Graduate School ETD Form 9 (Revised 12/07) PURDUE UNIVERSITY GRADUATE SCHOOL Thesis/Dissertation Acceptance This is to certify that the thesis/dissertation prepared By Entitled For the degree of Is approved by the final examining committee: Chair To the best of my knowledge and as understood by the student in the Research Integrity and Copyright Disclaimer (Graduate School Form 20), this thesis/dissertation adheres to the provisions of Purdue University’s “Policy on Integrity in Research” and the use of copyrighted material. Approved by Major Professor(s): ____________________________________ ____________________________________ Approved by: Head of the Graduate Program Date DEEPAK THIRUMURTHY DESIGN AND ANALYSIS OF NOISE SUPPRESSION EXHAUST NOZZLE SYSTEMS MASTER OF SCIENCE IN AERONAUTICS AND ASTRONAUTICS Dr. ANASTASIOS S. LYRINTZIS Dr. GREGORY A. BLAISDELL Dr. JOHN P. SULLIVAN Dr. ANASTASIOS S. LYRINTZIS Dr. ANASTASIOS S. LYRINTZIS JANUARY 14TH, 2010
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Design and Analysis of Noise Suppression Exhaust Nozzle Systems
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Graduate School ETD Form 9 (Revised 12/07)
PURDUE UNIVERSITY GRADUATE SCHOOL
Thesis/Dissertation Acceptance
This is to certify that the thesis/dissertation prepared
By
Entitled
For the degree of
Is approved by the final examining committee:
Chair
To the best of my knowledge and as understood by the student in the Research Integrity and Copyright Disclaimer (Graduate School Form 20), this thesis/dissertation adheres to the provisions of Purdue University’s “Policy on Integrity in Research” and the use of copyrighted material.
Approved by Major Professor(s): ____________________________________
____________________________________
Approved by: Head of the Graduate Program Date
DEEPAK THIRUMURTHY
DESIGN AND ANALYSIS OF NOISE SUPPRESSION EXHAUST NOZZLE SYSTEMS
MASTER OF SCIENCE IN AERONAUTICS AND ASTRONAUTICS
Dr. ANASTASIOS S. LYRINTZIS
Dr. GREGORY A. BLAISDELL
Dr. JOHN P. SULLIVAN
Dr. ANASTASIOS S. LYRINTZIS
Dr. ANASTASIOS S. LYRINTZIS JANUARY 14TH, 2010
Graduate School Form 20 (Revised 6/09)
PURDUE UNIVERSITY GRADUATE SCHOOL
Research Integrity and Copyright Disclaimer
Title of Thesis/Dissertation:
For the degree of ________________________________________________________________
I certify that in the preparation of this thesis, I have observed the provisions of Purdue University Executive Memorandum No. C-22, September 6, 1991, Policy on Integrity in Research.*
Further, I certify that this work is free of plagiarism and all materials appearing in this thesis/dissertation have been properly quoted and attributed.
I certify that all copyrighted material incorporated into this thesis/dissertation is in compliance with the United States’ copyright law and that I have received written permission from the copyright owners for my use of their work, which is beyond the scope of the law. I agree to indemnify and save harmless Purdue University from any and all claims that may be asserted or that may arise from any copyright violation.
______________________________________ Printed Name and Signature of Candidate
______________________________________ Date (month/day/year)
*Located at http://www.purdue.edu/policies/pages/teach_res_outreach/c_22.html
DESIGN AND ANALYSIS OF NOISE SUPPRESSION EXHAUST NOZZLE SYSTEMS
MASTER OF SCIENCE IN AERONAUTICS AND ASTRONAUTICS
DEEPAK THIRUMURTHY
02/22/2010
DESIGN AND ANALYSIS OF
NOISE SUPPRESSION EXHAUST NOZZLE SYSTEMS
A Thesis
Submitted to the Faculty
of
Purdue University
by
Deepak Thirumurthy
In Partial Fulfillment of the
Requirements for the Degree
of
Master of Science in Aeronautics and Astronautics
May 2010
Purdue University
West Lafayette, Indiana
UMI Number: 1479646
All rights reserved
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ii
To my Parents and dear Sister, who enabled me to pursue my dreams.
iii
ACKNOWLEDGMENTS
I would like to express my gratitude towards my major professors, Dr. Anasta-
sios S. Lyrintzis and Dr. Gregory A. Blaisdell for their support, encouragement and
instruction.
My sincere appreciation goes to Dr. John P. Sullivan and his design team for their
constant suggestions on the nozzle design and support in the form of experimen-
tal results. I would also like to thank Dr. Stephen D. Heister, director, Rolls-Royce
University Technology Center in High Mach Propulsion, Dr. Jack S. Sokhey, senior en-
gineering consultant, Rolls-Royce, Indianapolis, USA and Mr. John R. Whurr, senior
project engineer, Rolls-Royce, Derby, UK for their support.
I am grateful to Dr. John Matlik, Dr. Loren Garrison and Patricia A. Ellis, Rolls-
Royce, Indianapolis, USA for being instrumental in liaisoning the Purdue University
- Rolls-Royce University Technology Center activities and helping in obtaining pub-
lication approval.
The work summarized in this thesis was part of Task 8, nozzle acoustics analysis,
of the supersonic business jet program, sponsored by Rolls-Royce and the Gulfstream
4.2 Calculation of the corrected inlet axial velocity magnitude for the CFDsimulations using the minimization of the RMS difference. . . . . . . . 77
5.1 Dimensions of the chevron on the 3-D ejector nozzle with clamshell doorsfor Design I and Design II. . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.2 Boundary conditions for the CFD simulation of the ejector nozzle withclamshell doors and chevrons. . . . . . . . . . . . . . . . . . . . . . . . 116
5.3 The effect of chevrons on the ejector mass flow. . . . . . . . . . . . . . 121
vii
LIST OF FIGURES
Figure Page
1.1 History of the commercial and military supersonic transport aircraft andits progress. (Reproduced courtesy of P. Henne [3].) . . . . . . . . . . . 2
1.2 The noise distribution from the individual components of the airbreathingjet engine propulsion system [6]. . . . . . . . . . . . . . . . . . . . . . . 4
1.3 A schematic representation of the 3-D ejector nozzle with clamshell doors [7]. 5
2.1 Jet noise as a result of the shear layer mixing phenomenon. . . . . . . . 9
2.2 Requirements for the pressure ratio and the area ratio as Mach numberincreases [16]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Operational modes of the ejector nozzle with clamshell doors (1) Subsonictake-off, (2) Supersonic cruise and (3) Subsonic approach. . . . . . . . 14
3.4 3BB axial velocity magnitude contour plot corresponding to the standardk-ε turbulence model on the Z=0 plane. . . . . . . . . . . . . . . . . . 37
3.5 3BB axial velocity magnitude contour plot corresponding to the realizablek-ε turbulence model on the Z=0 plane. . . . . . . . . . . . . . . . . . 37
viii
Figure Page
3.6 3BB axial velocity magnitude contour plot corresponding to the standardk-ω turbulence model on the Z=0 plane. . . . . . . . . . . . . . . . . . 38
3.7 3BB axial velocity magnitude contour plot corresponding to the k-ω shearstress transport turbulence model on the Z=0 plane. . . . . . . . . . . 38
3.8 3BB axial velocity magnitude contour plot corresponding to the Reynoldsstress turbulence model on the Z=0 plane. . . . . . . . . . . . . . . . . 38
3.9 3BB turbulent kinetic energy contour plot corresponding to PIV experi-ments on the Z=0 plane [20]. . . . . . . . . . . . . . . . . . . . . . . . 39
3.10 3BB turbulent kinetic energy contour plot corresponding to the standardk-ε turbulence model on the Z=0 plane. . . . . . . . . . . . . . . . . . 39
3.11 3BB turbulent kinetic energy contour plot corresponding to the realizablek-ε turbulence model on the Z=0 plane. . . . . . . . . . . . . . . . . . 39
3.12 3BB turbulent kinetic energy contour plot corresponding to the standardk-ω turbulence model on the Z=0 plane. . . . . . . . . . . . . . . . . . 40
3.13 3BB turbulent kinetic energy contour plot corresponding to the k-ω shearstress transport turbulence model on the Z=0 plane. . . . . . . . . . . 40
3.14 3BB turbulent kinetic energy contour plot corresponding to the Reynoldsstress turbulence model on the Z=0 plane. . . . . . . . . . . . . . . . . 40
3.15 Centerline axial velocity profiles for different turbulence models and com-parison with the experimental result. . . . . . . . . . . . . . . . . . . . 41
3.16 Centerline total temperature profiles for different turbulence models andcomparison with the experimental result. . . . . . . . . . . . . . . . . . 41
3.17 Dimensions for the design of alternating chevrons [21]. . . . . . . . . . 43
3.18 The CAD geometry of the three-stream separate-flow chevron nozzle [24]. 44
4.19 Experimental survey of the plenum chamber in the absence of the noz-zle showing the nonuniformity involved in the axial velocity magnitudedistribution [44]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.20 RMS difference distribution in the axial velocity magnitude atX/DEQ=1.0downstream of the nozzle throat. . . . . . . . . . . . . . . . . . . . . . 77
