

 3150 35 0.171 92.98 89.76 86.44 83.49

 4000 36 0.217 92.88 89.75 86.41 83.45

 5000 37 0.271 91.82 89.04 85.61 82.29

 6300 38 0.342 90.17 87.81 83.93 80.63

 8000 39 0.434 87.41 85.09 81.26 77.78

10000 40 0.543 83.27 81.34 77.26 73.49

12500 41 0.679 76.98 74.93 71.01 67.35

16000 42 0.869 66.34 64.75 60.60 56.82

20000 43 1.086 52.17 50.92 46.66 42.77

25000 44 1.357 32.14 31.34 27.03 22.84

31500 45 1.710 5.13 4.73 3.01 3.01

40000 46 2.171 3.01 3.01 3.01 3.01

50000 47 2.714 3.01 3.01 3.01 3.01

63000 48 3.420 3.01 3.01 3.01 3.01

80000 49 4.343 3.01 3.01 3.01 3.01

100000 50 5.429 3.01 3.01 3.01 3.01

OASPL DIRECTIVITY 101.60 98.82 95.67 92.88

3.1.4 Shielded Side Primary Input File––“jsi-mix.inp”

Several parameters discussed earlier in the context of file “jsi-mix.inp” should be modified when 

preparing input relevant to a far-field observer on the shielded side of a nearby surface. In the first place 

block 1 in Figure 4 is now considered as shielded from the observer—therefore stream-wise source 
NASA/CR—2017-219528 13

integration skips all blocks positioned upstream of the TE (Start_block = 2, j_start = 1),

and flag (I_Side = 0) points to the shielded side. For convenience, polar angles are introduced with a 

positive sign as before, however, RANS files are flipped with respect to x1x2 surface, i.e., a negative sign 

multiplies transverse coordinate x3 as well as the corresponding momentum variable. The new RANS

files, shown here with padded name “flip”, should be ordered such that an increase in x3 would point to 

the shielded side of the surface. A table of the predicted “mixing/scrubbing” noise component along the 

shielded side of the aforementioned surface is provided in a lossless format (Section 3.1.5).

$TITLE

 CaseTitle = ' JSI-MIX 8:1 Rectangular Jet, N8Z(H19, XTE12, SP07) '

&END

&CFD_FILES

GFILE = './N8Z_sp07_h19_xte12_jsi_flip.x' ! Grid file 

QFILE = './N8Z_sp07_h19_xte12_jsi_flip.q' ! Q file

TFILE = './N8Z_sp07_h19_xte12_jsi_flip.t' ! Turb file

&END 

&JET_DATA

Exit_block = 1 ! Block# for evaluating jet exit conditions

Jexit = 1 ! Axial index for exit plane conditions within "Exit_block"

Dj = 0.0558 ! Nozzle minor-axis (ft)

Start_block = 2 ! Slice integration starts at "Start_block"

End_block = 2 ! Slice integration ends at "End_block"

 ! (for complete integration, set "End_block" larger than 

 ! total No. of blocks; this will also over-ride "j_end")

I_Wall= 1 ! Block# less than or equal to I_wall interact with the surface

I_Side = 0 ! Integer Flag 

 ! (1:Reflected side; 0: Shielded side)

j_start= 1 ! Axial slice# to start slice integration within "Start_block"

 ! (All following blocks start at j_start =1)

j_end =77 ! Ends slice integration at "j_end" within "End_block" 

 ! (blocks prior to End_block are integrated completely)

! (set "j_end" larger than the Max of slices in 

! "End_block" for complete integration)

j_inc= 1 ! Axial increment for slice integration - applicable 

 ! to all blocks

L_start = 14 ! starting slice in x2-direction

L_END = 69 ! ending slice in x2-direction

L_inc= 1 ! increment for sector integration in Z-direction

Pinf = 2102.4 ! Reference pressure - psf

Tinf = 529.0 ! Reference temperature - R

h_r = 70.0 ! Percentage ambient relative humidity 

Rgas=1716.0 ! Gas constant - ft^2/(s^2 * R)

Gamma=1.4 ! Specific heats ratio

Lref=1.0 ! Reference length (ft) in grid file

Noz_scale=1.0 ! A factor to scale to a new nozzle diameter

 ! Use 1.0 if desired nozzle diameter is not different 

 ! from that in RANS solution 

N_Arc=1 ! Integer (1: Arc; 2: sideline)

Robs = 17.81 ! Distance (ft) at 90-deg

St_min =1.0d-2 ! Strouhal limits; (St= f Dj/Uj), Dj is nozzle minor-axis

 ! in x3 direction

St_max= 10.0 ! 

