paper on nozzle throat optimization

7/24/2019 Paper on Nozzle throat optimization

1/17

American Institute of Aeronautics and Astronautics

1

Nozzle throat optimization for supersonic jet noise reduction

K. M. Bernhard Gustafsson1

Volvo Aero Corporation

Daniel Cuppoletti2and Ephraim Gutmark3

University of Cincinnati

Haukur E. Hafsteinsson4and Lars-Erik Eriksson5

Chalmers University of Technology

Erik Prisell6

FMV

Noise from engines that operate at supersonic conditions, especially high performance military aircraft,

often utilize a converging-diverging nozzle with variable area control. This design usually includes a sharp

nozzle throat which creates internal shock formation. Turbulent structure interaction with these shocks

results in additional noise components other than turbulent mixing noise to be introduced to the jet noise

spectrum. The present study investigates how weakening the internal shocks affects the flow and acoustics of

a Mach 1.6 jet. RANS simulations were used to minimize internal shock formation and optimize the flow

contours of the converging portion and throat of a C-D nozzle. A response surface methodology was used to

evaluate 3000 possible designs using the RANS results as model inputs. An experimental investigation was

conducted with a splined nozzle design that is virtually free of internal shocks. The flow field was measured

using PIV for comparison with RANS and LES. Mean velocity and turbulence was captured well by the

computations for the sharp throat and splined nozzles. Although the throat shocks were nearly eliminated,

the overall shock strength was relatively unchanged. Far-field acoustic results showed little difference at

thrust matched conditions since the overall shock strength was unchanged. The nozzle performance is greatly

improved through throat optimization, providing equivalent thrust with 4% less pressure with no acoustic

penalty.

Nomenclature

A = area PIV = particle image velocimetry

AR = ratio of exit area to throat area r = radial coordinate

BBSN = broad-band shock associated noise RC = radius of throat corner

Cd = discharge coefficient RT = throat radius

Cfg = gross thrust coefficient RANS = Reynolds Averaged Navier-Stokes

Dj = jet exit diameter T = temperature

= rate of dissipation of k TKE; k = turbulent kinetic energy

LC = length of convergent section Uj = isentropic jet exit velocity

LES = large eddy simulation x = axial coordinate

NPR = nozzle pressure ratio,Ptot,in/Pamb conv = angle of convergent section

OASPL = overall sound pressure level = turbulent frequency

P = pressure

Pamb = ambient pressure

1Ph.D. Eng. Method Specialist, Aerothermodynamics, Volvo Aero Corp, SE 461 81 Trollhttan, Sweden, Senior Member AIAA.2Ph.D. Graduate Student, Aerospace Engineering, 745 Baldwin Hall, ML0070, Student Member AIAA.3Distinguished Professor and Ohio Eminent Scholar, Aerospace Engineering Dept., 799 Rhodes Hall, ML0070, Fellow AIAA.4Ph.D. Student, Applied Mechanics Dept., Chalmers University of Technology, SE 412 96 Gothenburg, Sweden.

5Professor, Applied Mechanics Dept., Chalmers University of Technology, SE 412 96 Gothenburg, Sweden.6Strategic Specialist, Aero Propulsion and Power, Swedish Defence Materiel Administration, Sweden.

50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition09 - 12 January 2012, Nashville, Tennessee

AIAA 2012-024

Copyright 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


2/17


2

I.

Introduction

UPERSONIC noise reduction of high performance jet engines is a persisting problem that has had marginal

progress in recent years. In contrast to subsonic jets, supersonic jets have noise components associated with

shocks generated by the nozzle throat or exit. Shock and expansion waves in a supersonic jet flow reflect from the

jet boundaries creating a shock train inside the jet potential core. These shocks are pseudo-stationary and radiate

noise through interaction with turbulent eddies convected through the shocks. Turbulent interaction with the quasi-

periodic shock cells in the jet gives rise to broadband shock associated noise (BBSN)1-3

. Shock noise is stronglydirectional and radiates primarily at the sideline and upstream angles to the jet. It is the dominant noise source at

these angles and intensity depends on the strength of the shocks in the jet. Discrete tones in an acoustic spectrum of

a supersonic jet are known as a screech tones. Screech tones are generated from a feedback cycle of perturbations in

the jet shear layer and the nozzle boundaries. Screech tones are highly sensitive to the jet conditions and reflecting

surfaces around the jet nozzle and radiate primarily upstream. BBSN and screech are coupled phenomena and the

focus of this investigation is on reducing shock strength and quantifying the effect on nozzle performance and

acoustics.

Research into jet noise reduction methods has had renewed interest in the past few decades as noise regulations

have become stricter and noise from aircraft has caused issues ranging from community annoyance to long-term

health issues for runway workers. Two major methods of noise reduction are chevrons and fluidic injection. Both

methods create vorticity in the shear layer to redistribute turbulent energy in the jet, increase jet mixing, and interact

with the jet shock structure. Rask et al.4 and Munday et al.5 have shown that chevrons are adequate at reducing

BBSN by disrupting the internal shock train of a supersonic jet. Chevrons have not found widespread use onsupersonic jets because of the performance penalty incurred with static obstructions being placed in the jet flow.

Cuppoletti et al.6showed significant reduction of BBSN and screech through use of fluidic injection at the nozzle

exit to interrupt the jet shock structure. Experiments have been performed at the University of Cincinnati and LES

computations have been performed at Chalmers University of Technology, where the noise from a convergent-

divergent nozzle was studied7,8. These studies were conducted on a conical converging-diverging (C-D) nozzle with

a sharp throat. The nozzle produced a double-diamond shock train internal to the jet due to the additional shocks

from the nozzle throat.