4.21 Contour plot of the normalized axial velocity magnitude on the Z=0 planefor the 3-D ejector nozzle with clamshell doors corresponding to the k-ωshear stress transport turbulence model. . . . . . . . . . . . . . . . . . 80
4.22 Contour plot of the normalized axial velocity magnitude on the Z=0 planefor the 3-D ejector nozzle with clamshell doors corresponding to the real-izable k-ε turbulence model with Thies and Tam’s model constants for jetflows. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.23 Experimental U/UPL contour plot at X/DEQ=1.0 from the throat [44]. 82
4.24 Computational U/UPL contour plot at X/DEQ=1.0 from the throat. . 82
4.25 Experimental U/UPL contour plot at X/DEQ=1.5 from the throat [44]. 83
4.26 Computational U/UPL contour plot at X/DEQ=1.5 from the throat. . 83
4.27 Experimental U/UPL contour plot at X/DEQ=2.0 from the throat [44]. 84
4.28 Computational U/UPL contour plot at X/DEQ=2.0 from the throat. . 84
4.29 Experimental U/UPL contour plot at X/DEQ=3.0 from the throat [44]. 85
xii
Figure Page
4.30 Computational U/UPL contour plot at X/DEQ=3.0 from the throat. . 85
4.31 Normalized axial velocity profile at X/DEQ=1.0 and on the Z=0 plane. 86
4.32 Normalized axial velocity profile at X/DEQ=1.0 and on the Y=0 plane. 86
4.33 Normalized axial velocity profile at X/DEQ=1.5 and on the Z=0 plane. 87
4.34 Normalized axial velocity profile at X/DEQ=1.5 and on the Y=0 plane. 87
4.35 Normalized axial velocity profile at X/DEQ=2.0 and on the Z=0 plane. 88
4.36 Normalized axial velocity profile at X/DEQ=2.0 and on the Y=0 plane. 88
4.37 Normalized axial velocity profile at X/DEQ=3.0 and on the Z=0 plane. 89
4.38 Normalized axial velocity profile at X/DEQ=3.0 and on the Y=0 plane. 89
4.39 Computational U/UPL contour plot at X/DEQ=3.0 downstream of thenozzle throat corresponding to the realizable k-ε turbulence model. . . 90
4.40 Computational U/UPL contour plot at X/DEQ=3.0 downstream of thenozzle throat corresponding to the standard k-ε turbulence model. . . . 90
4.41 Comparison of centerline axial velocity profiles among experiments, thek-ω SST, the realizable k-ε and the standard k-ε turbulence models. . . 91
4.42 Comparison of axial velocity profiles at X/DEQ=3.0 and on the Z=0 planebetween the k-ω SST and the realizable k-ε turbulence model. . . . . . 92
4.43 Comparison of axial velocity profiles at X/DEQ=3.0 and on the Y=0 planebetween the k-ω SST and the realizable k-ε turbulence model. . . . . . 92
4.44 Contour plot of the normalized axial velocity magnitude of the 3-D ejectornozzle with clamshell doors on the Z=0 plane with streamlines showingthe flow separation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.45 Experimental U/UPL contour plot at X/DEQ=0.42 from the throat [44]. 95
4.46 Computational U/UPL contour plot at X/DEQ=0.42 from the throat. . 95
4.47 Experimental U/UPL contour plot at X/DEQ=1.0 from the throat [44]. 96
4.48 Computational U/UPL contour plot at X/DEQ=1.0 from the throat. . 96
4.49 Experimental U/UPL contour plot at X/DEQ=1.5 from the throat [44]. 97
4.50 Computational U/UPL contour plot at X/DEQ=1.5 from the throat. . 97
4.51 Experimental U/UPL contour plot at X/DEQ=2.0 from the throat [44]. 98
4.52 Computational U/UPL contour plot at X/DEQ=2.0 from the throat. . 98
xiii
Figure Page
4.53 Experimental U/UPL contour plot at X/DEQ=3.0 from the throat [44]. 99
4.54 Computational U/UPL contour plot at X/DEQ=3.0 from the throat. . 99
4.55 Normalized axial velocity profile at X/DEQ=0.42 and on the Z=0 plane. 100
4.56 Normalized axial velocity profile at X/DEQ=0.42 and on the Y=0 plane. 100
4.57 Normalized axial velocity profile at X/DEQ=1.0 and on the Z=0 plane. 101
4.58 Normalized axial velocity profile at X/DEQ=1.0 and on the Y=0 plane. 101
4.59 Normalized axial velocity profile at X/DEQ=1.5 and on the Z=0 plane. 102
4.60 Normalized axial velocity profile at X/DEQ=1.5 and on the Y=0 plane. 102
4.61 Normalized axial velocity profile at X/DEQ=2.0 and on the Z=0 plane. 103
4.62 Normalized axial velocity profile at X/DEQ=2.0 and on the Y=0 plane. 103
4.63 Normalized axial velocity profile at X/DEQ=3.0 and on the Z=0 plane. 104
4.64 Normalized axial velocity profile at X/DEQ=3.0 and on the Y=0 plane. 104
4.65 Mach number contour plot on the Z=0 symmetry plane of the 3-D ejectornozzle with clamshell doors at take-off conditions. . . . . . . . . . . . . 105
4.66 Mach number contour plot at X/DEQ=0.5 plane downstream of the 3-Dejector nozzle throat at take-off conditions. . . . . . . . . . . . . . . . . 106
5.1 The phenomenon of the ejector flow with chevrons. . . . . . . . . . . . 109
5.2 CAD geometry of the ejector nozzle with clamshells and chevrons, DesignI - X-section at the throat. . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.3 CAD geometry of the ejector nozzle with clamshells and chevrons, DesignII - X-section at the throat. . . . . . . . . . . . . . . . . . . . . . . . . 112
5.11 Mach number contours on Y Z-plane at X/DEQ = 0.5 for the ejector nozzlewithout chevrons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.12 Mach number contours on the plane in between two chevrons for the ejectornozzle with chevrons - Design I. . . . . . . . . . . . . . . . . . . . . . . 124
5.13 Mach number contours on Z=0 symmetry plane for the ejector nozzle withchevrons - Design I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.14 Mach number contours on Y Z-plane at X/DEQ = 0.5 for the ejector nozzlewith chevrons - Design I. . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.15 Mach number contours on Z=0 symmetry plane for the ejector nozzle withchevrons - Design II. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.16 Mach number contours on the plane in between two chevrons for the ejectornozzle with chevrons - Design II. . . . . . . . . . . . . . . . . . . . . . 126
5.17 Mach number contours on Y Z-plane at X/DEQ = 0.5 for the ejector nozzlewith chevrons - Design II. . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.19 Centerline total temperature profiles corresponding to the ejector nozzlewith and without chevrons. . . . . . . . . . . . . . . . . . . . . . . . . 127
xv
ABBREVIATIONS
AMG Algebraic multigrid
AST Advanced subsonic transport program
BBSAN Broadband shock-associated noise
BC Boundary conditions
BPR Bypass ratio of the jet engine
CAA Computational aeroacoustics
CAD Computer-aided-design
CFD Computational fluid dynamics
CFL Courant-Friedrichs-Lewy number
CRAFT Combustion Research and Flow Technology
DARPA Defence Advanced Research Projects Agency
EPS Encapsulated post script file format
FA Fundamental aeronautics program
GRC Glenn Research Center
HSR High speed research program
ICAO International Civil Aviation Organization
JAXA Japanese aeronautical research agency
LES Large eddy simulation
NASA National Aeronautics and Space Administration
NPR Nozzle pressure ratio
PIV Particle image velocimetry
QST Quiet supersonic transport program
QSJ Quiet supersonic jet
RANS Reynolds-averaged Navier-Stokes
RMS Root mean square
xvi
RSM Reynolds stress turbulence model
SA Spalart-Allmaras turbulence model
SCAR Supersonic cruise aircraft research program (1972-1985)
SSBJ Supersonic business jet program
SST Supersonic transport program (1963-1971)
SST Shear stress transport turbulence model
STEP Standard for the exchange of product model data file format
TKE Turbulent kinetic energy
URANS Unsteady Reynolds-averaged Navier-Stokes
xvii
NOMENCLATURE
A Area m2
A∗ Nozzle throat area m2
Ae Nozzle exit area m2
D Diameter m
DC Control diameter of the nozzle m
DEQ Equivalent diameter of the nozzle throat m
Dfan Diameter of the fan nozzle m
H Semi-height of the 2-D ejector nozzle m
I Turbulent intensity
LS Length of the mixing duct in ejectors m
M Mach number
Me Exit Mach number
Mthroat Throat Mach number
P◦ Total pressure Pa or atm
Ps Static pressure Pa or atm
ReD Reynolds number based on the nozzle diameter
T◦ Total temperature K or R
Ts Static temperature K or R
U Axial velocity m/s or ft/sec
UPL Axial velocity inside the plenum chamber m/s or ft/sec
V Velocity magnitude m/s or ft/sec
k Turbulent kinetic energy m2/s2
mej Secondary mass flow entrained through the ejector slot kg/m3
min Primary nozzle mass flow kg/m3
y Wall normal distance m
xviii
y+ Normalized wall distance
Greek Alphabets
γ Ratio of specific heats
∆ Dimension of the secondary nozzle m
β Turbulent viscosity ratio
ε Dissipation rate of the turbulent kinetic energy m2/s3
µ Dynamic viscosity kg/m/s
µt Turbulent eddy viscosity kg/m/s
ν Kinematic viscosity m2/s
νt Spalart-Allmaras variable m2/s
ρ Density kg/m3
ω Specific dissipation rate of turbulent kinetic energy 1/s
xix
ABSTRACT
Thirumurthy, Deepak M.S.A.A., Purdue University, May 2010. Design and Analysisof Noise Suppression Exhaust Nozzle Systems. Major Professors: Anastasios S.Lyrintzis and Gregory A. Blaisdell.