I_restart = 0 ! Integer Flag ( 0: no restart file;

 ! 1: solution uses restart file fort.53)

I_band=3 ! Integer Flag (0 : narrow-band spectra; 3: 3rd-octave spectra) 

TurbModel= 1 ! Integer Flag to identify Turbulence Model;

 ! (1 : k-e; 2: k-Omega )

Zimp_r = 0.0 ! Real and imaginary parts of Normalized Surface Impedance

Zimp_i = 0.0 ! default values (0.0, 0.0) indicate a rigid surface.

 
NASA/CR—2017-219528 14

&END

&Polar

Nang = 4 ! No. of observer angles

Thetd = 40.0, 60.0, ! Polar Angles (deg) wrt downstream axis X1.

 90.0, 120.0 

&END

&Azimuthal

Azimuth = 90.0 ! A single Azimuthal angle (deg) wrt X2 axis. 

&END

3.1.5 Shielded Side Primary Output File––“fort.55” 

**********************************************

* JSI-MIX.f90 (Alpha Version) * 

**********************************************

------------------------ input --------------------

 Title= JSI 8:1 Rectangular Jet, N8Z(H19, XTE12, SP07) 

Grid file: 

./N8Z_sp07_h19_xte12_jsi_flip.x 

 

Q file: 

./N8Z_sp07_h19_xte12_jsi_flip.q 

 

Tke file: 

./N8Z_sp07_h19_xte12_jsi_flip.t 

 

.

Spectral density is calculated in 3rd-octave Band

 *** Mixing/Scrubbing Noise ***

 17.81 FT. ARC

 Unattenuated spectra / Angle from down-stream axis

 Freq Band St 40 60 90 120

 160 22 0.009 62.00 61.42 60.01 58.75

 200 23 0.011 65.26 64.59 63.04 61.67

 250 24 0.014 68.31 67.53 65.84 64.32

 315 25 0.017 71.24 70.31 68.43 66.75

 400 26 0.022 73.99 72.86 70.79 68.92

 500 27 0.027 76.29 74.95 72.68 70.66

 630 28 0.034 78.39 76.83 74.37 72.19

 800 29 0.043 80.30 78.49 75.85 73.52

 1000 30 0.054 81.84 79.82 77.04 74.57

 1250 31 0.068 83.17 80.97 78.05 75.45

 1600 32 0.087 84.37 82.06 78.98 76.22

 2000 33 0.109 85.18 82.87 79.62 76.69

 2500 34 0.136 85.68 83.49 80.06 76.94

 3150 35 0.171 85.85 83.91 80.26 76.96

 4000 36 0.217 85.66 84.08 80.20 76.72

 5000 37 0.271 85.15 83.99 79.92 76.30

 6300 38 0.342 84.31 83.67 79.43 75.69

 8000 39 0.434 83.20 83.13 78.75 74.93

10000 40 0.543 81.99 82.48 78.01 74.13

12500 41 0.679 80.68 81.73 77.19 73.27

16000 42 0.869 79.17 80.81 76.22 72.28

20000 43 1.086 77.79 79.93 75.32 71.35

25000 44 1.357 76.44 79.02 74.39 70.41

31500 45 1.710 75.10 78.06 73.41 69.43

40000 46 2.172 73.75 77.05 72.39 68.40
NASA/CR—2017-219528 15

50000 47 2.715 72.54 76.09 71.43 67.44

63000 48 3.421 71.31 75.10 70.43 66.44

80000 49 4.344 70.06 74.07 69.40 65.41

100000 50 5.430 68.94 73.10 68.43 64.44

OASPL DIRECTIVITY 95.71 94.83 91.03 87.77

3.1.6 File Summary

Simulation of mixing/scrubbing noise component uses the following input (Table II) and output files

(Table III).