The present study focused on reducing the internal shock strength by geometrically modifying the throat section.

By doing so it is hypothesized that the shock-associated noise will be reduced. The internal flow contour was

optimized in order to minimize internal shocks while keeping the length of the nozzle as short as possible. A design

of experiments was done and 12 designs were studied with CFD. Response surfaces were created and the optimal

design was found from these surfaces. PIV and acoustic measurements were conducted at University of Cincinnati

on two nozzle designs; the baseline nozzle with a sharp throat corner and a nozzle with convergent section

constructed with a spline (5thorder polynomial) so that a very smooth transition to the divergent section is obtained.This splined nozzle is virtually free from internal shocks at the throat, and the effect this has on the flow field and

far-field acoustics is investigated. Validation computations were done by Volvo Aero using RANS and Chalmers

University of Technology using LES.

II.

Methodology

The baseline nozzle used is a conical converging-diverging nozzle with a very small radius at the throat that

simulates sharp throat nozzle contours of tactical supersonic jet engines. In order to study the effect of the nozzle

throat contour on acoustics of a supersonic jet, a computational study using ANSYS CFX v12.1 and ANSYS

DesignModeler was conducted to minimize shock formation at the nozzle throat. The nozzle model was

parameterized with two parameters; the throat corner radius and the angle of the convergent section.

The flow field of a sharp throat, i.e. baseline, and a splined throat nozzle were computed in ANSYS CFX at

Volvo Aero using steady RANS simulations and at Chalmers using LES with the in-house software G3D. The flow

field and acoustic characteristics of both nozzles were investigated experimentally at University of Cincinnati.

Comparison of the computational and experimental flow fields is conducted to validate the computations and

quantify changes in nozzle performance. The changes in the flow field are related to the acoustic measurements to

identify how the nozzle throat contour affects acoustics.

A. Nozzle Design Approach

A parametric model of the convergent-divergent nozzle was created in ANSYS DesignModeler. The convergent

part of the nozzle consists of a concave and a convex arc section connected by a straight line. The model allows

S


3/17


3

changes in throat corner radius (RC) and convergent section angle (conv) while preserving wall tangency (C1-

continuous) constraints, seeFigure 1.The diverging portion of the nozzle was not altered, only the flow contour of

the converging portion of the nozzle was modified. Twelve flow simulations were done with different values onRC

and conv. The flow simulations were run at room temperature conditions with a nozzle pressure ratio of 4.0 that is

common for a large number of military jet engines. The nozzle has an exit to throat ratio A9/A8= 1.23, which for an

ideal nozzle results in a pressure-matched condition at the nozzle exit plane. The simulation conditions were total

pressurePtot,in= 4 bar, total temperature Ttot,in= 288.15 K, ambient pressure Ps,amb= 1 bar, and ambient temperatureTamb= 288.15 K. The turbulent flow solver was a Reynolds Averaged Navier Stokes (RANS) solver in ANSYS CFX

v12.1 using the SST-k-turbulence model by Menter9.

Figure 1: Representative nozzle geometry showing design variablesRC, LCand conv.

The convergent part consists of two arc-shaped sections and one straight l ine.

The scale of the model corresponds to the scale of the experiments performed at University of Cincinnati. The

results from the flow simulations were evaluated at the nozzle exit plane. Response surfaces were created for each

of these output data, using the input data, RC, and, conv, as variables. The response surfaces were used for

evaluating about 3000 virtual designs. A Latin hypercube algorithm was used to sample the design space (RC, conv).

Outlet Mach number, thrust and velocity profile deviations were used as objectives for the optimization. The length

of the convergent,LC, was used as a constraint, as it was desired to keep the length short or if possible same as for

the baseline nozzle.

A design was found that minimized outlet Mach number and outlet velocity profile uniformity, keeping the

length of the nozzle same as for the baseline nozzle. CFD studies revealed that there still were some small shock

waves generated at the throat, owing to the jump in curvature at the throat. In order to study the effect the internal

shock generation has on noise, a nozzle with a splined convergent section and throat (5 th order polynomial) was

designed and fabricated. CFD simulations with the splined convergent sections showed that shock generation at the

throat was much reduced. This splined nozzle has a longer convergent section than the baseline and short optimized

nozzles. The splined nozzle was manufactured and tested experimentally at University of Cincinnati, and Volvo

Aero and Chalmers University did flow field computations that also validates the models.

B. Computational ApproachFlow simulations were done at Volve Aero using steady RANS and at Chalmers University using LES. The

baseline and splined nozzles were studied at the same conditions in the experiments at the University of Cincinnati.

RANS ComputationsThe RANS simulations were done with the ANSYS CFX v12.1 software with two different turbulence models;

Shear-Stress Transport k- model (SST-k- by Menter9, and the SSG Reynolds Stress Model (SSG-RSM) by

Speziale, Sarkar & Gatski10. The SSG-RSM is based on the -equation for dissipation and a quadratic pressure-strain

term10. The SST-k- model is based on the BSL-k- model by Menter9. The BSL-k- model tries to solve the

problems of free-stream sensitivity with the -equation and the low-Reynolds number formulation with the -

equation. The model uses a blending function to go from an -formulation in the free-stream and an -formulation

in the near-wall regions. The SST-k-behaves much like a k-model in the free-stream regions. Simulations with

LC

conv

RT

x/Dj=0.0

Dj

RC


4/17


4

the standard k-model were done and the results were similar to that of the SST- k-model and therefore excluded

in this paper

Since the Reynolds stress models solve six additional transport equations of the turbulent stresses, they can

account for anisotropic turbulence that two-equation models, such as the SST-k-model, cannot do. Reynolds stress

models use the exact term for turbulent kinetic energy production, which two-equation models only model. It is thus

expected that RSM better can predict the turbulence field and hence the spread rate of the jet.