The exhaust nozzle is an integral part of a jet engine and critical to its overall
system performance. Challenges associated with the design and manufacturing of
an exhaust nozzle become greater as the cruise speed of the aircraft increases. The
exhaust nozzle of a supersonic cruise aircraft requires additional capabilities such
as variable throat and exit area, noise suppression, and reverse thrust. The present
work is an effort to study the design and analysis of jet engine exhaust nozzle systems
such as the axisymmetric plug nozzle, the chevron nozzle and the ejector nozzle with
clamshells.
High-bypass-ratio jet engines with two or more flow streams have superior noise
suppressing and thrust characteristics. Much research has been done in the past to
study and understand the flow physics of these engines. In the present work a com-
putational fluid dynamics-based approach was used to study the jet engine exhaust
nozzle systems. First, a computer-aided-design model of a three-stream separate-flow
axisymmetric plug nozzle was created and axisymmetric flow simulations were per-
formed to study the flow field. The mean flow and turbulent kinetic energy fields
were compared with the particle image velocimetry results available in the literature.
Next, computational fluid dynamics was used to study the performance of passive
chevron mixers in enhancing the turbulent mixing. Three-dimensional calculations
were carried out to study the effect of enhanced mixing on the mean velocity and
turbulent kinetic energy flow fields. Different turbulence models were used to study
their performance in predicting chevron-based jet flows.
xx
Gas turbine engine manufacturer Rolls-Royce, and business class aircraft man-
ufacturer Gulfstream Aerospace Corporation, are collaborating on the development
of technologies for a supersonic jet. As part of this collaborative research and de-
velopment program, an ejector nozzle with clamshell doors, similar to that on an
Olympus-593 engine, which powered the Concorde aircraft, was designed and tested.
The ejector nozzle offers additional advantages such as thrust augmentation and noise
suppression.
Numerical simulations of this ejector nozzle with clamshell doors at 11.5◦ clamshell
angle and without clamshell doors were performed as part of the validation task. Mean
flow fields were predicted for low subsonic experimental conditions and compared with
the experimental data. Flow separation and recirculation zones were encountered near
the inner surface of clamshell doors. Simulations at higher nozzle pressure ratios were
also performed to simulate actual flight conditions. Flow separation prevailed at this
condition as well.
The existing new supersonic noise suppression exhaust nozzle design was improved
by the addition of chevrons and its flow field was analyzed using computational fluid
dynamics. The jet engine exhaust nozzle consisted of three-dimensional ejectors in
the form of clamshell doors and chevrons as passive mixers. Chevrons were placed
in the ejector slot to introduce streamwise vorticity and enhance mixing. It was
observed that the flow separation zone was almost removed and an improvement in
the ejector performance was obtained. Computational simulations corresponded to
take-off conditions with a nozzle pressure ratio of 1.7 and freestream Mach number
of 0.3.
1
1. Introduction
Mankind has witnessed a remarkable change in the speed of transporting goods and
people. During the 19th century the transportation method changed from horse-
powered carts traveling at 10 kmph to high speed trains transporting passengers and
cargo at 100 kmph. Speed has no limits as evidenced by the advent of subsonic
airplanes of the 20th century capable of flying at 1000 kmph [1]. Mankind was
skeptical of flying at a speed greater than the speed of sound until October 1947,
when United States Air Force Capt. Charles Yeager crossed the sound barrier and
reached Mach 1.02 in his XS-1 experimental aircraft [2].
This fascinating and challenging supersonic flight motivated many aerospace or-
ganizations to start programs related to the design of supersonic cruise aircraft and
develop related technologies. On November 29, 1962, the Concorde project, an Anglo-
French partnership, was launched and remains one of two supersonic cruise passenger
aircraft that traveled at speeds exceeding 2000 kmph, more than twice the speed of
sound. As airport regulations became more stringent, the Concorde failed to meet
requirements for performance, operating economics, development cost and environ-
mental acceptance. British Airways and Air France ended their Concorde service in
2003.
The Tupolev Tu-144 supersonic transport aircraft was a Soviet Union (now Russia)
effort to make supersonic civil transport a viable option. The project started two
years later than the Concorde. Although the Tu-144 was technically comparable
to the Concorde with a cruise Mach number of 2.5, the Tu-144 lacked a passenger
market within the Soviet Union and service was halted after only about 100 scheduled
flights. Initial plane crashes and high maintenance cost led the Soviet Union to cease
the program in 1983.
2
Figure 1.1 shows various supersonic aircraft, both military and civil, that were
designed with the motivation of supersonic cruise. No supersonic civil transport
aircraft has been produced since the end of the Concorde program. However, speed
continues to hold attraction for the civil aviation world, particularly in the executive
and corporate markets. Hence, the supersonic business jet (SSBJ) started gaining
traction despite the rising environmental concerns [2].
1940 1950 1960 1970 1980 1990 2000 2010 20200
0.5
1
1.5
2
2.5
3
3.5
X−1
F−100
D−558 B−58
F−104
X−B70
SR−71
Concorde UK/Fr
Tupolov−144 Russia
B−2707 US−Never Built
Year
Cru
ise
Mac
h N
umbe
r
MilitaryCommercial
30 Years with no NewSupersonic Civil Transport
55 Years of Subsonic Civil Jet Transports
Figure 1.1. History of the commercial and military supersonic trans-port aircraft and its progress. (Reproduced courtesy of P. Henne [3].)
1.1 Supersonic Civil Transport
The technical challenges associated with supersonic flight such as sonic boom,
airport community noise, engine emissions and developmental cost are reduced with
a smaller business jet compared to a 100-seater passenger aircraft, such as the Con-
corde. Several programs were initiated to develop a viable supersonic business jet
3
aircraft design in various research and development organizations. These include
the Defence Advanced Research Projects Agency’s (DARPA) quiet supersonic plat-
form program (QSP); the National Aeronautics and Space Administration (NASA)-
Gulfstream quiet spike expendable nose-probe program; various NASA supersonic
transport programs, such as the supersonic transport (SST: 1963-1972), supersonic
cruise aircraft research (SCAR: 1975-1981) and high speed research (HSR) programs;
supersonic transport research plans of the Japanese Aeronautical Research Agency
(JAXA); Aerion’s supersonic business jet and Supersonic Aerospace International’s
quiet supersonic transport program [3].
Along with a challenging high speed aerodynamic design, supersonic aircraft re-
quire a variable cycle propulsion system that can provide high performance during
different operational modes, such as subsonic take-off, transonic acceleration, super-
sonic cruise and subsonic approach. Gas turbine engine manufacturer Rolls-Royce,
and business class aircraft manufacturer Gulfstream Aerospace Corporation are col-
laborating on the development of supersonic jet technologies. This involves developing
technologies related to the airframe and propulsion system necessary for supersonic
cruise, such as the quiet supersonic jet (QSJ) inlet and noise suppressing shrouded
plug nozzle [4]. The present work for the design and analysis of an ejector nozzle is
also a part of this program.
Interest in supersonic civil transport encouraged NASA to start a new initia-
tive to develop necessary related technologies. A new research and development
project, known as the supersonic project under the fundamental aeronautics (FA)
program [5], was started to address the challenges involved in supersonic transport.
Some of the objectives of this program were to develop better tools for the simulation
of jet engine exhaust nozzle geometries, noise improvements via new engine designs
and other noise-reduction concepts, innovative low-noise nozzles, and propulsion in-
tegration concepts.
4
1.2 Challenges Associated with Supersonic Transport
Aircraft noise, unwanted sound from the aircraft, is generated when the airflow
over the aircraft structure or its propulsion system causes fluctuating pressure distur-
bances that propagate to an observer either sitting in the aircraft or on the ground.
For a subsonic cruise aircraft, these pressure fluctuations are significant during take-
off and approach, when the landing gear and high-lift devices (slats and flaps) are
deployed. In addition, if the aircraft is capable of supersonic cruise, additional noise
sources in the form of sonic boom and shock-generated jet noise add to the overall
pressure fluctuations causing severe annoyance to the community beneath the aircraft.
As previously mentioned, the effect of aircraft noise is more significant during
take-off and approach phases. Several sources can combine to increase the overall
sound pressure level. Of all the aircraft noise sources, the major noise sources during
take-off and approach are noise from the powerplant and airframe noise. Powerplant
noise is much more complex than airframe noise.
High Bypass RatioLow Bypass RatioNoise of a typical 1960s engine Noise of a typical 1990s engine
Compressor Fan
Compressor
Jet JetShock
Turbine & Core
Turbine & Core
Figure 1.2. The noise distribution from the individual components ofthe airbreathing jet engine propulsion system [6].
Most of the components of a typical gas turbine engine contribute to the overall
powerplant noise, as shown in Figure 1.2. Pressure fluctuations in the airflow through
5
the propulsion system due to the fan, compressors, turbines, mixing of hot and cold
flows, nozzle and exhaust jet are the sources of powerplant noise. Based on the type
of spectral distribution, these noises can be classified as broadband noise and discrete
tones. Detailed discussion on various powerplant noise sources, except jet noise, is
outside the scope of the present work.
1.3 Noise Suppression Propulsion System
The performance of the exhaust nozzle is critical to the overall system performance
in the sense that it produces the required thrust efficiently during different phases
of the flight, such as subsonic take-off, transonic acceleration, supersonic cruise and
subsonic approach. In addition to the performance, noise associated with the high
speed exhaust jet is a concern in modern supersonic cruise nozzles. The aircraft
jet engine must comply with the federal aviation regulation (FAR) Stage IV noise
regulations during all the phases of flight. This poses additional requirements in the
design and performance of jet engine exhaust systems. Figure 1.3 shows a schematic
representation of a variable cycle engine with an ejector nozzle in the form of clamshell
doors.