TABLE II.—INPUT FILES

Unit Description

10 Namelist file “jsi-mix”—defines input parameters

27 Unformatted grid file—specify file name in jsi-mix

28 Unformatted Q file—specify file name in jsi-mix

29 Unformatted turbulence file—specify file name in jsi-mix

53 Restart file fort.53 (see output unit 54)

TABLE III.—OUTPUT FILES

Unit Description

6 Formatted output shows—calculation progress

54 Formatted restart file fort.54—should be copied to fort.53 when I_restart=1

55 Primary output file fort.55—sound spectral density tables

3.2 Trailing Edge Noise Component––“JSI-TEN”

The source/GF integration is now carried out on a span-wise plane dA = dy2dy3 along the TE of the 

surface. In the transverse direction y3 starts from the surface and reaches as far as yo where U(yo) attains a 

maximum (i.e., ∂U/∂y3 → 0)). In the span-wise direction y2 covers the wetted edge of the surface, i.e., 

sources that make relatively significant contribution to the TE noise component. Since source strength as 

related to turbulent kinetic energy (TKE) is stored as per unit volume, its stream-wise span should be 

scaled with an appropriate length-factor L. This parameter is ultimately combined with a second 

calibration constant present in front of the equation. The directivity factor (or GF) comprises of two 

observer angles in addition to the local mean velocity and flight Mach number, and displays a cardioid 

pattern centered at the edge. The integrated spectrum, as formulated for power spectral density (Ref. 2) 

exhibits a U5 velocity scaling.

Here the input parameter j_start=49 is assigned to the location of the integration plane (selected 

as two grid points upstream of the surface TE, j_Edge=51). Additionally, a new sub-list within block 

data, declared as “EdgeData”, identifies the TE for a nearby surface.

Since the TE noise directivity factor is symmetric with respect to the edge, the predicted spectra are 

considered as valid on both sides of the surface. A complete input file applicable to this noise component 

is provided in Section 3.2.1, followed by the associated primary output in Section 3.2.2.

3.2.1 Primary Input File––“jsi-ten.inp”

$TITLE

 CaseTitle = ' JSI 8:1 Rectangular Jet, N8Z(H19, XTE12, SP07) '

&END

&CFD_FILES

GFILE = './N8Z_sp07_h19_xte12_jsi.x' ! Grid file 
NASA/CR—2017-219528 16

QFILE = './N8Z_sp07_h19_xte12_jsi.q' ! Q file

TFILE = './N8Z_sp07_h19_xte12_jsi.t' ! Turb file

&END 

&JET_DATA

Exit_block = 1 ! Block# for evaluating jet exit conditions

Jexit = 1 ! Axial index for exit plane conditions within "Exit_block"

Dj = 0.0558 ! Nozzle minor-axis (ft)

H_offset = 0.158333 ! Standoff distance h (ft)

!K_start= 1 ! Starting index – transverse direction (defaults to 1) 

j_start= 49 ! J_start should be < (j_Edge - j_inc) within "Edge_block"

 ! Noise is always evaluated at (j_Edge - j_inc)

j_inc= 1 ! Increment for slice integration - (stream-wise x1)

L_start = 14 ! Starting slice index (span-wise x2)

L_END = 69 ! Ending slice index, plane of symmetry (span-wise x2)

L_inc= 1 ! Increment in sector index (span-wise x2)

Pinf = 2102.4 ! Reference pressure - psf

Tinf = 529.0 ! Reference temperature - R

h_r = 70.0 ! ambient relative humidity - %

Rgas=1716.0 ! Gas constant - ft^2/(s^2 * R)

Gamma=1.4 ! Specific heats ratio

Lref=1.0 ! Reference length (ft) in grid file

Noz_scale=1.0 ! A factor to scale nozzle diameter

 ! Use 1.0 if desired diameter equals that in RANS solution 

N_Arc=1 ! Integer (1: Arc; 2: sideline)

Robs = 17.81 ! Distance (ft) at 90-deg

St_min =1.0d-2 ! Strouhal limits; (St= f Dj/Uj), Dj is nozzle minor-axis

 ! parallel to the surface

St_max= 10.0 ! 

