Ching Y. Loh

Taitech, Inc., Beavercreek, Ohio

Lennart S. Hultgren

Glenn Research Center, Cleveland, Ohio

Near-Field Noise Computation for a

Supersonic Circular Jet

NASA/TM—2005-213816

October 2005

AIAA–2005–3042
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Ching Y. Loh

Taitech, Inc., Beavercreek, Ohio

Lennart S. Hultgren

Glenn Research Center, Cleveland, Ohio

Near-Field Noise Computation for a

Supersonic Circular Jet

NASA/TM—2005-213816

October 2005

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

11th Aeroacoustics Conference

cosponsored by the American Institute of Aeronautics and Astronautics

and the Confederation of European Aerospace Societies

Monterey, California, May 23–25, 2005

AIAA–2005–3042
Acknowledgments

The authors thank Jayanta Panda for supplying his experimental data and insightful discussions. This work

received support from the Quiet Aircraft Technology Project Office at NASA Glenn Research Center.

Available from

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7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

This report contains preliminary

findings, subject to revision as

analysis proceeds.

Available electronically at http://gltrs.grc.nasa.gov
NEAR-FIELD NOISE COMPUTATION FOR A SUPERSONIC CIRCULAR JET

Abstract

A fully expanded, high-Reynolds-number, supersonic circular jet of Mach number 1.4 is

simulated, using a 3-D finite-volume NavierStokes solver, with emphasis on the near field

noise. The numerical results are generally

in good agreement with existing experimental

findings.

1 Introduction

The reduction of aircraft noise is an important technological challenge as a result of the environmental limitations and economical consequences of airport noise pollution. Jet noise, a major noise component for modern

commercial aircraft engines, consists of turbulent mixing noise and, in the case of imperfectly expanded supersonic jets, broadband shock-associated noise (as well

as, discrete screech tones under certain circumstances).

Jet noise has been a vital part of aeroacoustics since the

early 1950s and continues to be a topic of many experimental and theoretical investigations; Refs. [1–3] provide a comprehensive discussion and further references.

A rapid advance in its understanding has occurred during

the last decade, perhaps in conjunction with the development of computational aeroacoustics (CAA), as well as

better measurement techniques. The issues, challenges,

and contributions of CAA are discussed in Refs. [4–6],

and the Rayleigh-scattering technique [7–9] is an example of advances in experimental methods for high-speed

jets.

For supersonic jet mixing noise, it is generally agreed

that there are two different sources [10–12]. One is associated with the convection/evolution of large-scale turbulence structures in the jet and which produces intense

sound propagating downstream at angles close to the jet

axis. Traditionally, this has been referred to as eddy

Mach wave radiation. The other noise source is associated with the fine scale turbulence in the jet shear flow

and which produces sound propagating predominantly in

the lateral (90o) direction [13–16]. The work in this paper concerns the sound produced by the large-scale structures in the jet.

Substantial progress in numerical computation of jet

mixing noise associated with the large-scale structures

has been made during recent years by using large-eddy

simulation (LES) techniques. Mankbadi et al. [17] performed an axisymmetric LES computation of a supersonic, high-Reynolds-number jet and determined its farfield radiated sound using an acoustic analogy technique.

Zhao et al. [18], Bogey et al. [19], Uzun et al. [20] computed jet flow and the associated noise by using fully 3-

D LES at a Mach number of 0.9. The Reynolds number in these simulations were low to moderate, however,

5, 000, 65, 000, and 100, 000, respectively. DeBonis and

Scott [21] used LES to calculate the hydrodynamics of

a high-Reynolds-number, supersonic jet of Mach number 1.4 [8, 9]. In all of the above work, the numerical

schemes are of high-order finite-difference type.

In the present paper, encouraged by the successful

computation of 2-D axisymmetric and 3-D screech noise

for round jets [22–25], a second-order (in space and time)

finite-volume scheme of low dissipation is adopted for

LES computation of a supersonic jet of Mach number

1.4. The scheme is the 3-D CE/SE Navier-Stokes solver

using a hexahedral grid.