The meshes used have hexahedral cells and comprise a quarter sector of a full model. The computational domainis 20Djlong and it extends 4.35 Djin the radial direction. The inlet of the nozzle has a total pressure inlet boundary

condition with a turbulence level of 1% and a turbulent viscosity ratio, t/, of 1. The free-stream inlet boundary

condition has an axial velocity set to 10 m/s, and the free-stream boundary condition is of a type that allows an

entrainment flow and the ambient pressure set on those surfaces. The first near-wall grid node was placed at y+

around 30 in the divergent part of the nozzle. The fluid properties were those of air, and the specific heat capacity,

viscosity and thermal heat conductivity were all temperature dependent.

LES Computations

The flow field is obtained by solving the compressible form of the continuity, momentum and energy equations,

e.g. the Navier-Stokes equations, in which the viscous stress is defined using Newtons law and the heat flux with

Fouriers heat law.The system of governing equations is closed by two assumptions of the thermodynamics of gas.

First, the gas is considered thermally perfect meaning that it follows the gas law. Secondly, the gas is calorically

perfect, implying that internal energy and enthalpy are linear functions of temperature. The Favre-filtered Navier-

Stokes equations are solved with a finite volume solver belonging to the G3D family of codes developed by

Eriksson11

. The code solves the compressible flow equations in a conservative form on a boundary-fitted, curvilinear

non-orthogonal multi-block mesh. The convective fluxes are solved with a low-dissipation third-order upwind-

biased scheme, a second-order central difference scheme is used for the diffusive fluxes and a second-order three-

stage Runge-Kutta technique for time marching. The Smagorinsky part of the model proposed by Erlebacher et al 12

is used as subgrid-scale model. Another important item is the use of a specially modified pressure sensor which

ensures that the extra added numerical dissipation needed for shocks is applied only locally and dynamically.

Detailed description of the numerical scheme and the implementation of boundary conditions are given in the

references11,13,14.

The computational domain was discretized using a hexahedral block-structured boundary-fitted mesh with 249

mesh blocks and approximately 19 million nodes for both the baseline nozzle and the splined nozzle. The

geometries of the nozzles are obtained from CAD drawings. The domain is divided into three parts; a high-

resolution region near the nozzle exit, a medium-resolution region further downstream and a 2D entrainment regionas shown inFigure 2 andFigure 3.The mesh uses a combination of Cartesian and polar mesh blocks to ensure mesh

homogeneity in radial direction throughout the domain. Furthermore, a smoothing routine is swept through the

domain to achieve as orthogonal cells as possible, which increases numerical accuracy. As boundary conditions,

total pressure and total temperature are specified at the nozzle inlet. At the co-flow inlet, the density, velocity and

total temperature are set, as well as at the inlet of the 2D entrainment region which has additionally a periodical

boundary condition in the azimuthal direction. Its purpose is to achieve correct mass flow in and out of the domain

to avoid back-flow. Ambient pressure is specified at the outlet and a damping zone (buffer region) is added at the

end of the domain to minimize reflections from the outlet.

Figure 2: The computational domain used in the LES simulations.
http://arc.aiaa.org/action/showImage?doi=10.2514/6.2012-247&iName=master.img-013.jpg&w=467&h=104


5/17


5

(a) (b)

Figure 3: Cross-sectional view of the computational grid for LES simulations. Every other node is drawn. The

darker lines mark block boundaries. Zoomed on (a) Axial plane near nozzle lip, (b) Radial plane at nozzle

exit

C. Experimental Approach

Flowfield Measurements

The sharp throat and splined throat nozzles were tested at the University of Cincinnatis Aeroacoustic Test

Facility (ATF) in the Gas Dynamics and Propulsion Lab. Flow field measurements are made using a LaVision PIV

system including a double-pulsed Nd:YAG laser (New wave Research Solo-PIV), two Imager Intense CCD cameras

with a resolution of 1367x1040 pixels, and a dedicated computer for data acquisition and post-processing. PIVprovides mean and rms velocity measurements of the jet flow field with high spatial resolution. The system

provides no temporal information of the jet velocity with a constant sampling rate of 5 Hz. The primary and

secondary flows were seeded with atomized olive oil particles on the order of 1m. To provide reliable mean and

rmsvelocities, 500 image pairs were taken at near nozzle locations and 1000 image pairs at downstream locations.

Post-processing of the velocity vectors is done in LaVision Davis 7.2, which is also used for acquisition. A final

window size of 16x16 pixels was used for the correlations. Smaller windows provided better resolution of shocks in

the mean velocity field but increased the error in the turbulence statistics. The spatial resolution of PIV depends

strongly on the zoom of the camera lens, distance of the camera from the measurement plane, and the camera

resolution. In order to adequately resolve the jet shock structure, slightly more than half of the jet was measured to

increase the spatial resolution of the measurement. With two PIV cameras the field of view was approximately 3Dj.