I_band=3 ! Integer Flag (0 : narrow-band spectra; 3: 3rd-octave spectra) 

TurbModel= 1 ! Integer Flag to identify Turbulence Model 

 ! (1 : k-e; 2: k-Omega ) 

&END

&Polar

Nang = 4 ! No. of observer angles

Thetd = 40.0, 60.0, ! Polar Angles (deg) wrt downstream axis X1.

 90.0, 120.0 

&END

&Azimuthal

Azimuth = 90.0 ! Azimuthal Angles (deg) wrt X2 axis. 

&END

&EdgeData

Edge_block = 1 ! Block# at the Trailing Edge (TE)

 j_Edge = 51 ! Axial slice index for TE within "Edge_block"

&END

3.2.2 Primary Output File––“fort.55”

 **********************************************

* JSI-TEN.f90 (Alpha Version) * 

**********************************************

------------------------ input --------------------

 Title= JSI 8:1 Rectangular Jet, N8Z(H19, XTE12, SP07) 

Grid file: 

./N8Z_sp07_h19_xte12_jsi.x 

 

Q file: 

./N8Z_sp07_h19_xte12_jsi.q 

 

Tke file: 

./N8Z_sp07_h19_xte12_jsi.t 

 
NASA/CR—2017-219528 17

Exit_block = 1

 Dj = 0.55800E-01

 H_offset = 0.15833E+00

 Jexit = 1

 K_start = 1

 j_start = 49

 j_inc = 1

 L_start = 14

 L_inc = 1

 L_end = 69

 Pinf = 2102.40

 Tinf = 529.00

 h_r = 70.00

 Rgas = 1716.00

 Gamma = 1.40

 Lref = 1.000000

 Noz_Scale = 1.000000

 Robs = 17.81

 N_Arc = 1

 St_min = 0.0100

 St_max = 10.00

Edge_block = 1

 J_Edge = 51

 I_band = 3

 TurbModel = 1

Nang = 4

 Polar Angles (deg. from X1) =

 40.0 60.0 90.0 120.0

 Azimuthal Angle (deg. from X2) = 90.0

 ------------------------------------ 

 GFILE was opened successfully.

 QFILE was opened successfully.

 TFILE was opened successfully.

 

RANS input consists of 2 Blocks

 Grid points in the order of: 

 Axial, Radial (normal to surface), Azimuthal (spanwise)

 Block# 1 Grid: 51 65 137

 Block# 2 Grid: 77 93 137

 *** Note:

 - Edge is within the specified integration range -

 ***

 

 Deallocating block# 1 in Evaluate_At_Exit

 Deallocation (Evaluate_At_Exit) in Block# 1 was successful

Aref= 0.11273E+04fps, Rhoref= 0.23160E-02 slug/cft

 

Exit/Ambient conditions are evaluated at Block# 1 as:

Max Velocity at J= 1 (K,L)=( 19 60) is Uexit= 1027.67 fps

 ------------------------------------

 Calculated AMBIENT values (from CFD) 

 

 Velocity = 0.752202657172966 fps

 Density = 2.336729508750347E-003 slug/cft

 Pressure = 2116.22673422241 psf

 Static Temp = 527.759998742854 R

 Sound Speed = 1126.00649242348 fps

Ambient Mach(Mamb)= 6.680269272284703E-004

 ------------------------------------
NASA/CR—2017-219528 18

 Exit values are evaluated within Block# 1 at Jexit = 1

 Exit Plane is at X_exit = 0.258379E+00 ft

 Diameter = 5.580000000000000E-002 ft

 ---

 At X_exit, at the point of Max Velocity (j,k)= ( 1, 19) :

 Uexit = 1027.67159986442 fps

 Density = 2.720093119774312E-003 slug/cft

 Pressure = 2137.67619625854 psf

 Static Temp = 457.974045096322 R

 Sound Speed = 1048.92175396423 fps

 Mach No. = 0.979740953965824 

 Jet Thickness = 5.580000000000000E-002 ft

 Stag Temp. Ratio = 1.03193799692194 

 

Umax = 1027.67 is used for Convection velocity and Strouhal Freq.