2 The 3-D Supersonic Jet Noise Problem

The current computation is for the conditions in the

Panda and Seasholtz [8, 9] experiments on a circular, high-Reynolds-number, supersonic, cold jet at Mach

number 1.4. In these experiments, a nominally fully expanded jet is issuing from a convergent-divergent (C-D)

nozzle.

In what follows, the exit diameter D of the of the nozzle, the density ρ∞, the speed of sound a∞, and the temperature T∞ in the ambient fluid are used as scales to

make all the dependent variables nondimensional. UsChing Y. Loh and Lennart S. Hultgren

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

NASA/TM—2005-213816 1
ing the ideal gas isentropic relations and conservation of

mass gives that the reservoir and jet exit Mach numbers

are given by

Mr = (Ae/Ar)(Pe/Pr)

(γ+1)/2γMe , (1)

Me =



2[(Pr/Pe)(γ−1)/γ − 1]

(γ − 1)[1 − (Ae/Ar)2(Pe/Pr)2/γ] , (2)

respectively, where the subscripts ’e’ and ’r’ denote jetexit and reservoir conditions, P is the nondimensional

static pressure, Ar/Ae is the area ratio of the nozzle, and

γ is the constant specific heat ratio. Since the jet is nominally fully expanded

Pe = 1/γ. (3)

Furthermore, it also follows that

ρe = 1/Te, (4)

Te = Tr(1 + γ−1

2 M2

r )/(1 + γ−1

2 M2

e ) , (5)

ue = Me

Te , (6)

ρr = γPr/Tr , (7)

ur = Mr

Tr , (8)

where ρ, T , and u denote the nondimensional density,

static temperature and axial velocity, respectively. In

the experiment [8], Pr/Pe = 3.16, Tr = 1.01, and

Ar/Ae = 9, which together with (1)-(8) largely define

the experimental conditions.

3 Numerical Method

In this work, the three-dimensional numerical scheme

is designed to solve an LES version of the compressible

Navier-Stokes equations. The numerical scheme adopted

in this work is a variation of the low-dissipation finitevolume CE/SE scheme. The CE/SE scheme has formal

second-order accuracy in both space and time [26, 27]

and naturally captures shocks and other discontinuities

in the flow.

3.1 Computational Domain and Unstructured

Hexahedral Grid

The computational domain including the C-D nozzle is

sketched in Fig. 1. The numerical simulation begins at

the inlet of the C-D nozzle. The geometrical specification of the C-D nozzle is given in [8, 9]. In nondimensional form, the C-D nozzle extends from x = −4.9 to

x = 0 and the external domain ranges from x = −0.2

to x = 17, where x is the streamwise coordinate. The

external domain diameter is about 10.8.

For fully 3-D computations of complicated problems

such as the current jet noise problem where several distinct and disparate length scales need to be resolved [4],

Figure 1: Geometry of the computational domain, comprising the interior of the C-D nozzle and an external domain; the nozzle extends into the external domain by two

internal nozzle exit diameters.

a large number of computational cells are needed to provide sufficient numerical resolution. The choice of an

unstructured hexahedral grid for the CE/SE method leads

to a significant reduction of the number of computational

cells, with an associated reduction in computer memory

and CPU time requirements, as compared to the commonly used tetrahedral one. The drawback is a modest

increase in numerical dissipation.

The unstructured hexahedral grid is generated in the

following manner [30]: first, a 2-D unstructured quadrilateral grid is generated in a circular region (Fig. 2) and

then the circular disc is advanced one step in the streamwise direction with step size ∆x. The advancing front

technique is carried until x = 17. The step size ∆x

ranges from 0.02 at the nozzle exit (x = 0) to about

0.06 at x = 15. Between x = 15 and x = 17 there

is a buffer zone in which ∆x increases exponentially in

size to provide high numerical damping. Inside the CD nozzle, ∆x is much refined. Totally, there are 3.17

million cells in the computational domain, including the

the buffer zone. The domain covers the near-field region

which is the source region for the noise.