Figure 1.3. A schematic representation of the 3-D ejector nozzle withclamshell doors [7].
6
During the past 50 years, several high speed propulsion systems have been designed
to address these challenges. Research and development programs such as SST, SCAR,
HSR and FA were initiatives to address problems related to supersonic civil trans-
port. During these programs, special emphasis was given to the jet engine exhaust
system design. Many noise suppression approaches were studied and combinations
of technologies were formulated into acoustically effective, optimum configurations
based on quantitative analyses [8]. At the supersonic cruise point, the lift to drag
ratio (L/D) of the aircraft is low and the specific fuel consumption is high relative
to subsonic jetliners. The aircraft payload weight thus becomes highly sensitive to
the nozzle efficiency. For example, the Concorde, at the cruise speed of Mach 2.2, a
1% decrease in nozzle performance was estimated to be equivalent to an 8% loss in
weight [9].
1.4 Objectives
The aim of this thesis was to study the design and analysis of noise suppression ex-
haust nozzle systems for a business class supersonic transport. A Reynolds-averaged
14 S = sqrt((b/2)2 + (lp)2), length of chevron side 1.1753
15 P = N x 2S (perimeter of all chevrons) 28.21
16 l/PHD = Normalized chevron length 0.207
17 P/PHD = Normalized chevron perimeter 7.08
Figure 3.17. Dimensions for the design of alternating chevrons [21].
not axisymmetric but symmetric about a pair of alternating chevrons, a 30 degree
section was used for the CFD study and the computational grid was created. The
grid extended circumferentially from the tip of the inward-facing chevron to the tip of
the outward-facing chevron. A nonuniform, multiblock structured mesh was created,
as shown in Figure 3.19 with a good boundary layer resolution and sufficient number
of grid points in the shear layer. The grid had a total of 4.78 million cells. A variable
wall spacing was used to keep the y+ value within the range of 30 ∼ 300 which was
good for the application of wall functions.
44
Figure 3.18. The CAD geometry of the three-stream separate-flowchevron nozzle [24].
Figure 3.19. The computational mesh for the three-stream separate-flow chevron nozzle.
45
3.4.3 Boundary Conditions and CFD Methodology
The flow conditions were the same as used in the CFD simulation of the baseline
three-stream separate-flow axisymmetric plug nozzle, with a NPR of 1.7. Therefore,
similar pressure-based boundary conditions were used for the CFD simulations. The
boundary conditions were pressure-inlet at the inflow boundary, inviscid wall along
the symmetry planes, pressure far field along the outer freestream boundary and
pressure-outlet at the exit. The numerical values of the flow boundary conditions are
given in Table 3.2.
Table 3.2 Boundary conditions for the CFD simulation of the three-stream separate-flow chevron nozzle (3A12B) [24].
Variables Core Fan
Total pressure (atm) 1.65 1.80
Total temperature (K) 833.3 333.3
Freestream static pressure (atm) 0.98
Freestream total pressure (atm) 1.04
Freestream total temperature (K) 298.8
Freestream Mach number 0.28
The ANSYS FLUENT version 6.3.26 flow solver was used for all the CFD simu-
lations. The density-based explicit solver was used for high subsonic flow conditions.
RANS-based flow governing equations were solved in a coupled manner and the sys-
tem was closed using turbulence equations. The density was defined by the ideal gas
equation and Sutherland’s three coefficient method was used to calculate the value
of the molecular viscosity. The convergence of the density-based explicit algorithm
is defined primarily by the CFL number. A low CFL value is required for stability
reasons. Hence a CFL value of 1.0 was used to get the converged first-order solution.
This was different from the three-stream separate-flow axisymmetric plug nozzle case
46
where a CFL of 5.0 was used because of the pressure-based explicit solver. The
solutions presented here are second-order accurate.
The ANSYS FLUENT flow solver was run using 5 nodes of the Booster cluster
of the School of Aeronautics & Astronautics, Purdue University. Booster is a Linux
based computing cluster with a total of 56 nodes. Each node consists of 4 AMD 64
bit based processors. Booster used a portable batch system called Torque for job
scheduling.
3.4.4 Results
Computational results of the three-stream separate-flow chevron nozzle are pre-
sented in this section and are compared with the experiments, documented in refer-
ence [24]. Contours of the axial velocity and turbulent kinetic energy on the inward-
facing chevron mid-plane (symmetry plane passing through the middle of a chevron)
and outward-facing chevron mid-plane are used for the comparison. All spatial co-
ordinates are normalized using the fan stream exit diameter (DF = 9.621 in.). As
mentioned before, various two-equation turbulence models are used in the present
study and their accuracy in the prediction of chevron jet flows is studied.
The computational results in the form of mean and turbulent flow fields corre-
sponding to various turbulence models are presented in the following sections. The
experimental and WIND-CFD axial velocity contours on the inward-facing chevron
mid-plane are shown in Figures 3.20 and 3.21, respectively. The mean axial ve-
locity contours obtained from the CFD using the turbulence models are shown in
Figures 3.22-3.25. Similarly, the mean axial velocity contour plots on the outward-
facing chevron mid-plane are shown in Figure 3.26 for experiments, Figure 3.27 for
WIND-CFD result and Figures 3.28-3.31 for various turbulence models.
The experimental turbulent kinetic energy contours are shown in Figure 3.32 and
the WIND-CFD turbulent kinetic energy contours are shown in Figure 3.33. The
corresponding CFD results with various turbulence models are given in Figures 3.34-
47
3.37. Similarly, the turbulent kinetic energy contour plots on the outward-facing
chevron mid-plane are shown in Figure 3.38 for experiments, Figure 3.39 for WIND-
CFD result, and Figures 3.40-3.43 for various turbulence models.
Launder and Spalding’s k-ε Turbulence Model
Figures 3.23 and 3.35 show the distribution of the axial velocity and turbulent
kinetic energy for the standard k-ε turbulence model on the inward-facing chevron
mid-plane. It is evident that the length of the potential core is shorter compared to
the experiments. This is consistent with the results obtained from the CFD simulation
of the three-stream baseline axisymmetric plug nozzle. Figure 3.35 shows nonphysical
overprediction of the turbulent kinetic energy near the core nozzle exit because of the
high shear-rate. The problem is known and addressed by using a realizable limit in
the definition of the turbulent viscosity, as discussed in Section 3.3.4. Figures 3.29
and 3.41 show the distribution of the axial velocity and turbulent kinetic energy for
the standard k-ε turbulence model on the outward-facing chevron mid-plane.
Shih’s Realizable k-ε Turbulence Model
The realizability limit, used in the definition of the turbulent viscosity, results in
overcoming the overprediction of the turbulent kinetic energy corresponding to the
standard k-ε turbulence model. The realizable k-ε turbulence model gives a good
prediction of the mean flow field and the turbulent kinetic energy contours are in
better comparison with the experimental results. Figures 3.24 and 3.36 show the
contours of the axial velocity and the TKE on the inward-facing chevron mid-plane.
Also the contours of the axial velocity and TKE corresponding to the outward-facing
chevron are shown in Figures 3.29 and 3.41, respectively. The realizable k-ε turbulence
model is also recommended in the ANSYS FLUENT flow solver’s best practice guide
for CFD simulations involving external flows [29].
48
Thies and Tam’s k-ε Turbulence Model
As discussed in Section 2.3.2, Thies and Tam proposed few modifications in the
standard k-ε turbulence model constants for the better prediction of the turbulent
jet flows. These constants can be implemented in the ANSYS FLUENT flow solver
using the turbulence model selection user interface. Figure 3.25 and 3.31 show the
mean velocity contours on the inward-facing and outward-facing chevron mid-planes,
respectively. Similarly, Figures 3.37 and 3.43 show the turbulent kinetic energy con-
tours on the inward-facing and outward-facing chevron mid-planes, respectively. It
can be easily observed that, even though the above mentioned modifications to the
model constant result in a better prediction of the mean flow fields, it is very diffusive
for the prediction of the turbulent kinetic energy, resulting in smeared contours.
Menter’s k-ω Shear Stress Transport Turbulence Model
Menter proposed a blending turbulence model as a compromise between the inflow
turbulence sensitivity of the standard k-ω turbulence model and the accuracy of
the standard k-ε turbulence model. Figure 3.22 shows the distribution of the axial
velocity on the inward-facing chevron mid-plane downstream of the fan nozzle exit
plane. Figure 3.34 shows the contour of the turbulent kinetic energy. The contours
of TKE on the outward-facing chevron mid-plane are presented in Figure 3.40.
For the turbulent jet class of flows, one of the important variable to look at is the
variation of the centerline velocity magnitude with respect to the axial distance. This
gives further insight into the length of the potential core, centerline velocity decay
rate, spreading of the jet etc. which are the characteristics of any jet flow. Figure
3.44 shows the comparison of the centerline velocity magnitude of the three-stream
separate-flow chevron nozzle (3A12B), predicted by different turbulence models with
experiments. Figure 3.45 shows the centerline total temperature distribution which
gives information about the radial spreading of the jet.
49
Figure 3.20. 3A12B axial velocity magnitude contour plot correspond-ing to PIV experiments on the Z=0 and inward-facing chevron mid-plane [24].
Figure 3.21. 3A12B axial velocity magnitude contour plot correspond-ing to WIND-CFD results on the Z=0 and inward-facing chevronmid-plane [24].
Figure 3.22. 3A12B axial velocity magnitude contour plot correspond-ing to the k-ω SST turbulence model on the Z=0 and inward-facingchevron mid-plane.
50
Figure 3.23. 3A12B axial velocity magnitude contour plot correspond-ing to the standard k-ε turbulence model on the Z=0 and inward-facing chevron mid-plane.