Uexit/Ainf = 0.91

Texit/Tinf = 0.87 Static Temp Ratio

 Deallocation (Evaluate_At_Exit) in Block# 1 was successful

 

 Strouhal number (f a/U) calculated based on:

 o Freq Range (f) = 160 100000 (Hz) 

 o Exit Minor Axis (a) = 0.5580E-01 (ft) 

 o Exit Velocity (U) = 0.1028E+04 (fps)

 o Strouhal Range = 0.8688E-02 0.5430E+01

 

 o X_exit = 0.258379E+00 (ft) 

 * ************************************************ *

 * RANS Turb. file was read as a k-epsilon solution *

 * ************************************************ *

 

Block# 1 Grid: 51 65 137 & Q file were successfully processed

Integrating Block# 1 Along Slice At J= 50

FIRST SLICE WAS CALLED AT (J_loc, L_azimuth) = 50 14

 ********************************************************

 * Trailing Edge Noise is evaluated at J= 50 in Block 1 *

 ********************************************************

 ...

 ...

LAST SLICE WAS CALLED AT (J_loc, L_azimuth) = 50 69

 Deallocating block# 1 in Main Prog.

 Deallocation (Main program) completed in Block# 1 istat= 0

 -- Azimuthal Angle FI = 90.0DEG. --

Spectral density is calculated in 3rd-Octave Band

 *** Trailing Edge Noise ***

 17.81 FT. ARC

 Unattenuated spectra / Angle from down-stream axis

 Freq Band St 40 60 90 120

 160 22 0.009 72.96 74.29 74.74 74.68

 200 23 0.011 76.48 77.79 78.22 78.13

 250 24 0.014 79.81 81.10 81.49 81.38

 315 25 0.017 82.98 84.24 84.59 84.44

 400 26 0.022 85.84 87.06 87.35 87.16

 500 27 0.027 87.98 89.15 89.38 89.15

 630 28 0.034 89.48 90.62 90.79 90.51

 800 29 0.043 90.12 91.21 91.33 91.00

 1000 30 0.054 89.77 90.83 90.89 90.53

 1250 31 0.068 88.48 89.51 89.54 89.15

 1600 32 0.087 86.04 87.05 87.05 86.64
NASA/CR—2017-219528 19

 2000 33 0.109 83.06 84.06 84.04 83.61

 2500 34 0.136 79.52 80.51 80.47 80.04

 3150 35 0.171 75.41 76.39 76.35 75.91

 4000 36 0.217 70.84 71.81 71.76 71.32

 5000 37 0.271 66.36 67.33 67.28 66.83

 6300 38 0.342 61.59 62.56 62.50 62.05

 8000 39 0.434 56.56 57.53 57.47 57.02

10000 40 0.543 51.82 52.78 52.72 52.27

12500 41 0.679 47.03 48.00 47.93 47.48

16000 42 0.869 41.71 42.68 42.62 42.16

20000 43 1.086 36.89 37.86 37.79 37.34

25000 44 1.357 32.06 33.03 32.96 32.51

31500 45 1.710 27.05 28.02 27.96 27.50

40000 46 2.172 21.87 22.84 22.77 22.32

50000 47 2.715 17.03 18.00 17.93 17.48

63000 48 3.421 12.01 12.98 12.92 12.46

80000 49 4.344 6.83 7.79 7.73 7.28

100000 50 5.430 1.98 2.95 2.89 2.43

OASPL DIRECTIVITY 97.55 98.65 98.78 98.47

Spectral density is calculated in 3rd-Octave Band

 *** Trailing Edge Noise ***

 17.81 FT. ARC

 Attenuated spectra at 70.0 % Rel. Humidity and 529.0 deg. R

 Angle from down-stream axis

 Freq Band St 40 60 90 120

 160 22 0.009 72.95 74.28 74.73 74.66

 200 23 0.011 76.46 77.77 78.20 78.11

 250 24 0.014 79.79 81.08 81.47 81.36

 315 25 0.017 82.96 84.22 84.56 84.42

 400 26 0.022 85.81 87.03 87.32 87.13

 500 27 0.027 87.94 89.11 89.35 89.11

 630 28 0.034 89.43 90.56 90.73 90.45