Employing a hexahedral grid instead of a tetrahedral

one for the current CE/SE scheme helps to reduce the

number of cells from tens of millions to a few millions. Still, the number of computational cells is very

large and the simulation is implemented using parallelcomputation techniques. To accomplish this, the unstructured hexahedral grid generated for the entire computational domain is decomposed into subdomains (12

at present) using the efficient mesh partitioning code

METIS [28]. Figure 3 illustrates a typical partition of the

computational domain for the current circular jet noise

problem. The CE/SE flow solver uses message-passinginterface (MPI) library calls to exchanging pertinent information between neighboring subdomains during the

simulation.

NASA/TM—2005-213816 2
mesh details at the center

Figure 2: 2-D quadrilateral mesh in a cross section in a

3-D hexahedral grid

3.2 Conservation Form of the 3-D Unsteady

Compressible Navier-Stokes Equations

The Navier-Stokes equations for a perfect gas can be

written in the following nondimensional vector form,

e.g. [29]:

Ut + Fx + Gy + Hz = 0, (9)

where x, y, and z are the streamwise, transverse, and

spanwise coordinates, and t is time. The five components of the conservative flow variable vector U are: the

density, the three momentum components, and the total

energy per unit volume, i.e.,

U1 = ρ, U2 = ρu, U3 = ρv, U4 = ρw,

U5 = p/(γ − 1) + ρ(u2 + v2 + w2)/2,

where, as before, ρ, u, and p denote the density, streamwise velocity, and static pressure, and v and w denote

Figure 3: Partition of the computational domain for parallel computation

the transverse and spanwise velocities. The flux vectors

in the x, y, and z directions, F, G, and H, respectively,

have both inviscid and viscous contributions and the details of these flux components may be found in a textbook [29] or in a previous paper [30] by the present authors. Note that in the latter, μ is to be interpreted here

as the nondimensional viscosity.

The nondimensional equations above could form the

basis for a direct numerical simulation (DNS). Currently,

this is not feasible for the high-Reynolds-number flows

of interest here. The present computations are of the

LES type, where the effects of the unresolved scales,

i.e., scales smaller than the grid resolution, are modeled.

In this case, the equations above are considered the filtered ones governing the resolved scales, where ρ and

p are interpreted as simply averaged and the other dependent variables are interpreted as Favr ́e, (i.e., densityweighted) averaged over the subgrid scale. The simplest

model for the effects of the unresolved scales, or subgrid scales (SGS), on the motion is obtained by using a

Boussinesq eddy-diffusivity assumption for the subgrid

shear stresses and heat flux coupled by Smargorinsky’s

model for the eddy viscosity (eg. [31]). That is, μ occuring in the viscous contribution to the flux terms in Eq. (9)

is replaced by

μ = 1/Re + (Csδ)

2(SijSij )1/2, (10)

where Sij = 1

2

 ∂ui

∂xj + ∂uj∂xi



is the Favr ́e averaged rateof-strain tensor, δ = (δxδyδz)1/3 is a local measure

of the grid size, Cs is a (nondimensional) constant, and

Re = a∞D/ν∞ is the Reynolds number for the computation. The inverse Reynolds number 1/Re = 1.8×10−6

in the present computations, which corresponds to the

value for the jet Reynolds number, Re j = ueD/νe, of

1.2 × 106 in the experiments [8, 9]. Also, note that the

simplifying assumption is also made that the subgridscale Prandtl number equal the laminar one, which is

taken to have the value 0.72.

NASA/TM—2005-213816 3
By considering (x, y, z, t) as coordinates of a fourdimensional Euclidean space, E4, and using Gauss’ divergence theorem, it follows that Eq. (9) is equivalent to

the following integral conservation law:



S(V )

Im · dS = 0, m = 1, 2,..., 5, (11)

where S(V ) denotes the surface around a volume V in

E4 and Im = (Fm, Gm, Hm, Um). These equations are

discretized and solved using a modified verison of the

weighted-average CE/SE scheme with a weghting factor

α = 0.8.

Note that Fureby and Grinstein [32] point out that

applying flux limiters to finite-volume methods (as is

done in the current CE/SE scheme), even in the absence

of any explicit LES assumptions, effectively leads to

LES schemes with minimal implicit SGS models. They

demonstrated through an ‘error’ analysis of a particular

scheme that the flux-limiters (essentially low-pass frequency filters) build into the algorithm produces additional terms in the equivalent differential forms of the

momentum and energy equations that can be interpreted

as the SGS stress tensor and flux, respectively. Hence,

there is an additional implicit SGS model inherent in the

particular CE/SE scheme used in addition to the explicit

assumption in Eq. (10).