Figure 3.24. 3A12B axial velocity magnitude contour plot correspond-ing to the realizable k-ε turbulence model on the Z=0 and inward-facing chevron mid-plane.
Figure 3.25. 3A12B axial velocity magnitude contour plot correspond-ing to Thies and Tam’s k-ε turbulence model on the Z=0 and inward-facing chevron mid-plane.
51
Figure 3.26. 3A12B axial velocity magnitude contour plot correspond-ing to PIV experiments on the outward-facing chevron mid-plane [24].
Figure 3.27. 3A12B axial velocity magnitude contour plot corre-sponding to WIND-CFD results on the outward-facing chevron mid-plane [24].
Figure 3.28. 3A12B axial velocity magnitude contour plot correspond-ing to the k-ω SST turbulence model on the outward-facing chevronmid-plane.
52
Figure 3.29. 3A12B axial velocity magnitude contour plot corre-sponding to the standard k-ε turbulence model on the outward-facingchevron mid-plane.
Figure 3.30. 3A12B axial velocity magnitude contour plot corre-sponding to the realizable k-ε turbulence model on the outward-facingchevron mid-plane.
Figure 3.31. 3A12B axial velocity magnitude contour plot correspond-ing to Thies and Tam’s k-ε turbulence model on the outward-facingchevron mid plane.
53
Figure 3.32. 3A12B turbulent kinetic energy contour plot correspond-ing to PIV experiments on the Z=0 and inward-facing chevron mid-plane [24].
Figure 3.33. 3A12B turbulent kinetic energy contour plot correspond-ing to WIND-CFD results on the Z=0 and inward-facing chevronmid-plane [24].
Figure 3.34. 3A12B turbulent kinetic energy contour plot correspond-ing to the k-ω SST turbulence model on the Z=0 and inward-facingchevron mid-plane.
54
Figure 3.35. 3A12B turbulent kinetic energy contour plot correspond-ing to the standard k-ε turbulence model on the Z=0 and inward-facing chevron mid-plane.
Figure 3.36. 3A12B turbulent kinetic energy contour plot correspond-ing to the realizable k-ε turbulence model on the Z=0 and inward-facing chevron mid-plane.
Figure 3.37. 3A12B turbulent kinetic energy contour plot correspond-ing to Thies and Tam’s k-ε turbulence model on the Z=0 and inward-facing chevron mid-plane.
55
Figure 3.38. 3A12B turbulent kinetic energy contour plot correspond-ing to PIV experiments on the outward-facing chevron mid-plane [24].
Figure 3.39. 3A12B turbulent kinetic energy contour plot corre-sponding to WIND-CFD results on the outward-facing chevron mid-plane [24].
Figure 3.40. 3A12B turbulent kinetic energy contour plot correspond-ing to the k-ω SST turbulence model on the outward-facing chevronmid-plane.
56
Figure 3.41. 3A12B turbulent kinetic energy contour plot corre-sponding to the standard k-ε turbulence model on the outward-facingchevron mid-plane.
Figure 3.42. 3A12B turbulent kinetic energy contour plot corre-sponding to the realizable k-ε turbulence model on the outward-facingchevron mid-plane.
Figure 3.43. 3A12B turbulent kinetic energy contour plot correspond-ing to Thies and Tam’s k-ε turbulence model on the outward-facingchevron mid-plane.
57
0 5 10 15 20 250
200
400
600
800
1000
1200
1400
1600
X/Dfan
Cen
terli
ne V
eloc
ity U
CL ft
/sec
PIV experiment (NASA/CR−2000−210039)WIND k−ω SST (Koch, 2004)Standard k−ε turbulence modelRealizable k−ε turbulence modelStandard k−ε with Thies−Tam’s correctionk−ω SST turbulence model
Figure 3.44. Centerline axial velocity profiles for different turbulencemodels and comparison with the experimental result.
0 5 10 15 20 25300
400
500
600
700
800
900
X/Dfan
Tot
al T
empe
ratu
re T o K
Experiment (Birch, 2003)Zonal k−ε (Birch, 2003)Standard k−ε turbulence modelRealizable k−ε turbulence modelStandard k−ε with Thies−Tam’s correctionk−ω SST turbulence model
Figure 3.45. Centerline total temperature profiles for different turbu-lence models and comparison with the experimental result.
58
3.5 Conclusion
The computational study of the three-stream separate-flow axisymmetric plug
nozzle with and without chevrons was successfully completed. The results obtained
from the CFD simulations were compared with experiments available in the litera-
ture. The primary concentration in the present work was to study the ability of the
turbulence models, available in the ANSYS FLUENT flow solver, in predicting the
jet flow characteristics.
For the baseline three-stream separate-flow axisymmetric plug nozzle, most of
the turbulence models performed well in predicting the length of the potential core.
However, computations overpredicted the jet spreading rate and resulted in a faster
centerline velocity decay rate. Among various turbulence models used, the realizable
k-ε turbulence model and the Menter’s k-ω SST turbulence model performed well and
are recommended for further CFD simulations.
For the chevron based three-stream separate-flow plug nozzle, it was found that the
realizable k-ε turbulence model with Thies and Tam’s jet flow corrections performed
well in the prediction of the mean flow field. However, it failed in predicting the
turbulent kinetic energy field. A suitable compromise was provided by the Menter’s
k-ω SST turbulence model which predicted the turbulent kinetic energy profiles in
the jet region very well with an overprediction in the jet potential core length. The
standard k-ε turbulence model suffered from a severe overprediction of the turbulent
kinetic energy at the high shear region near the nozzle exit.
59
4. Ejector Nozzles
4.1 Introduction
Noise is a major problem associated with the high speed propulsion system design.
Although there are no clear cut restrictions on the noise levels for high speed aircraft,
it is reasonable to assume that the noise levels in the terminal area will be governed
by the restrictions similar to that of the subsonic aircrafts. Supersonic jet noise is an
important contributor to the overall propulsion system noise. It is essential to mini-
mize the jet noise during take-off and landing where it is more pronounced and tough
noise regulations apply. These requirements pose additional design requirements on
the exhaust nozzle design. Nozzles such as the separate-flow nozzle, the plug noz-
zle, the chevron nozzle and the mixer-ejector nozzle are examples for addressing this
challenge. In recent years, chevron and ejector nozzle designs received special atten-
tion because of their improved noise reduction characteristics and low thrust penalty.
The history and performance of ejector nozzles are discussed in Section 2.2.1. The
present chapter is dedicated to the discussion of the results obtained from the CFD
simulation of the 3-D ejector nozzle with and without clamshell doors at low-speed
experimental and high-speed take-off conditions.
4.2 Objectives
The primary objective of the present study was to perform the CFD simulations
of the 3-D ejector nozzle with clamshell doors, whose experimental performance at
subsonic conditions was studied by [44]. Initially, the computational study of the
NASA 2-D ejector nozzle test case was carried out to perform the validation of the
CFD tool. Next, the CFD simulation of the 3-D ejector nozzle without clamshell
60
doors as well as with clamshell doors at 11.5◦ were performed and the results are
compared with the experiments. The analysis of the 3-D ejector nozzle was extended
by the application of different turbulence models and performing the CFD simulation
at higher nozzle pressure ratios corresponding to the take-off conditions.
4.3 2-D Ejector Nozzle Test Case
4.3.1 Introduction
Experimental investigation of the ejector nozzle performance is limited to low
nozzle pressure ratios and experimental scales. Over the past fifteen years, significant
improvements in the field of CFD have enhanced the prediction capability of the
nozzle performance. This flow is dominated by the primary flow which mixes with
the entrained secondary flow resulting in improved thrust and noise characteristics.
Since numerical methods involve errors such as truncation errors and discretization
errors, they have to be validated against experimental results for simple cases before
using them for complex 3-D geometries. For this reason, a 2-D ejector nozzle test case
was considered for the validation of the ANSYS FLUENT flow solver in the prediction
of the ejector nozzle flow fields. The CFD results obtained from this simulation are
verified using WIND-CFD results from reference [45] and validated using experimental
results from reference [46].
4.3.2 Geometry and Mesh Generation
Gilbert and Hill (1973) [46] investigated a turbulent, two-dimensional ejector noz-
zle flow through a rectangular section experimentally. Figure 4.1 shows the experi-
mental geometry with primary nozzle and mixing section. The setup consisted of a
discharge slot as the primary nozzle, opening into a rectangular area mixing section
of constant width of 8 in. through a pair of contoured walls placed symmetrically on
either side of the primary nozzle. The experimental data used in the present study
61
−5 0 5 10 15 20
−4
−3
−2
−1
0
1
2
3
4
Axial Length (in)
Mixing Section Diffuser SectionSecondary Inlet
Primary Nozzle
Figure 4.1. Experimental setup for the 2-D ejector nozzle. (Repro-duced courtesy of [46].)
for comparison consists of the velocity and temperature measurements at different
axial locations viz. 3.0, 5.0, 7.0 and 10.5 in. downstream of the primary nozzle exit
plane.
The two-dimensional experimental setup was symmetric about the X-axis and
hence only the half-section of the ejector nozzle was used for the computational sim-
ulation. A structured, two-dimensional, multiblock mesh, similar to the one used
in reference [45] for simulations using WIND-CFD, was created using the Pointwise
GRIDGEN version 15.10. The grid consisted of 131 nodes in the horizontal direction
and 121 nodes in the vertical direction. Figure 4.2 shows the structured computa-
tional mesh in which the upstream contoured secondary flow region was neglected to
avoid highly skewed cells and to be consistent with WIND-CFD simulations.