 800 29 0.043 90.04 91.13 91.24 90.92

 1000 30 0.054 89.65 90.71 90.77 90.41

 1250 31 0.068 88.29 89.33 89.36 88.97

 1600 32 0.087 85.75 86.76 86.75 86.35

 2000 33 0.109 82.62 83.61 83.59 83.17

 2500 34 0.136 78.83 79.81 79.78 79.35

 3150 35 0.171 74.32 75.30 75.25 74.81

 4000 36 0.217 69.09 70.06 70.01 69.56

 5000 37 0.271 63.64 64.61 64.55 64.11

 6300 38 0.342 57.29 58.26 58.20 57.75

 8000 39 0.434 49.68 50.65 50.59 50.14

10000 40 0.543 41.17 42.13 42.07 41.62

12500 41 0.679 30.64 31.61 31.54 31.09

16000 42 0.869 15.54 16.50 16.44 15.99

20000 43 1.086 0.00 0.00 0.00 0.00

25000 44 1.357 0.00 0.00 0.00 0.00

31500 45 1.710 0.00 0.00 0.00 0.00

40000 46 2.172 0.00 0.00 0.00 0.00

50000 47 2.715 0.00 0.00 0.00 0.00

63000 48 3.421 0.00 0.00 0.00 0.00

80000 49 4.344 0.00 0.00 0.00 0.00

100000 50 5.430 0.00 0.00 0.00 0.00

OASPL DIRECTIVITY 97.42 98.52 98.66 98.35
NASA/CR—2017-219528 20

3.2.3 File Summary

The input/output files applicable to the TE noise component are numbered similar to those stated 

earlier for the mixing/scrubbing noise component in Section 3.1.6. The only caveat is that a restart file 

‘fort.54” is not generated. 

4.0 Code Implementation

Each noise component is packaged with two Fortran codes.

4.1 Obtaining the Source Code

Abbas.Khavaran@nasa.gov

1) mixing/scrubbing noise 

jsi-mix.f90

jsi-mix-modules.f90

2) trailing edge noise

jsi-ten.f90

jsi-ten-modules.f90

4.2 Creating the Executable

JSI codes are written in FORTRAN-90. The current version runs on a single processor platform. The 

execution may be achieved in a command mode such as a Unix environment. For example, using an 

available Intel Fortran compiler, the executable “a.out” is created as:

ifort -c jsi-mix-modules.f90

ifort -c jsi-mix.f90

ifort *.o

rm –rf *.o *.mod

The last command removes “*.o” and “*.mod” files created during compilation. The executable 

could be submitted interactively, and with the standard “fort.6” output directed to an arbitrary file 

“ProgressFile”

./a.out > ProgressFile &

or, alternatively, the executable may be addressed within a PBS script for queue submission. Code “jsimix.f90” represents the main program as well as all associated subroutines, in one package.

The executable for the trailing edge noise component is generated in a similar fashion:

ifort -c jsi-ten-modules.f90

ifort -c jsi-ten.f90

ifort *.o

rm –rf *.o *.mod
NASA/CR—2017-219528 21

The path to three RANS files is specified within input “jsi-mix.inp” and “jsi-ten.inp” as 

noted earlier.

5.0 Sample Computational Results

Numerical simulations are presented for an aspect ratio 8:1 rectangular jet exhaust with a nearby 

semi-infinite surface place at standoff h = 1.90-in., and length XTE = 12.0-in. Table IV details nozzle 

pressure ratio (NPR), stagnation temperature ration (NTR), and exhaust Mach number Mj = Uj/aj , and the 

acoustic Mach number Ma = Uj/a∞ at three subsonic conditions.