3.3 Initial and Boundary Conditions

Initially, the flow of the entire computational domain is

set at the ambient flow conditions, i.e.,

ρ0 = 1, p0 = 1

γ ,

u0 = 0, v0 = 0, w0 = 0.

At the exterior upstream inlet boundary, the conservative flow variables are specified to be the same as the

ambient flow and their spatial derivatives are held at zero.

At the nozzle inlet, the reservoir conditions as described

in §2 are imposed. Of course, vr, wr, and all spatial

derivatives are held at zero.

Type I CE/SE non-reflecting boundary conditions

[33, 34] are imposed at the circumferential and outflow

boundaries. The no-slip boundary condition is applied

on all the nozzle walls, external as well as internal.

3.4 Artificial Forcing

As is common, e.g. [19], in numerical studies of jet mixing noise, the simulation allows for a low-level, artificial

excitation, or turbulence seeding, of the jet shear layer

near the nozzle exit. This seeding is accomplished by

adding divergence-free velocity perturbations inside the

jet shear layer at x = 0.3. The disturbances are temporally random and are of the vortex-ring form used in [19],

namely

u = r − rp

r

F(x, r, θ; xp, rp), (12)

 v

w



= −x − xp

r

F(x, r, θ; xp, rp)

cos θ

sin θ



, (13)

where

F(x, r, θ; xp, rp) =

2δprp

∆p

exp −d2 ln 2/∆2

p

	


16

n=1

ncos(nθ + φn) (14)

and r = (y2 + z2)1/2 and θ = sin−1(z/r) are the radial and azimuthal coordiates; xp = 0.3, rp = 0.5 and

∆p = 0.02 define the location and spatial extent of the

perturbation, and d = [(x− xp)2 + (r − rp)2]

1/2; n and

φn are uniformly distributed random numbers between

−1 and 1, and 0 and 2π, respectively. They represent the

random perturbation amplitude and phase, and are generated at every time step. The overall perturbation amplitude δp is either set to zero (no forcing) or to 0.01 in the

present computations. The perturbations above are then

directly added to the velocity field in the latter case.

4 Numerical Results

The simulation starts from the uniform initial conditions described in §3.3, without any artificial forcing.

The simulation is first run 100, 000 time steps, or to

t = 100 with the time step ∆t = 0.001 used, to ensure that all start-up transients are convected out of the

computational domain and that the jet flow is fully established. This time, t = 100, corresponds roughly to

five acoustic times. The acoustic time is a measure of

how long it takes a sound wave to pass through the external computational domain. The simulation is then run

for an additional 340, 000 time steps to t = 440, or approximately an additional 17 acoustic times, to achieve

sufficient accuracy in the spectral analysis of time series

data that is saved at various locations in the computation

domain every 20 time steps. The artificial forcing is then

turned on with an amplitude δp = 0.01 and the simulation is again run 100, 000 time steps to remove any transients. The simulation is then run an additional 350, 000

time steps, with the random turbulence seeding in the jet

shear layer in the vicinity of the nozzle lip in effect, and

time series data is saved at the same locations as in the

unforced case, again every 20 time steps. The forced and

unforced results are compared below.

4.1 Time-Averaged Data

Figure 4 shows a comparison of the evolution of the

time-averaged centerline streamwise velocity between

the simulation (solid and dashed lines) and the experiments [8, 9]. In general, the agreement is good, particularly for the forced case, but with the end of the potential

NASA/TM—2005-213816 4
centerline velocity

x -8.0 0.0 8.0 16.0 24.0 

 0.00 

 0.50 

 1.00 

 1.50 

Figure 4: Time-averaged centerline streamwise velocity

evolution; solid line: computation with artificial forcing,

dashed line: computation with no forcing, symbols: experiment

core predicted by the simulation occurring somewhat too

far downstream.