Figure 4.2. Computational mesh for the 2-D ejector nozzle.
4.3.3 Boundary Conditions and Numerical Computation
Table 4.1 shows boundary conditions used in the CFD simulation which corre-
sponded to run nine in reference [46]. The pressure-based CFD boundary conditions
were used for the CFD simulation because of high nozzle pressure ratios in the exper-
iments. The pressure-inlet boundary condition was used for primary and secondary
flows with the stagnation pressure, the stagnation temperature and turbulence quan-
tities as input. The outflow was pressure-outlet with static pressure, measured in the
experiments, as input.
The ANSYS FLUENT version 6.3.26 flow solver was used for all the CFD simula-
tions. The operating conditions consisted of high nozzle pressure ratio and hence the
governing equations were solved using the density-based explicit solver. The details
63
of this solver are discussed in Section 2.3.1. Two turbulence models, viz. Menter’s k-ω
SST turbulence model and the Spalart-Allmaras turbulence (SA) model were used for
the turbulent flow simulation. The results presented here are second-order accurate.
Figure 4.3. Mach number contour plot of the 2-D ejector nozzle cor-responding to the k-ω SST turbulence model.
Figure 4.4. Mach number contour plot of the 2-D ejector nozzle cor-responding to the Spalart-Allmaras turbulence model.
64
4.3.4 Results
The velocity and stagnation temperature profiles at different axial locations down-
stream of the primary nozzle exit plane are plotted and compared with the experi-
mental and WIND-CFD results. The vertical distance is normalized using the semi-
height (H) of the rectangular channel. Figure 4.5 shows the velocity profile at 3 in.
downstream of the nozzle exit plane and its comparison with the experimental and
WIND-CFD results. It is evident that the Spallart-Allmaras turbulence model per-
forms well compared to the k-ω SST turbulence model. Similarly, Figures 4.6, 4.7,
and 4.8 show the velocity profiles at 5.0, 7.0, and 10.5 in. downstream, respectively.
The CFD predictions improve and match well with the experimental results as we
move downstream. Figures 4.9 and 4.10 show the stagnation temperature profiles
corresponding to 3.0 and 10.5 in. downstream, respectively. It is clear that the nu-
merical prediction of the temperature improves as we go downstream of the primary
nozzle exit plane. The ANSYS FLUENT results match well with the WIND-CFD
results.
65
0 200 400 600 800 1000 1200−1.5
−1
−0.5
0
0.5
1
1.5
Axial Velocity ft/s
Y/H
Experiments (Gilbert and Hill, 1973)k−ω SST turbulence model (WIND)k−ω SST turbulence modelSpalart−Allmaras turbulence model
Figure 4.5. 2-D ejector nozzle axial velocity profile at X=3.0 in.
0 200 400 600 800 1000 1200−1.5
−1
−0.5
0
0.5
1
1.5
Axial Velocity ft/s
Y/H
Experiments (Gilbert and Hill, 1973)k−ω SST turbulence model (WIND)k−ω SST turbulence modelSpalart−Allmaras turbulence model
Figure 4.6. 2-D ejector nozzle axial velocity profile at X=5.0 in.
66
0 200 400 600 800 1000 1200−1.5
−1
−0.5
0
0.5
1
1.5
Axial Velocity ft/s
Y/H
Experiments (Gilbert and Hill, 1973)k−ω SST turbulence model (WIND)k−ω SST turbulence modelSpalart−Allmaras turbulence model
Figure 4.7. 2-D ejector nozzle axial velocity profile at X=7.0 in.
0 200 400 600 800 1000 1200−1.5
−1
−0.5
0
0.5
1
1.5
Axial Velocity ft/s
Y/H
Experiments (Gilbert and Hill, 1973)k−ω SST turbulence model (WIND)k−ω SST turbulence modelSpalart−Allmaras turbulence model
Figure 4.8. 2-D ejector nozzle axial velocity profile at X=10.5 in.
67
540 550 560 570 580 590 600 610 620 630−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Total Temperature oR
Y/H
Experiments (Gilbert and Hill, 1973)k−ω SST turbulence model (WIND)k−ω SST turbulence modelSpalart−Allmaras turbulence model
Figure 4.9. 2-D ejector nozzle total temperature profile at X=3.0 in.
540 550 560 570 580 590 600 610 620 630−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Total Temperature oR
Y/H
Experiments (Gilbert and Hill, 1973)k−ω SST turbulence model (WIND)k−ω SST turbulence modelSpalart−Allmaras turbulence model
Figure 4.10. 2-D ejector nozzle total temperature profile at X=10.5 in.
68
4.4 3-D Ejector Nozzle with Clamshell Doors
4.4.1 Introduction
The CFD simulation of the 2-D ejector nozzle, as discussed in Section 4.3, was
necessary to perform the validation of the CFD tool before using it in the computa-
tional study of the 3-D ejector nozzle with and without clamshell doors. The objective
of this task was to carry out the CFD simulation of a 3-D supersonic cruise ejector
nozzle in subsonic ejector configuration and compare the computational results with
the experiments presented in reference [44]. Cases corresponding to the 3-D ejector
nozzle without clamshell doors and with clamshell doors at an ejector angle of 11.5◦
were considered. This study was further extended to higher pressure ratios and the
performance of the 3-D ejector nozzle was studied at the take-off conditions.
4.4.2 Experimental Investigation
Jones (2009) [44] conducted a set of wind-tunnel experiments to study the charac-
teristics of the ejector nozzle flow with ejectors at different incident angles viz. 0, 5.0,
9.0, 11.5 and 15.0 degrees and low subsonic conditions. One of the objectives of these
experiments was to develop a unique test model which can capture some of the funda-
mental aerodynamic features of the 3-D ejector nozzle. The result of his work was a
test nozzle of scale 0.123 operated at approximately Mthroat=0.25 and ReD=760, 000.
More details about the experimental conditions, the 7-hole probe data acquisition
system mounted on an automated 2-axis traverse instrument, used for the velocity
measurement, and the wind-tunnel setup are available in reference [44]. Experimen-
tal results are available in the form of axial velocity measurements on Y -Z planes at
different axial locations downstream of the nozzle throat.
69
Figure 4.11. CAD model of the 3-D ejector nozzle without clamshell doors [44].
4.4.3 Nozzle Design and CAD Geometry
Almost all of the ejector nozzle concepts studied before the 1970s were limited
to the research level and never materialized in practical supersonic air transport
Figure 4.12. CAD model of the 3-D ejector nozzle with clamshell doors [44].
70
applications. The only exception to this is the exhaust nozzle system of the Rolls-
Royce Olympus-593 engine, which powered the world’s first supersonic airliner, the
Concorde [47]. This design served as the key motivation to the present study of
an ejector nozzle with clamshell doors. It consisted of a baseline nozzle with two
asymmetric clamshells serving as ejectors. In order to facilitate the application of
the automated computer numerical controlled (CNC) machining techniques for the
fabrication of the complex 3-D ejector nozzle with clamshell doors design, a high
fidelity, design table driven CAD model was created using the CATIA V6 as part of
the experimental work. The CAD geometry reads the parameters through an MS-
Excel file. This allowed the user to vary the angle of the clamshell doors without the
necessity to redesign the entire nozzle. The same parametric CAD model was used
for the CFD simulations discussed in the present chapter. As mentioned before, two
configurations of the ejector nozzle, one without clamshell doors and the other with
clamshell doors were studied. Figures 4.11 and 4.12 show the CAD geometry of the
3-D ejector nozzle without clamshell doors and with clamshell doors, respectively.
(a) (b)
Figure 4.13. Computational mesh for nozzle walls (a) 3-D ejectornozzle without clamshell doors (Grid I), and (b) 3-D ejector nozzlewith clamshell doors (Grid II).
71
4.4.4 Grid Generation
As a first step towards the computational analysis of the ejector nozzle, a 3-D
grid for the CAD geometry was required. Grids were generated using the Pointwise
GRIDGEN Version 15.10 [48]. Nonoverlapping, multiblock hybrid grids were used for
this geometry. Because of the symmetry, only one quadrant of the domain was used
to save computational cost and time. In the present numerical study, three cases, viz.
an ejector nozzle without clamshell doors (Grid I), an ejector nozzle with clamshell
doors at 11.5◦ (Grid II) and an ejector nozzle with clamshells at 11.5◦ for the CFD
simulation at take-off nozzle pressure ratios (Grid III) were considered.
The computational mesh for the viscous walls of the ejector nozzle with and with-
out clamshell doors are shown in Figure 4.13. Because of the complex design of the
clamshell doors and the support handle on the nozzle, an unstructured mesh was cre-
Figure 4.14. Computational mesh (Grid II) for the entire flow domainof the 3-D ejector nozzle with clamshell doors for the CFD simulationat experimental conditions.
72
ated near the nozzle and a structured mesh was used in the rest of the flow domain, as
shown in Figure 4.14. Grid I, corresponded to the ejector nozzle without clamshells
and consisted of 20 blocks including one unstructured block near the nozzle throat,
resulted in a total of 1.29 million cells. Grid II, corresponding to the ejector nozzle
with clamshell doors consisted of the same topography with 20 blocks, resulted in a
total of 2.2 million cells. A variable wall spacing (y) was used for all the viscous wall
boundaries in both the cases to yield a y+ value in the range of 30 ∼ 300 and hence
wall functions were used for the near wall turbulence. y+ is defined as
y+ =
(yU
ν
), (4.1)
where U is the freestream velocity and ν is the dynamic viscosity.
Figure 4.15. Computational mesh (Grid III) for the entire flow domainof the 3-D ejector nozzle with clamshell doors for the CFD simulationat take-off conditions (higher NPR).