Measurements were taken very near the nozzle at ~0.01Djdownstream of the nozzle exit, and downstream 8-11Dj.

The PIV measurement resolves two components of velocity, so the calculation of turbulence kinetic energy

(TKE) includes twice the radial component of fluctuating velocity. This assumption is valid for an axisymmetric jet,but would not be valid for a jet with azimuthal variation in the flow field. The radial component of fluctuating

velocity is approximately 30% of the axial component. Twice the radial component was included in the TKEfrom

experiments (Eq. 1) since the TKE from computations (Eq. 2) was 3D and included three velocity components.

Examining the individual Reynolds stresses for the Reynolds Stress Models and LES computations validated this

assumption. It was found that there is less than 10% difference in the maximum .

( ) Eq. (1)

( ) Eq. (2)

Far-Field Acoustics

Acoustic measurements are made with Bruel & Kjaer model 4954 free -field condenser microphones with

frequency sensitivity up to 100 kHz. Far-field microphones are spaced 10

o

apart from 40

o

to 150

o

and onemicrophone at 35owhich is the furthest upstream angle achievable in the facility without interference from the rig.

The thirteen microphones are sampled at 204.8 kHz for 5-second continuous intervals and was repeated 3 times to

provide 15 seconds of data for averaging. The facility data acquisition system uses a National Instruments PXI-6225

card for low speed acquisition and a PXI-4498 DSA with 24-bit accuracy for simultaneous microphone sampling.

The data was acquired using LabVIEW to simultaneously measure the acoustics and facility parameters.

Narrowband frequency spectra were calculated using an FFT with blocks of 4,096 samples. This results in a

frequency spectra averaged over 750 occurrences and a narrowband frequency resolution of 50 Hz. The overall

sound pressure level (OASPL) for each microphone location was calculated as where .
http://arc.aiaa.org/action/showImage?doi=10.2514/6.2012-247&iName=master.img-015.jpg&w=77&h=84http://arc.aiaa.org/action/showImage?doi=10.2514/6.2012-247&iName=master.img-014.jpg&w=154&h=84


6/17


6

III.

Results

A. Nozzle Optimization

Figure 4a) and Figure 4b) show velocity profile uniformity and average Mach number at the nozzle outlet as a

function of convergent section length for all the virtual designs in a bubble plot. The optimal design lies on the Pareto

front, on which no design can be further improved without deteriorating any of the other design objectives. The

optimized design, having the same length as the baseline nozzle, is referred to as the short optimized nozzle. The lengthof the convergent part was kept the same as for the baseline nozzle by increasing the angle of the convergent section

when the throat corner radius was increased. The short optimized nozzle has higher thrust as compared to the baseline

nozzle at the same nozzle pressure ratio, NPR, and can thus produce the same thrust as the baseline nozzle at a lower

NPR, but with a higher mass flow, seeTable 1.

a) b)

Figure 4: Bubble plots showing 3000 virtual design responses versus convergent length ratio LC/RT. a) Outlet

velocity profile uniformity parameter. b) Average outlet Mach number.

Figure 5: Mach number for the baseline nozzle, short optimized nozzle, long nozzle, and the splined nozzle at

NPR= 4.0 (k- model).

Deviation from

uniform outlet

profile

Baseline nozzle

Short optimized nozzle

Baseline nozzle

Short optimized nozzle

Baseline AR=1.23

(Nozzle tested at UC)

Splined nozzle AR=1.26

(Nozzle tested at UC)

Short optimized nozzleAR=1.23

Long nozzle AR=1.23


7/17


7

The results show that thrust increases by 3.9 % and mass flow by 4.5 % with the short optimal nozzle design as

compared to the baseline nozzle atNPR= 4.0. The shock pattern is less pronounced with the short optimal design as

shown inFigure 5 toFigure 7.The maximum Mach number at the outlet plane is reduced from 1.77 to 1.64 with the

short optimal nozzle. InFigure 5 showing contour plots of Mach number, it is evident that the normal shock and

slip surface near the center axis is almost gone for the optimal case. The internal shock strength is further reduced in

a design named Long and the splined nozzle. The splined nozzle has higher peak Mach number compared to the

long nozzle (seeFigure 6). The reason for this is the higher area expansion ratio, AR= 1.26, as compared to AR=

1.23 for the other nozzles. The reason for increasing the area ratio of the splined nozzle is to achieve a better

pressure-match at the nozzle outlet. The effective throat area is smaller for the baseline nozzle than for the splined

nozzle. This means that the effective area expansion is larger than 1.23 for the baseline nozzle.

Figure 6: Axial profiles of Mach number at r /Dj = 0.05 is plotted for the baseline, short optimized, long and

splined nozzles at NPR= 4.0.

Figure 7: Radial profiles of outlet Mach number at the nozzle exit x/Dj= 0.0 for the baseline, short optimized,

long and splined nozzles at NPR = 4.0.


8/17


8

Figure 8: Radial profiles of static pressure ratioP/Pambat the nozzle exit x/Dj = 0.0 for the baseline, short

optimized, long and splined nozzles at NPR= 4.0.

Figure 9: Axial profiles of static pressure ratioP/Pambat r/Dj= 0.05 for the baseline , short optimized, long and

splined nozzles at NPR= 4.0.