Figure 5 shows comparisons of time-averaged radial

density profiles from the simulations (solid and dashed

lines) with experimental results [8, 9] for six streamwise

stations, x = 2, 4,..., 12. The agreement for the first

two stations (x = 2 and 4, respectively) is very good.

This indicates that the early jet shear layers are quite well

resolved in the simulations. The agreement for x = 6 is

still reasonable, but it is poor for x = 8 and 10, reflecting the discrepancy also seen in Fig. 4 at these stations.

However, the agreement is again quite good for x = 12.

This suggests that the simulation captures the more energetic/violent mixing process that occurs after the potential core is gone.

4.2 Instantaneous Flow Fields

Figure 6 shows the computed instantaneous u-velocity

field in the spanwise plane, y = 0, at t = 440 and

t = 890 for the no-forcing (top) and random-forcing

(bottom) cases, respectively. The rather weak shock-cell

like structures in the upstream part of the potential core

indicate that the expansion is not 100% perfect as a result

of either the C-D nozzle design, or the numerical discretization/implementation in the nozzle, or both. The

potential core is observed to end around 10 diameters

downstream of the nozzle exit and the mixing process

then rapidly gains strength. Comparing the two plots in

the figure, the instantaneous flows look qualitatively similar.

Figure 7 depicts the computed instantaneous spanwise

vorticity, ωy, in the same spanwise plane, y = 0, and

times t = 440 and t = 890 as in the previous figure.

y

density

x = 2

0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70

-1.0

0.0

1.0

y

density

x = 4

0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70

-1.0

0.0

1.0

y

density

x = 6

0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70

-1.0

0.0

1.0

y

density

x = 8

0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70

-1.0

0.0

1.0

y

density

x = 10

0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70

-1.0

0.0

1.0

y

density

x = 12

0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70

-1.0

0.0

1.0

Figure 5: Radial variation of time-averaged density at six

streamwise locations, x = 2, 4,..., 12; solid line: computation with artificial forcing, dashed line: computation

with no forcing, symbols: experiment

NASA/TM—2005-213816 5
The instantaneous flow in the case with random forcing (bottom) seems more mixed. Otherwise, the mixing

processes qualitatively look quite similar in both plots.

Figure 8 shows the computed instantaneous streamwise vorticity ωx in four streamwise (or cross-sectional)

planes, x = 3.75, 7.5, 11.25, and 15. The top panel is the

case without forcing at t = 440 and the bottom panel is

with random forcing at t = 890. These ωx plots clearly

show, in both cases, the 3-D nature of the unsteady motion at all stations. Again, the unsteady motion is qualitatively similar in both cases.

Figure 6: Instantaneous streamwise velocity distribution

in a spanwise plane; top, no forcing at t = 440; bottom,

random forcing at t = 890

Figure 9 shows the computed instantaneous 3-D pressure isosurfaces at t = 440 (without forcing) and t =

890 (random forcing) at the two levels of p = 0.71 and

p = 0.715. Note that the nondimensional ambient pressure is 1/1.4. The isosurfaces show downstream radiating 3-D sound waves caused by the large-scale coherent

structures in the jet flow, i.e. eddy-Mach wave radiation.

In the bottom plot, artifacts of the random forcing can

be seen in the vicinity of the nozzle exit, but these are

rapidly washed out in the downstream direction.

The computations show that the unsteady motion, as

in the experiments [8, 9], is truly three dimensional. It is

observed that the flow unsteadiness is sustainable even

without any explicit random forcing and qualitatively

similar unsteady structures are still generated. However,

the discretization and round-off errors that, in fact, supFigure 7: Instantaneous spanwise vorticity distribution

in a spanwise plane; top, no forcing at t = 440; bottom,

random forcing at t = 890

ply random forcing in this case are likely of too low an

intensity to be truly representative of the experimental

turbulence levels.