73
The CFD simulation at high nozzle pressure ratios, to simulate the take-off con-
ditions with a freestream Mach number of 0.3, required a higher number of nodes
near the walls compared to its low speed counterpart. Therefore, this mesh, termed
as Grid III, consisted of boundary layer grids, as shown in Figure 4.15 to accurately
capture the near wall boundary layers. Similar to Grid II, this mesh was a hybrid
grid with 29 blocks and 2.22 million cells. Grid III included nonuniform hexahedral
cells in the boundary layers, shear layers and freestream blocks, tetrahedral cells in
the unstructured block surrounding the clamshell doors, prism cells in the bound-
ary layers corresponding to the unstructured wall domains, and pyramid cells at the
interface between the structured and unstructured blocks.
Figure 4.16. Extent of the computational domain for the 3-D ejectornozzle with clamshell doors.
The present study involved the CFD simulation of the jet flows and hence the
outflow and far field boundaries should be far enough such that they do not affect the
jet flow dynamics and unrestricted entrainment. Hence the computational region, as
shown in Figure 4.16 extended 7 DC in the radial direction representing far field and
27 DC in the streamwise direction representing the outflow boundary, where DC is
the control diameter (outer diameter = 202.844 mm) of the nozzle plenum chamber,
as defined in reference [44].
74
4.4.5 Boundary Conditions
Two sets of boundary conditions (BC) were used for the computational meshes
described in Section 4.4.4. BC set I corresponded to the flow conditions used in the
experiments and reported in reference [44]. The numerical values of these boundary
conditions are shown in Figure 4.17. The experimental conditions were low subsonic
of the order of M ≤ 0.25 and hence the velocity-based boundary conditions were
used in the CFD analysis. The boundary conditions were velocity inlet at the inflow
boundary, inviscid wall along the symmetry planes, velocity-inlet along the outer
freestream boundary, and pressure-outlet at the exit. BC set II corresponded to the
take-off conditions which were subsonic of the order of M ≥ 0.3 and hence pressure-
based boundary conditions were used for this CFD simulation, which was an effort to
study the performance of the ejector nozzle in flight conditions. This set of boundary
condition is shown in Figure 4.18.
Figure 4.17. Schematic representation of experimental boundary con-ditions (Simulation I) and their numerical values.
75
Inlet Distortion
In the experiments, the inlet flow from the blower was passed into the test rig
through a flow straightener [44]. This helped in the straighting of the flow and re-
moved a lot of the flow nonuniformities. However, some nonuniformity in the velocity
distribution was still present. Figure 4.19 shows the snapshot of the axial velocity
magnitude, measured at the inside of the rig in the absence of the ejector nozzle. It
was evident that the experiments involved nonuniform velocity distribution and hence
an equivalent uniform velocity inlet was calculated for the CFD simulations using the
following procedure.
It was necessary to compute the correct mass flow rate through the rig for the
accurate comparison between the experiments and computations. The mass flow rate
of the nozzle was adjusted in the computation such that it matched the velocity profile
at X/DEQ=1.0. This corrected mass flow rate gave the magnitude of the velocity
inlet used in the CFD simulations. The corrected velocity inlet corresponded to the
Figure 4.18. Schematic representation of take-off boundary conditions(Simulation II) and their numerical values.
76
Figure 4.19. Experimental survey of the plenum chamber in the ab-sence of the nozzle showing the nonuniformity involved in the axialvelocity magnitude distribution [44].
least RMS difference between the experiments and computations at X/DEQ=1.0.
The RMS differences were plotted against the inlet velocity magnitude, as shown in
Figure 4.20, and the arithmetic mean of the differences in both Y=0 and Z=0 planes
were used to find the corrected inlet velocity magnitude. Numerical values for the
Simulation I are tabulated in Table 4.2.
4.4.6 Numerical Computation
The ANSYS FLUENT [29] version 6.3.26 computational solver was used to solve
RANS equations and the system of governing equations were closed using the turbu-
lence models. The CFD simulations of the ejector nozzle without and with clamshell
doors (Simulation I and Simulation II, respectively) at experimental conditions were
performed using the pressure-based coupled implicit solver [30]. As discussed in Sec-
77
44 44.5 45 45.5 46 46.5 47
0.075
0.08
0.085
0.09
0.095
0.1
0.105
0.11
0.115
Inlet Velocity (U) m/s
RM
S d
iffer
ence
in v
eloc
ity m
agni
tude
RMS AverageRMS Difference on Y=0 planeRMS Difference on Z=0 plane
Figure 4.20. RMS difference distribution in the axial velocity magni-tude at X/DEQ=1.0 downstream of the nozzle throat.
tion 2.3.1, this algorithm solves the continuity and momentum equations in a coupled
implicit manner using a pressure-velocity coupling algorithm and the coupled alge-
braic multigrid (AMG) solver. The density-based coupled explicit solver was used
Table 4.2 Calculation of the corrected inlet axial velocity magnitudefor the CFD simulations using the minimization of the RMS difference.
Inlet RMS difference RMS difference RMS RMS
velocity (Y=0 plane) (Z=0 plane) average difference(%)
1 44 0.0773 0.0873 0.0823 11.13
2 45 0.0819 0.0762 0.07905 9.11
3 45.5 0.0877 0.0733 0.0805 8.10
4 46 0.0954 0.0722 0.0838 7.09
5 47 0.1148 0.0758 0.0953 5.07
44.9 0.079 9.31
78
for the CFD simulation of the ejector nozzle at take-off conditions (Simulation III)
involving higher pressure ratios.
For Simulation I and Simulation II, corresponding to Grid I and Grid II respec-
tively, a constant density of 1.15 kg/m3 was used. The viscosity was calculated using
Sutherland’s three coefficient method. In the experiments, a region of flow separa-
tion and flow recirculation was identified at the inner surface of the clamshell doors.
Hence, in order to capture the separated flow well, Menter’s k-ω shear stress transport
turbulence model with wall functions was primarily used for the CFD simulations.
Shih’s realizable k-ε turbulence model with Thies and Tam’s jet flow correction was
also used for Simulation I. The flow domain was initiated using freestream conditions
and the final second-order accurate solution was obtained. A CFL value of 2 was
used for stability reasons. The underrelaxation factors were reduced from their de-
In order to check the convergence, along with the default solver residual monitor,
the iteration history of the mass-balance and velocity magnitude at one equivalent
diameter downstream of the nozzle throat were monitored. When the mass-balance
reached 1× 10−5 and the velocity magnitude reached a steady-state value, the solu-
79
tion was considered to be converged. For simulations involving flow separation and
recirculation zone, the velocity magnitude at the monitor point oscillated about a
steady-state value.
4.4.7 Results
The results from the numerical simulation of the ejector nozzle with and with-
out clamshell doors at experimental as well as take-off conditions are discussed in
the present section. The computational results are compared with the experimental
results. The quantitative velocity measurements are normalized using the upstream
plenum axial velocity UPL, which is the centerline axial velocity in the plenum cham-
ber, upstream of the nozzle and the length scale using the equivalent diameter of the
nozzle throat cross-section (DEQ = 5.642 in.), which is defined as,
At = π
(DEQ
2
)2
, (4.2)
where At is the throat area of the nozzle. At first, computational results from the CFD
simulation of the ejector nozzle without clamshell doors using Grid I (Simulation I) is
presented and compared with the experiments. This section is followed by a discussion
on the effect of turbulence models in the prediction of velocity profiles. Results
corresponding to the ejector nozzle with clamshell doors using Grid II are presented
as Simulation II and compared with the experimental measurements, followed by a
discussion on the region of flow separation. The computational results are presented
in the form of normalized axial velocity profiles at different Y -Z planes (different
X/DEQ locations) downstream of the nozzle throat and contour plots of the jet cross-
section at these locations. Finally, the results from the CFD simulation of the ejector
nozzle with clamshell doors at take-off conditions (Simulation III) are discussed. It
is observed that the flow separation near the inner surface of the clamshell doors is
attributed to the ejector nozzle design and not to the nozzle pressure ratio (NPR).
80
Simulation I: Ejector nozzle without clamshell doors (experimental condi-
tions)
Figure 4.21. Contour plot of the normalized axial velocity magnitudeon the Z=0 plane for the 3-D ejector nozzle with clamshell doorscorresponding to the k-ω shear stress transport turbulence model.
Results obtained from the CFD simulation of the ejector nozzle without clamshell
doors are discussed in this section. Without the clamshell doors, the jet behaves like
an elliptic jet because of the elliptic cross-section of the nozzle throat. As the nozzle
was convergent in nature and the conditions were subsonic, the flow was accelerated
to higher velocities. The velocity contour plots of the flow field at the Z=0 plane
corresponding to the k-ω shear stress transport turbulence model is shown in Figure
4.21. The CFD simulation of this configuration was necessary for initial comparison
with the experimental results before going to the more complicated configuration of
a nozzle with clamshells. The velocity contour plot of the flow field corresponding
to the realizable k-ε model with Thies and Tam’s correction is shown in Figure 4.22.
The lateral spreading (spreading of the jet along Y-axis) is more pronounced in the
81
case of the k-ω SST turbulence model compared to the k-ε model with Thies and
Tam’s correction.