Figure 8 andFigure 9 show the static pressure field as radial and axial profiles respectively. It can be seen from

these figures that the normal shock near the center axis inside the convergent part of the nozzle is lowered in

strength with the especially the long and splined nozzles. The pressure at the outlet plane is also better adapted to the

ambient pressure and more uniform with the short optimized nozzle and long nozzle. The reason for the slight over-

expansion of the splined nozzle is the higher area expansion of 1.26. The baseline nozzle exhibit large pressure

variations inside the nozzle and just outside the nozzle, but the pressure variations in the downstream positions are

reduced as compared to the other nozzles.


9/17


9

a) b)

Figure 10: Radial profiles at the nozzle exit x/Dj= 0.0 for the baseline and splined nozzles at pressure-matched

conditions. a) Mach number b) Static pressure ratio Ps/Pamb.Figure 10 shows the outlet Mach number and pressure profiles for the baseline and splined nozzle cases at

pressure matched conditions. The profiles are very much the same as the profiles inFigure 8.The baseline nozzle is

pressure-matched at NPR = 4.45 and the splined nozzle at NPR = 4.27, which also are the cases used in the

experiments.

Table 1: Nozzle performance at NPR= 4.0 computed with CFD (cold).

AR

[-]

Mass flow

[kg/s]

Gross Thrust

[N]

PtotalLoss

[%]

Ps,exit/Pamb

[-]

Cfg

[-]

Cd

[-]

Baseline 1.23 1.902 797.3 2.62% 0.893 0.963 0.933

Optimized 1.23 1.988 828.5 1.40% 0.959 0.958 0.975

Long 1.23 2.016 845.0 1.29% 0.985 0.964 0.988

Splined 1.26 2.016 843.7 1.45% 0.936 0.962 0.989

Table 1 lists the results for the RANS computations at NPR = 4.0 for four of the studied nozzles. One can

observe that with contoured throat sections, the discharge coefficient is much improved, whereas the gross thrust

coefficient is relatively unaffected. The gain in thrust is thus achieved by increased mass flow through the nozzle.

The outlet pressure is also better adapted to the ambient pressure, which improves thrust. Table 2 shows nozzle

performance parameters computed at pressure-matched conditions, which also are the conditions the tests were run

at. The splined nozzle can give the same thrust as the baseline nozzle at 4.0% lower NPR.

Table 2: Nozzle performance at pressure-matched conditions computed with CFD (cold).

AR

[-]Mass flow

[kg/s]Gross Thrust

[N]PtotalLoss

[%]Ps,exit/Pamb

[-]Cfg

[-]Cd

[-]

BaselineNPR= 4.45

1.23 2.116 915.9 2.59% 0.987 0.965 0.933

Splined

NPR= 4.271.26 2.152 915.9 1.39% 0.997 0.960 0.990


10/17


10

B. PIV Results and Comparison with CFDThe primary goal of the study was to identify how modification of the jet shock structure by throat optimization

affects the acoustics of the jet. This required a high level of detail of the jet shock structure, so flow field

measurements were taken with PIV very near the nozzle exit to resolve the shocks in the jet. The axial velocity

normalized to the isentropic jet exit velocity is shown inFigure 11at fully expanded conditions for the sharp throat

and splined throat nozzles. The double diamond shock structure is very apparent for the sharp throat nozzle with the

shock reflection from inside the nozzle exiting and reflecting from the shear layer 0.2Dj

downstream. A shock forms

at the nozzle lip at all NPRsince the flow is diverging at the nozzle exit plane and must be turned axially to satisfy

the ambient boundary conditions. This is true for both nozzles since they have conical diverging sections. The

shocks and expansions waves continue to reflect in the jet potential core. The splined throat nozzle also has a double

shock diamond pattern. However, the shock that comes from inside the nozzle is much weaker and exits just outside

the nozzle lip. The velocity at the nozzle exit plane is much more uniform due to the weaker shocks from the throat

section. The splined throat nozzle has a shock structure that is much closer to a single diamond shock train

representative of smoothly contoured nozzles.

Comparison between measured and computed velocity profiles are shown inFigure 13andFigure 14. The radial

profiles are shown at three axial locations. The measurements are compared with RANS turbulence models,

SST-k- and SSG Reynolds Stress Model, as well as LES results. The mean axial velocity has very good

comparison near the nozzle exit for both the sharp and splined throat nozzles. RANS and LES slightly over predict

the jet spreading rate which gives an artificially thick shear layer downstream and more rapid decay of the jet

velocity at the near nozzle locations. Downstream atx/Dj= 8.0 the measurement falls in between the SST-k-model

and the SSG-RSM & LES. The computations show a slipline at the jet centerline induced by a Mach disk formation

where the throat shocks reflect inside the nozzle diverging section. The slipline causes stronger shocks at the jet

centerline r/Dj = 0.0. Despite the presence of the slip line, the shock cell spacing is captured well by the

computation seen inFigure 14. The presence of the slipline does not significantly affect the surrounding flow as

witnessed by excellent comparison of the velocity at r/Dj= 0.25. For the splined nozzle, the computations match the

experiments very well at both radial locations. It is believed that presence of the slipline is sensitive to the method

that the pressure ratio was set in the experiment. Many NPRwere measured during these tests, starting at the highest

pressure and decreasing pressure to measure lower NPR, since the air is supplied from high pressure blowdown

tanks. Many authors have studied a hysteresis effect for shock reflections in which the range ofNPRthat a Mach

reflection is present is dependent on the approach to the setpoint and the angle of the convergent section 15-17. It has

been shown that in over-expanded jets, the Mach reflection exists for a large range of pressure ratios if the jet

pressure was increased from low to high, but the Mach reflection does not occur until a very low NPR if the jet

pressure starts high and is decreased15. This phenomenon will be experimentally investigated in future

measurements, however it does not seem to affect the shock cell spacing or significantly affect the rest of the flowfield away from the jet centerline as seen in the mean axial velocity comparisons away from the centerline.