4.3 Spectral Results

Figure 10 shows the power spectral density (PSD) of

the density fluctuations at three locations, (x, y, z), in

the flow field, namely (2, 0.48, 0), (4, 0.41, 0), and

(12, 0, 0). The first two locations are in the jet shear

layer, whereas the last one is on the centerline after the

end of the potential core. The solid and long-dashed lines

are simulation results with and without artificial forcing,

respectively. The short-dashed line represents the experimental results [8, 9]. The Strouhal number, consistent

with the scaling used here, is defined as S = fD/a∞,

where f is the dimensional frequency. It is quite common to use the jet velocity, rather than the ambient speed

of sound, in the definition of the Strouhal number—

dividing our Strouhal number by 1.2 (the present nondiNASA/TM—2005-213816 6
Figure 8: Instantaneous streamwise vorticity distribution

in four streamwise planes; top, no forcing at t = 440;

bottom, random forcing at t = 890

mensional jet velocity) converts it to the commonly used

one.

The top plot in Fig. 10 is for the measuring point in the

shear-layer closest to the nozzle, (2, 0.48, 0). The broad

hump in the experimental spectrum represents the hydrodynamic instability waves growing in the jet shear layer.

It includes large-scale to small-scale disturbances. Due

to limited grid resolution, and, of course, its general nature and underlying assumptions, the LES approach can

not be expected capture the small-scale disturbances, nor

maybe intermediate-scale ones. This is the reason for

the sharp drop off in the numerical PSD curves. The

agreement between the simulation and the experiments

is, however, quite good for low Strouhal numbers (up to

about 0.3), i.e., for large scale disturbances. The disagreement close to S = 0 is related to the very short

Figure 9: Instantaneous isobars; top, no forcing at t =

440; bottom, random forcing at t = 890

total observation time in the simulation compared to the

experiment. The simulation results are quite insensitive

to the artificial forcing. The middle plot in Fig. 10 corresponds to a location in the shear layer further downstream, (4, 0.41, 0). The agreement between simulation

and experiment is good also here for large-scale disturbances, and again the simulation results do not appear to

be influenced much by the random forcing.

The bottom plot in Fig. 10 compares the simulated

and experimental PSD for the density fluctuations at a

point on the centerline even further downstream, (12,

0,0). At this streamwise location, there is no longer a

potential core and the flow is highly unsteady and threedimensional. While the level of the simulation results

are too high, the decay rate is comparable to the experimental data for S less than about 0.6, and then becomes

steeper. This is an indication that for the current grid and

NASA/TM—2005-213816 7
LES approach, the cut-off Strouhal number is about 0.6.

The much higher level of the numerical results, indicates

that value of the Smargorinsky’s eddy viscosity constant

needs to be increased in this flow region, similar to our

experience in the jet screech computations [30]. Again,

there is practically no difference between the simulations

with and without artificial random forcing.

5 Concluding Remarks

The present mixing-noise computation for a fully expanded supersonic circular jet demonstrates that the nearfield large-scale noise can be determined using a loworder (2nd order) finite-volume LES scheme, such as the

current one. Generally, time-averaged results, such as for

the streamwise velocity and radial density profiles agree

well with existing experimental data. Near-field spectral

results also agree well with the experiments in the expected range of lower Strouhal numbers. Instantaneous

iso-surfaces of pressure show the radiating sound waves

(eddy Mach wave radiation) originating from the largescale structures in the jet. Instantaneous streamwisevelocity and vorticity results demonstrate the highly unsteady and three-dimensional nature of the flow. The current results are in good qualitative agreement with what

is generally understood about the flow physics of highspeed jets.

It is believed that the results can be further improved

by lowering the damping in the numerical simulation by

carefully reducing/optimizing the flux limiters and SGS

parameters in the scheme. Further research in this area is

currently being carried out.

References

[1] Tam, C. K. W., “Jet Noise Generated by Large

Scale Coherent Motion,” NASA RP-1258, pp. 311-

390 (1991).

[2] Seiner, J. M., “Advances in High Speed Jet Aeroacoustics,” AIAA Paper 84-2275 (1984).

[3] Tam, C. K .W., “Supersonic Jet Noise,” Ann. Rev.

Fluid Mech. vol. 27, pp. 17-43 (1995).

[4] Tam, C. K. W., “Computational Aeroacoustics: Issues and Methods,” AIAA J. vol. 33, pp. 1788-1796

(1995).