5.1 Flow Simulations––RANS Solver

Computational fluid dynamic simulations were carried with a commercially available RANS solver, 

SolidWorks® (SW) (SolidWorks Corporation) (Refs. 5 and 6), using a k–ε turbulence model. The flow 

solver employs an automatic (adaptive) gridding methodology that is convenient for jet simulation 

problems, however the solution needs to be post-processed, and mapped to a user-friendly grid for followon applications such as GF calculations in noise prediction. Representative SW results at three set points 

SP03, SP05 and SP07 (Table IV) are shown in Figure 6 in a stream-wise y1y3 plane of symmetry. Each 

figure shows, from top, normalized mean axial velocity U/Uj, turbulent kinetic energy ratio κ1/2 Uj, static 

temperature ratio T/T∞, and normalized turbulent length-scale κ3/2/(εDeq), to a distance of y1/Deq = 14

downstream of the jet exit (Deq = 2.136-in)). The nearby surface is highlighted (dark line) at y3/Deq = 1.04 

below the nozzle geometric center extending to y1/Deq = 5.62.

Simulations are also shown on a span-wise y2y3 plane at the trailing edge of a nearby surface, and 

compared with measurements (Ref. 7) at Mach number of M = 0.22. Mean velocity (Figure 7), turbulent 

kinetic energy TKE (Figure 8), and turbulent length scale (Figure 9), are all normalized to highlight selfsimilarity across Mach numbers.

Figure 8 shows that predicted TKE levels are slightly higher than measurements on the left. The selfsimilarity of the turbulent length-scale o eq D in Figure 9 shows that normalized time-scale 

( ) ( ) ( ) 0.5

o eq DU D U j o eq j τ =κ  should exhibit self-similarity as well. This fact is reflected in the 

source modeling, i.e., Strouhal scaling of the peak spectra for each noise components (Ref. 2).

TABLE IV.—SET POINT CONDITIONS

Set Point NPR NTR Mj Ma

SP03 1.19 1.0 0.51 0.50

SP05 1.42 1.0 0.72 0.70

SP07 1.86 1.0 0.98 0.90
NASA/CR—2017-219528 22

Figure 6.—Mean axial velocity, turbulent kinetic energy, static temperature, and turbulent length-scale in a streamwise plane of symmetry at acoustic Mach numbers Ma = 0.50 (top-left); 0.70 (top-right); and 0.90 (bottom) figures.
NASA/CR—2017-219528 23

Figure 7.—Mean flow simulations in a span-wise plane at the TE at acoustic Mach numbers of 0.50 and 0.70, and 

comparison with measurements (left) at Mach 0.22.

Figure 8.—Turbulent kinetic energy in a span-wise plane at the TE at acoustic Mach numbers of 0.50 and 0.90, 

and comparison with measurements (left) at Mach 0.22.
NASA/CR—2017-219528 24

Figure 9.—Turbulent length-scale in a span-wise plane at the TE at Ma = 0.50, 0.70, and 0.90.

Figure 10.—Stream-wise interpolation slices—acoustic grid.

5.2 Post Processing of the Mean Flow––Interpolation to Acoustic Grid

Mean flow and turbulence parameters suitable for input to JSI codes require an H-Grid structure. An

example was presented earlier (Figure 4 and Figure 5) using an Acoustic Grid with 2 blocks—each block 

comprised of slices stacked normal to the stream-wise x1 direction as highlighted in Figure 10. A 

dedicated interpolation routine is essential to the process, and it is crucial to examine the results carefully 

for possible “iblank” spots where zeros may have been inserted due to numerical failures. Such nodes 

could be corrected with an average value of the surrounding grid points. Sample mapping output for mean 

velocity and turbulent kinetic energy is shown in Figure 11. Interpolation outcome on a span-wise plane 

at the trailing edge of the nearby surface is also shown in Figure 12 at set point 5 (Table IV). 

5.3 Acoustic Results

Jet noise spectra are examined below at operating conditions listed in Table IV. Individual noise 

components, designated as Scrubbing Noise and Trailing Edge Noise, are presented and their sum Total 

Noise (Analysis) is compared with Measurement (Refs. 8 and 9) at selective number of observer polar

angles at azimuth φ = 90°. Results are presented on an arc R = 17.80-ft (i.e., R = 100Deq) on both sides of 
NASA/CR—2017-219528 25

Figure 11.—Interpolated flow––stream-wise plane of symmetry. Mean axial velocity 

(top), turbulent kinetic energy (bottom) at set point SP05.