The axial variation of the mean axial velocity is smoother for the splined throat nozzle as shown in Figure 14.

The weak internal shock is not apparent in the profile and it appears that there is only one shock present in the flow.

The initial hypothesis was that by weakening the internal shock, the overall shock strength in the jet would be

reduced, subsequently reducing broadband shock associated noise. Comparing the mean axial velocity profiles in

Figure 15reveals that this is not actually the case. Even though the internal shock has been nearly eliminated, the

shock from the nozzle lip actually increased in strength since the velocity at the nozzle exit was increased. This

results in nearly the same maximum and minimum velocities as seen in the profiles at r/Dj= 0 and 0.25. The double

shock structure of the sharp throat nozzle had essentially the same overall shock strength as the optimized nozzle

with effectively a single shock structure. Although the overall shock strength has not been reduced, the optimized

nozzle has increased performance as discussed in the optimization results. The optimized nozzle provides the same

thrust with 4% less pressure while effectively maintaining the same overall shock strength in the jet potential core.

Turbulence measurements are compared with RANS and LES inFigure 16.Radial profiles are shown at x/Dj=0.5, 2.0, and 8.0. Turbulence is presented as the square root of TKE normalized to the jet velocity Vj. Near the

nozzle, the turbulence is lower than what is captured in the computations since the PIV spatially filters some of the

small turbulence scales from the 16x16 window size. Downstream at x/Dj = 8.0 the measured turbulence falls

between the SST-k- model and the SSG-RSM/LES. The RANS computations have no turbulence in the jet

potential core which is not physical, while the LES captures some of the turbulence present in the jet. Most

importantly, the only notable difference in the turbulence for the sharp throat and splined throat nozzles is slightly

higher fine scale turbulence near the nozzle from the additional perturbation of the shear layer from the double

shock pattern.


11/17


11

C. Acoustics MeasurementsFar-field acoustic measurements were taken to determine how the changes in the flow field affect the

acoustic spectra at thrust matched, fully expanded conditions.Figure 17shows the far field narrowband spectra

at three microphone locations and OASPL for the sharp throat and splined throat nozzles. There is very little

difference in the acoustics since the nozzles have been thrust matched. The splined throat nozzle has slightly

stronger screech which is evident in the small increase in noise at the upstream microphone angle (35 o). The

initial hypothesis for optimizing the nozzle throat was that if the shocks from the throat were weakened or

eliminated, then the shock associated noise would be reduced. Interestingly enough, the shock associated noise is

virtually unchanged in magnitude and frequency with the splined throat nozzle even though the flow field

measurements showed significant reduction in the throat shocks. Figure 15 shows that the maximum and

minimum velocities of the axial profiles are very close even though the throat shocks were eliminated. The

combined shock strength of the double shock pattern is equivalent to the single shock of the splined throat

nozzle. A slight reduction in high frequency mixing noise occurs with the splined throat. This is attributed to less

shock interaction with the shear layer with the splined nozzle. The double shock diamond pattern perturbs the

shear layer more, creating increased fine scale turbulence.

Figure 11: PIV measurements of normalized axial velocity andTKEfor the sharp throat (top) and splined

throat (bottom) nozzles at the fully-expanded conditions.

Figure 12: Schematic illustrating velocity and turbulence profiles and locations.

TKE/TKEmax

u/Uj

u/Uj

TKE/TKEmax

CL

CL

CL

x/Dj = 0.1 x/Dj = 0.5 x/Dj = 2.0

x

r


12/17


12

(a) (b)

Figure 13: Comparison of computed and measured radial profiles of axial velocity for fully expanded

conditions. Axial locationsx/Dj= 0.1, 2.0, and 8.0 for (a) Sharp throat nozzle and (b) Splined Nozzle.

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

r/Dj

u/U

j

x/Dj= 0.1

SST-k-

SSG-RSM

LES

PIV

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

r/Dj

u/U

j

x/Dj= 0.1

SST-k-

SSG-RSM

LES

PIV

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

r/Dj

u/U

j

x/Dj= 2.0

SST-k-

SSG-RSM

LES

PIV

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

r/Dj

u/U

j

x/Dj= 2.0

SST-k-

SSG-RSM

LES

PIV

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

r/Dj

u/U

j

x/Dj= 8.0

SST-k-

SSG-RSM

LES

PIV

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

r/Dj

u/U

j

x/Dj= 8.0

SST-k-

SSG-RSM

LES

PIV


13/17


13

(a) (b)

Figure 14: Comparison of computed and measured axial profiles of axial velocity for fully expanded

conditions. Radial locations r/Dj= 0.25, and 0. 50 (a) sharp throat nozzle and (b) splined throat nozzle.

(a) (b)

Figure 15: Comparison of measured axial profiles of axial velocity sharp throat and splined throat for fully

expanded conditions. Radial locations (a) r/Dj= 0.0 and (b) r/Dj= 0.25.