[5] Tam, C. K. W., “Computational Aeroacoustics: An

Overview of Computational Challenges and Applications,” Inter. J. Comp. Fluid Dyn. vol. 18, pp.

547-567 (2004).

log(PSD)

Strouhal number

x = 2 r = 0.48

0.00 0.30 0.60 0.90 1.20 1.50 1.80 2.10 2.40

-9.0

-7.5

-6.0

-4.5

-3.0

-1.5

0.0

log(PSD)

Strouhal number

x = 4 r = 0.41

0.00 0.30 0.60 0.90 1.20 1.50 1.80 2.10 2.40

-9.0

-7.5

-6.0

-4.5

-3.0

-1.5

0.0

log(PSD)

Strouhal number

x = 12 r = 0.0

0.00 0.30 0.60 0.90 1.20 1.50 1.80 2.10 2.40

-9.0

-7.5

-6.0

-4.5

-3.0

-1.5

0.0

Figure 10: Density power spectral density (PSD) vs.

Strouhal number at three locations; solid line: computation with artificial forcing, long-dashed line: computation with no forcing, short-dashed line: experiment [6] Bailly, C. and Bogey, C., “Contributions of Computational Aeroacoustics to Jet Noise Research and

Prediction,” Inter. J. Comp. Fluid Dyn. vol. 18, pp.

481-491 (2004).

NASA/TM—2005-213816 8
[7] Panda, J. and Seasholtz, R. G., “Density Measurement in Underexpanded Supersonic Jets Using

Rayleigh Scattering,” AIAA Paper 98-0281 (1998)

[8] Panda, J. and Seasholtz, R. G., “Velocity and

Temperature Measurement in Supersonic Free Jets

Using Spectrally Resolved Rayleigh Scattering,”

AIAA Paper 99-0296 (1999).

[9] Panda, J. and Seasholtz, R. G., “Density Fluctuation Measurement in Supersonic Fully Expanded

Jets Using Rayleigh Scattering,” AIAA Paper 99-

1870 (1999).

[10] Tam, C. K. W. and Chen, P., “Turbulent Mixing

Noise from Supersonic Jets,” AIAA J. vol. 32, pp.

1774-1780 (1994).

[11] Tam, C. K. W., Golebiowski, M. and Seiner, J.

M., “On the Two Components of Turbulent Mixing

Noise from Supersonic Jets,” AIAA Paper 96-1716

(1996).

[12] Tam, C. K. W. and Pastouchenko, N. N., “On the

Two Sources of Supersonic Jet Noise”, AIAA Paper 2003-3163 (2003).

[13] Tam, C. K. W. and Auriault, L., “Mean Flow Refraction Effects on Sound Radiated from Localized

Sources in a Jet,” J. Fluid Mech. vol. 370, pp. 149-

174 (1998).

[14] Tam, C. K. W. and Auriault, L., “Jet Mixing Noise

from Fine-Scale Turbulence,” AIAA J. vol. 37, pp.

145-153 (1999).

[15] Tam, C. K. W. and Pastouchenko, N. N, “Noise

from Fine-Scale Turbulence of Nonaxisymmetric

Jets,” AIAA J. vol. 40, pp. 456-464 (2003).

[16] Wundrow, D. W. and Khavaran, A., “On the Applicability of High-Frequency Approximations to Lilley’s Equation,” J. Sound Vibr. vol. 272, pp. 793-

830 (2004).

[17] Mankbadi, R. R., Hayer, M. E. and Povinelli, L. A.,

“ Structure of Supersonic Jet Flow and Its Radiated

Sound,” AIAA J. vol. 32, pp. 897-906 (1994).

[18] Zhao, W., Frankel, S. H. and Mongeau, L.,“Large

Eddy Simulation of Sound Radiation from a

Subsonic Turbulent Jet.” AIAA Paper 2000-2078

(2000).

[19] Bogey, C., Bailly, C. and Juve, D. “Noise Investigation of a High Subsonic, Moderate Reynolds Number Jet Using a Compressible Large Eddy Simulation,” Theor. Comp. Fluid Dyn. vol. 16, pp. 273-

297 (2003).