Figure 12.—Interpolated flow––span-wise plane at the TE of the nearby surface. Mean 

axial velocity (left), turbulent kinetic energy (right) at set point SP05.

a nearby surface. Although the predicted TE noise component is symmetric with respect to the edge due 

to symmetry in the propagator, measurements for the majority of cases are not quite symmetric and 

exhibit a slightly larger peak on the reflected side of the surface. Turbulent mixing/scrubbing noise 

component has a greater presence on the reflected side, as expected. Figure 13 to Figure 18 show that the 

peak in the predicted TE component could differ from measurements by as much as 4 dB due to lack of 

symmetry in measured data, however, the general trend is in agreement with data across the three Mach 

numbers. The overall sound pressure level (OASPL) associated with the TE noise component follows a 

U 5 velocity scaling in the current modeling (Ref. 4). 

Directivity predictions for the TE noise component as well as the total noise are shown in Figure 19

(bottom)—and are compared with measurements (top figure) at conditions of Table IV. As anticipated, 

the TE noise component (dashed-line) overwhelms the directivity factor due to its dominant spectral peak 

level. Only at small angles to the jet axis the mixing noise component contributes significant enough to 

weight noticeably on the total noise.
NASA/CR—2017-219528 26

Figure 13.—Spectrum on the reflected side of Mach 0.51 jet 

(SP03-N8ZH19XTE12) at inlet polar angles of 60°, 90°, and 

120°: Jet mixing/scrubbing noise (blue), TE noise (red), total 

predicted (dark line), measured data for total noise (symbol).

Figure 14.—As in Figure 13, but on the shielded side. 
NASA/CR—2017-219528 27

Figure 15.—Spectrum on the reflected side of Mach 0.72 jet 

(SP05-N8ZH19XTE12) at inlet polar angles of 60°, 90°, and 

120°: Jet mixing/scrubbing noise (blue), TE noise (red), total 

predicted (dark line), measured data for total noise (symbol).

Figure 16.—As in Figure 15, but on the shielded side.
NASA/CR—2017-219528 28

Figure 17.—Spectrum on the reflected side of Mach 0.98 jet 

(SP07-N8ZH19XTE12) at inlet polar angles of 60°, 90°, and 

120°: Jet mixing/scrubbing noise (blue), TE noise (red), total

predicted (dark line), measured data for total noise (symbol).

Figure 18.—As in Figure 17, but on the shielded side.
NASA/CR—2017-219528 29

Figure 19.—OASPL directivity––shielded side of Mach 0.51, 0.72, 

and 0.98 rectangular jets (N8ZH19XTE12), measurements (top), 

predictions (bottom).

References

1. Khavaran, A., “Acoustics of Jet Surface Interaction – Scrubbing Noise,” AIAA Paper 2014-3314, 

June 1024.

2. Khavaran, A., Bozak, R. F., and Brown, C. A., “Jet Surface Interaction Noise in a Planar Exhaust,” 

AIAA Paper 2016-2863, May 2016.

3. Khavaran, A., “Jet Surface Interaction – Scrubbing Noise in a Transversely Sheared Mean Flow,” 

International J. Aeroacoustics, 14(3, 4), (2015), p. 373-412.

4. Goldstein, M. E., Afsar, M. Z., and Leib, S. J., “Non-homogeneous rapid distortion theory on 

transversely sheared mean flows,” J. Fluid Mechanics, 736, (2013), p. 532-569.

5. “Advanced Boundary Cartesian Meshing Technology in SolidWorks Flow Simulation,” Dassault 

Systems SolidWorks Corporation Technical Paper.

6. “Enhanced Turbulence Modelling in SolidWorks Flow Simulation,” Dassault Systems SolidWorks 

Corporation Technical Paper.

7. Zaman, K. B. M. Q., Brown, C. A., and Bridges, J., “Interaction of a Rectangular Jet with a Flat-Plate 

Parallel to the Flow,” AIAA Paper 2013-2184, 2013.

8. Brown, C. A., “Jet-Surface Interaction Test: Far-Field Noise Results,” ASME paper GT2012-69639, 

June 2012.

9. Bridges, J., “Noise Measurements of High Aspect Ratio Distributed Exhaust Systems,” AIAA Paper 

2015-3119, June 2015.