0.5 1 1.5 2 2.5 3

0

0.2

0.4

0.6

0.8

1

x/Dj

u/U

j

r/Dj= 0.25

SST-k-

SSG-RSM

LES

PIV

0.5 1 1.5 2 2.5 3

0

0.2

0.4

0.6

0.8

1

x/Dj

u/U

j

r/Dj= 0.25

SST-k-

SSG-RSM

LES

PIV

0.5 1 1.5 2 2.5 3

0

0.2

0.4

0.6

0.8

1

x/Dj

u/U

j

r/Dj= 0.5

SST-k-

SSG-RSM

LES

PIV

0.5 1 1.5 2 2.5 3

0

0.2

0.4

0.6

0.8

1

x/Dj

u/U

j

r/Dj= 0.5

SST-k-

SSG-RSM

LES

PIV

0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

x/Dj

u/U

j

r/Dj

= 0.0r/Dj

= 0.0

SharpSplined

0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

x/Dj

u/U

j

r/Dj

= 0.25r/Dj

= 0.25

SharpSplined


14/17


14

(a) (b)Figure 16: Comparison of computed and measured radial profiles of turbulence for fully expanded

conditions. Axial locationsx/Dj= 0.5, 2.0, and 8.0 for (a) sharp throat nozzle and (b) splined nozzle.

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

r/Dj

x/Dj= 0.5

SST-k-

SSG-RSM

LES

PIV

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

r/Dj

x/Dj= 0.5

k-

SSG-RSM

LES

PIV

0 0.2 0.4 0.6 0.8 1

0

0.05

0.1

0.15

0.2

r/Dj

x/Dj= 2.0

SST-k-

SSG-RSM

LESPIV

0 0.2 0.4 0.6 0.8 1

0

0.05

0.1

0.15

0.2

r/Dj

x/Dj= 2.0

k-

SSG-RSM

LESPIV

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

r/Dj

x/Dj= 8.0

SST-k-

SSG-RSM

LES

PIV

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

r/Dj

x/Dj= 8.0

SST-k-

SSG-RSM

LES

PIV


15/17


15

Figure 17: Far-field narrowband spectra at 35o, 90

o, 140

o, and OSAPL for the sharp throat and splined

nozzles at fully expanded conditions.

IV. Conclusion

A sharp throat supersonic nozzle representative of current variable-area nozzles was studied and the internal

flow contours were optimized to improve nozzle performance and reduce internal shock strength generated from the

sharp nozzle throat. The splined nozzle provides equivalent thrust as the sharp throat nozzle with 4% less pressure

required. The splined nozzle nearly eliminated the internal shocks resulting in a shock structure very near a single

diamond pattern and a more uniform velocity profile at the nozzle exit. The splined nozzle had slightly lower

turbulence levels due to less shock interaction with the shear layer. Very good comparison of the computational and

experimental mean flow field was shown at the near nozzle and downstream locations. The best comparison was

seen with the RSM-SSG RANS model and the LES computations. The shock cell spacing was captured accurately

in the computations for both the sharp throat and splined throat nozzle. It was found that the shock associated noise

is dominated by the overall shock strength in the jet and not merely by the number of shock cells. Weakening the

internal shocks created a stronger shock at the nozzle lip which had the total shock strength of two weaker shocks in

the sharp throat nozzle. Although the nozzle efficiency was increased and the throat shocks were minimized, no

reduction in the shock associated noise was measured. Slight reduction in the high frequency noise was measured

from reducing the fine scale turbulence by reducing the amount of shock interaction with the shear layer. The

splined nozzle provided equivalent thrust as the sharp throat nozzle at a reduced nozzle pressure ratio with no

acoustic penalty.

Acknowledgments

The authors would like to acknowledge the support of the Swedish Defense Materiel Administration (FMV) for

providing financial support for this research.

103

104

60

70

80

90

100

110

120

Frequency [Hz]

S

PL[dB]

= 35o

103

104

60

70

80

90

100

110

120

Frequency [Hz]

S

PL[dB]

= 90o

103

104

60

70

80

90

100

110

120

Frequency [Hz]

SPL

[dB]

= 140o

20 40 60 80 100 120 140 160120

122

124

126

128

130

132

134

Mic Angle

OASPL[dB]

Sharp Throat

Splined Throat


16/17


16

References

1Tam, C.K.W., "Jet Noise Generated by Large-Scale Coherent Motion,"Aeroacoustics of Flight Vehicles, edited by

H.H. Hubbard, Vol. 1, Acoustical Society of America, 1994, pp. 311-390.

2Munday, D., Heeb, N., Gutmark, E., "Supersonic Jet Noise from a Conical C-D Nozzle with Forward Flight

Effects," 47th AIAA Aerospace Sciences Meeting, AIAA, Orlando, FL, 2009,

3Henderson, B., and Bridges, J., "An MDOE Investigation of Chevrons for Supersonic Jet Noise Reduction," 16th

AIAA/CEAS Aeroacoustics Conference, AIAA, Stockholm, Sweden, 2010,

4Rask, O., Kastner, J., and Gutmark, E., "Understanding How Chevrons Modify Noise in a Supersonic Jet with

Flight Effects,"AIAA Journal, Vol. 49, No. 8, 2011, pp. 1569-1576.