[20] Uzun, A., Blaisdell, G. A. and Lyrintzis, A. S.,“3-

D Large Eddy Simulation for Jet Aeroacoustics,”

AIAA Paper 2003-3322 (2003).

[21] Debonis, J. and Scott, J., “A Large Eddy Simulation

of a Turbulent Compressible Round Jet,” AIAA Paper 2001-2254 (2001).

[22] Loh, C. Y., Hultgren, L. S., and Jorgenson, P. C.

E., “Near Field Screech Noise Computation for an

Underexpanded jet by the CE/SE Method,” AIAA

Paper 2001-2252 (2001).

[23] Loh, C. Y. and Hultgren, L. S., “Jet Screech Noise

Computation,” NASA/TM-2003-212626 (2003).

[24] Loh, C. Y. and Hultgren, L. S., “Computing Jet

Screech - A Complex AeroacousticFeedback System”, presented at the 2nd Int’l Conference on CFD

(ICCFD2), also NASA/TM-2002-211807 (2002).

[25] Jorgenson, P. C. E. and Loh, C. Y., “Computing Axisymmetric Jet Screech Tones Using Unstructured

Grids”, AIAA Paper 2002-3889 (2002).

[26] Chang, S.-C., Wang, X.-Y. and Chow, C.-Y., “The

Space-Time Conservation Element and Solution

Element Method—A New High Resolution and

Genuinely Multidimensional Paradigm for Solving

Conservation Laws,” J. Comp. Phys. vol. 159, pp.

89-136 (1999).

[27] Wang, X.-Y. and Chang S.-C., “A 2-D Non-splitting

Unstructured Triangular Mesh Euler Solver Based

on the Space-Time Conservation Element and Solution Element Method,” C.F.D. J. vol. 8, pp. 309-325

(1999).

[28] Karypis, G. and Kumar, V. “Multilevel k-way Partitioning Scheme for Irregular Graphs,” Univ. of

Minnesota Dept. of Comp. Sci./Army HPC Research Center Tech. Report 95-064 (1995).

[29] Anderson, D. A., Tannehill, J. C. and Pletcher,

R. H., Computational Fluid Mechanics and Heat

Transfer, MacGraw-Hill Book Company (1984).

[30] Loh, C. Y., Himansu, A. and Hultgren, L. S., “A 3-

D Navier-Stokes Solver with Unstructured Hexahedral Grid for Computation of Nearfield Jet Screech

Noise,” AIAA Paper 2003-3207 (2003).

[31] Lesieur, M. and M ́etais, O., “New Trends in LargeEddy Simulation of Turbulence,” Ann. Rev. Fluid

Mech. vol. 28, pp. 45-82 (1996).

[32] Fureby, C. and Grinstein, F. F., “Monotonically

Integrated Large Eddy Simulation of Free Shear

Flows,” AIAA J., vol. 37, pp. 544-556 (1999).

[33] Loh, C. Y., “On a Non-Relecting Boundary Condition for Hyperbolic Conservation Laws,” AIAA

Paper 2003-3975 (2003).

[34] Loh, C. Y. and Jorgenson, P. C. E., “A Robust

Absorbing Boundary Condition for Compressible

Flows,” AIAA Paper 2005-4716 (2005).

NASA/TM—2005-213816 9
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15

Near-Field Noise Computation for a Supersonic Circular Jet

Ching Y. Loh and Lennart S. Hultgren

Supersonic jet noise; Numerical simulation

Unclassified -Unlimited

Subject Categories: 02, 71, and 64

Prepared for the 11th Aeroacoustics Conference cosponsored by the American Institute of Aeronautics and Astronautics

and the Confederation of European Aerospace Societies, Monterey, California, May 23–25, 2005. Ching Y. Loh, Taitech,

Inc., 1430 Oak Court, Suite 301, Beavercreek, Ohio 45430; and Lennart S. Hultgren, NASA Glenn Research Center.

Responsible person, Ching Y. Loh, organization code RTS, 216–433–3981.

A fully expanded, high-Reynolds-number, supersonic circular jet of Mach number 1.4 is simulated, using a 3-D

finite-volume Navier-Stokes solver, with emphasis on the near field noise. The numerical results are generally in good

agreement with existing experimental findings.