5Munday, D., "Acoustic Effect of Chevrons on Jets Exiting Conical C-D Nozzles," 15th AIAA/CEAS Aeroacoustics

Conference, AIAA, Miami, FL, 2009,

6Cuppoletti, D., Perrino, M., and Gutmark, E., "Fluidic Injection Effects on Acoustics of a Supersonic Jet at Various

Mach Numbers," 17th AIAA/CEAS Aeroacoustics Conference, AIAA, Portland, OR, 2011,

7Burak, M., Eriksson, L.E., Munday, D., "Experimental and Numerical Investigation of a Supersonic C-D Nozzle,"

15th AIAA/CEAS Aeroacoustics Conference, 2009,

8Burak, M., Eriksson, L.E., Munday, D., "Experimental and Numerical Investigation of a Supersonic C-D Chevron

Nozzle," 39th AIAA Fluid Dynamics Conference, 2009,

9Menter, F.R., "Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications," AIAA Journal,

Vol. 32, No. 8, 1994, pp. 1598-1605.

10Speziale, C.G., Sarkar, S., and Gatski, T.B., "Modeling the Pressure-Strain Correlation of Turbulence: an Invariant

Dynamical Systems Approach,"Journal of Fluid Mechanics, Vol. 227, 1991, pp. 245-272.

11Eriksson, L.E., "Development and Validation of Highly Modular Flow Solver Versions in G2DFLOW and

G3DFLOW," Series for Compressible Viscous Reacting Flow, 9970-1162, 1995.

12Erlebacher, G., Hussanaini, M., Speziale, C., "Toward the large-eddy simulation of compressible turbulent flows,"

Journal of Fluid Mechanics, Vol. 238, 1992, pp. 155-158.

13Andersson, N., "A study of subsonic turbulent jets and their radiated sound using Large-Eddy Simulations," 2005,

14Burak, M., "Large Eddy Simulation for the Analysis of Supersonic Jet Noise Suppression Devices," 2010,

15Shimshi, E., Ben-Dor, G., and Levy, A., "Viscous simulation of shock-reflection hysteresis in overexpanded planar

nozzles,"Journal of Fluid Mechanics, Vol. 635, 2009, pp. 189-206.

16Yasunobu, T., Matsuoka, K., Kashimura, H., "Numerical Study for Hysteresis Phenomena of Shock Wave

Reflection in Overexpanded Axisymmetric Supersonic Jet,"Journal of Thermal Science, Vol. 15, No. 3, 2006, pp.

220-225.

17Ivanov, M.S., Vandromme, D., Fomin, V.M., "Transition between regular and Mach reflection of shock waves:

new numerical and experimental results," Shock Waves,pp. 207.
http://arc.aiaa.org/action/showLinks?crossref=10.1007%2Fs11630-006-0220-6http://arc.aiaa.org/action/showLinks?crossref=10.1017%2FS0022112092001678http://arc.aiaa.org/action/showLinks?crossref=10.1017%2FS0022112091000101http://arc.aiaa.org/action/showLinks?crossref=10.1017%2FS002211200900771Xhttp://arc.aiaa.org/action/showLinks?system=10.2514%2F1.J050628http://arc.aiaa.org/action/showLinks?system=10.2514%2F3.12149


17/17

This article has been cited by:

1. Qiang Shen, Weizheng Yuan, Xiaoping Li, Jianbing Xie, Honglong Chang. 2015. An orthogonal analysis method for decouplingthe nozzle geometrical parameters of microthrusters. Microsystem Technologies21, 1157-1166. [CrossRef]

2. Daniel Cuppoletti, Ephraim Gutmark, Haukur Hafsteinsson, Lars-Erik Eriksson. 2014. The Role of Nozzle Contour onSupersonic Jet Thrust and Acoustics.AIAA Journal52:11, 2594-2614. [Abstract] [Full Text] [PDF] [PDF Plus]

3. Daniel R. Cuppoletti, Ephraim Gutmark. 2014. Fluidic Injection on a Supersonic Jet at Various Mach Numbers.AIAA Journal

52:2, 293-306. [Abstract] [Full Text] [PDF] [PDF Plus]4. Daniel Cuppoletti, Ephraim Gutmark, Haukur Hafsteinsson, Lars-Erik Eriksson, Erik PrisellA Comprehensive Investigation of

Pulsed Fluidic Injection for Active Control of Supersonic Jet Noise . [Citation] [PDF] [PDF Plus]

5. Daniel Cuppoletti, Ephraim Gutmark, K.M. Gustafsson, Haukur Hafsteinsson, Lars-Erik Eriksson, Erik PrisellNozzle ThroatOptimization on Acoustics and Performance of a Supersonic Jet . [Citation] [PDF] [PDF Plus]
http://arc.aiaa.org/doi/pdfplus/10.2514/6.2012-2256http://arc.aiaa.org/doi/pdf/10.2514/6.2012-2256http://dx.doi.org/10.2514/6.2012-2256http://arc.aiaa.org/doi/pdfplus/10.2514/6.2013-9http://arc.aiaa.org/doi/pdf/10.2514/6.2013-9http://dx.doi.org/10.2514/6.2013-9http://arc.aiaa.org/doi/pdfplus/10.2514/1.J010000http://arc.aiaa.org/doi/pdf/10.2514/1.J010000http://arc.aiaa.org/doi/full/10.2514/1.J010000http://dx.doi.org/10.2514/1.J010000http://arc.aiaa.org/doi/pdfplus/10.2514/1.J052974http://arc.aiaa.org/doi/pdf/10.2514/1.J052974http://arc.aiaa.org/doi/full/10.2514/1.J052974http://dx.doi.org/10.2514/1.J052974http://dx.doi.org/10.1007/s00542-014-2240-6

paper on nozzle throat optimization

Documents