As discussed earlier, experimental results are available in the form of velocity
measurements on the Y=0 and Z=0 planes and on the Y -Z planes at different X/DEQ
locations downstream of the nozzle throat. Figures 4.23-4.30 show the comparison
of normalized axial velocity magnitude contours at different axial locations between
the experiments and computations. The velocity profiles match very well with the
experimental results at X/DEQ=1.0, 1.5 and 2.0. For the case of X/DEQ=3.0, there
is an overprediction of the axial velocity magnitude. This is believed to be due to
the inability of the turbulence model to predict the length of the potential core of the
jet. At X/DEQ=3.0, as it can be inferred from the experimental results, the potential
core ends and the shear layers start to merge with each other. Figures 4.31-4.38 show
the comparison of the normalized axial velocity profiles between the experiments and
computations.
Figure 4.22. Contour plot of the normalized axial velocity magnitudeon the Z=0 plane for the 3-D ejector nozzle with clamshell doorscorresponding to the realizable k-ε turbulence model with Thies andTam’s model constants for jet flows.
82
Figure 4.23. Experimental U/UPL contour plot at X/DEQ=1.0 from the throat [44].
Figure 4.24. Computational U/UPL contour plot at X/DEQ=1.0 from the throat.
83
Figure 4.25. Experimental U/UPL contour plot at X/DEQ=1.5 from the throat [44].
Figure 4.26. Computational U/UPL contour plot at X/DEQ=1.5 from the throat.
84
Figure 4.27. Experimental U/UPL contour plot at X/DEQ=2.0 from the throat [44].
Figure 4.28. Computational U/UPL contour plot at X/DEQ=2.0 from the throat.
85
Figure 4.29. Experimental U/UPL contour plot at X/DEQ=3.0 from the throat [44].
Figure 4.30. Computational U/UPL contour plot at X/DEQ=3.0 from the throat.
86
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Y/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.31. Normalized axial velocity profile at X/DEQ=1.0 and onthe Z=0 plane.
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Z/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.32. Normalized axial velocity profile at X/DEQ=1.0 and onthe Y=0 plane.
87
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Y/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.33. Normalized axial velocity profile at X/DEQ=1.5 and onthe Z=0 plane.
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Z/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.34. Normalized axial velocity profile at X/DEQ=1.5 and onthe Y=0 plane.
88
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Y/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.35. Normalized axial velocity profile at X/DEQ=2.0 and onthe Z=0 plane.
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Z/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.36. Normalized axial velocity profile at X/DEQ=2.0 and onthe Y=0 plane.
89
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Y/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.37. Normalized axial velocity profile at X/DEQ=3.0 and onthe Z=0 plane.
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Z/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.38. Normalized axial velocity profile at X/DEQ=3.0 and onthe Y=0 plane.
90
Figure 4.39. Computational U/UPL contour plot at X/DEQ=3.0downstream of the nozzle throat corresponding to the realizable k-ε turbulence model.
Figure 4.40. Computational U/UPL contour plot at X/DEQ=3.0downstream of the nozzle throat corresponding to the standard k-εturbulence model.
91
−5 0 5 10 15 20 25 30 350.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
X/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
Experiments (Jones, 2009)k−ω SST turbulence modelRealizable k−ε with Theis and Tam’s ConstantsStandard k−ε turbulence model
Figure 4.41. Comparison of centerline axial velocity profiles amongexperiments, the k-ω SST, the realizable k-ε and the standard k-εturbulence models.
Effect of Turbulence Models In addition to the Menter’s k-ω shear stress trans-
port turbulence model, Shih’s realizable k-ε turbulence model with Thies and Tam’s
jet flow correction was used to study the effect of turbulence model in predicting the
separated ejector jet flow. Figure 4.39 shows the velocity magnitude contour of jet
cross-section at X/DEQ=3.0 corresponding to Thies and Tam’s k-ε turbulence model.
It is evident that the lateral spreading is more pronounced in the latter compared to
the k-ω SST model, but no significant improvement is observed in terms of the axial
velocity profiles.
92
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Z/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
Experimentsk−ω SSTReal. k−ε
Figure 4.42. Comparison of axial velocity profiles at X/DEQ=3.0and on the Z=0 plane between the k-ω SST and the realizable k-εturbulence model.
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Y/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
Experimentsk−ω SSTReal. k−ε
Figure 4.43. Comparison of axial velocity profiles at X/DEQ=3.0and on the Y=0 plane between the k-ω SST and the realizable k-εturbulence model.
93
Simulation II: Ejector nozzle with clamshell doors (experimental condi-
tions)
In addition to the case of the ejector nozzle without clamshell doors, the CFD
simulation of the ejector nozzle with clamshell doors at 11.5◦ was considered in the
present study to complement the experimental findings. In addition to the survey
planes similar to the case without clamshell doors, at X/DEQ=1.0, 1.5, 2.0, 3.0 down-
stream of the nozzle exit, experimental values were also measured at X/DEQ=0.42
which was inside the clamshell doors. This survey plane helps in the understanding
of the separated flow and provides a better comparison between the experiments and
computations.
Figure 4.44. Contour plot of the normalized axial velocity magnitudeof the 3-D ejector nozzle with clamshell doors on the Z=0 plane withstreamlines showing the flow separation.
94
The contours of the velocity magnitude on the Z=0 symmetry plane (ejector
plane) is shown in Figure 4.44. A region of flow separation and recirculation, as
found during the experiments, is encountered. This is because of the inability of
the resulting free shear layer to attach to the inner surface of the clamshells, as
discussed in Section 2.2.1 and thereby allows the external atmospheric flow to affect
the nozzle exhaust. Figures 4.45-4.54 show the comparison of the jet cross-section
axial velocity contours between the experiments and computations. As with the case
without clamshell doors, similar good agreement at X/DEQ=0.42, 1.0, 1.5, 2.0 and
overprediction at X/DEQ=3.0 are found. The quantitative comparisons of normalized
axial velocity in the Y=0 and Z=0 planes and at different axial locations are shown
Figure 4.46. Computational U/UPL contour plot at X/DEQ=0.42 from the throat.
96
Figure 4.47. Experimental U/UPL contour plot at X/DEQ=1.0 from the throat [44].
Figure 4.48. Computational U/UPL contour plot at X/DEQ=1.0 from the throat.
97
Figure 4.49. Experimental U/UPL contour plot at X/DEQ=1.5 from the throat [44].
Figure 4.50. Computational U/UPL contour plot at X/DEQ=1.5 from the throat.
98
Figure 4.51. Experimental U/UPL contour plot at X/DEQ=2.0 from the throat [44].
Figure 4.52. Computational U/UPL contour plot at X/DEQ=2.0 from the throat.
99
Figure 4.53. Experimental U/UPL contour plot at X/DEQ=3.0 from the throat [44].
Figure 4.54. Computational U/UPL contour plot at X/DEQ=3.0 from the throat.
100
−1.5 −1 −0.5 0 0.5 1 1.5
−0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Y/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.55. Normalized axial velocity profile at X/DEQ=0.42 andon the Z=0 plane.
−1.5 −1 −0.5 0 0.5 1 1.5
−0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Z/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.56. Normalized axial velocity profile at X/DEQ=0.42 andon the Y=0 plane.
101
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Y/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.57. Normalized axial velocity profile at X/DEQ=1.0 and onthe Z=0 plane.
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Z/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.58. Normalized axial velocity profile at X/DEQ=1.0 and onthe Y=0 plane.
102
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Y/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.59. Normalized axial velocity profile at X/DEQ=1.5 and onthe Z=0 plane.
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Z/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.60. Normalized axial velocity profile at X/DEQ=1.5 and onthe Y=0 plane.
103
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Y/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.61. Normalized axial velocity profile at X/DEQ=2.0 and onthe Z=0 plane.
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Z/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.62. Normalized axial velocity profile at X/DEQ=2.0 and onthe Y=0 plane.
104
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Y/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.63. Normalized axial velocity profile at X/DEQ=3.0 and onthe Z=0 plane.
−1.5 −1 −0.5 0 0.5 1 1.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Z/DEQ
Axi
al F
low
Sp
eed
U/U
PL
EN
UM
ExperimentsCFD
Figure 4.64. Normalized axial velocity profile at X/DEQ=3.0 and onthe Y=0 plane.
105
Simulation III: Ejector nozzle with clamshell doors (take-off conditions)
The overall objective of the design and analysis of the 3-D ejector nozzle with
clamshell doors was to study the performance of the nozzle for subsonic take-off
conditions. As discussed in Chapter 2, the optimum performance of the exhaust
system during subsonic take-off and approach with minimum noise is as challenging
as supersonic cruise. The performance study of nozzle during take-off required a
CFD analysis with take-off conditions because experimental conditions were limited
to low subsonic Mach numbers. Hence a third simulation was performed with take-off
conditions and results are presented in this section.
Figure 4.65. Mach number contour plot on the Z=0 symmetry planeof the 3-D ejector nozzle with clamshell doors at take-off conditions.
The primary objective of this analysis was to predict if the flow separation occurs
even at higher nozzle pressure ratios. Figure 4.65 shows the presence of the flow
separation and recirculation zone at the inner surface of the clamshell doors even
at a higher nozzle pressure ratio which is detrimental to the overall performance of
the exhaust nozzle system. The contours of Mach number at X/DEQ=0.5 plane are
106
shown in Figure 4.66. The zone of reverse flow is observed near the clamshell inner
surface.
Figure 4.66. Mach number contour plot at X/DEQ=0.5 plane down-stream of the 3-D ejector nozzle throat at take-off conditions.
4.5 Conclusion
A comprehensive computational study of the ejector nozzle has been carried out.
At first, a 2-D ejector nozzle test case was used to perform the validation task of the
available computational tool. It was found that the CFD results from the ANSYS
FLUENT flow solver were in good agreement with experiments and WIND-CFD
results for 2-D ejector nozzle test case. The one-equation Spalart-Allmaras turbulence
model performed better than the k-ω SST turbulence model in the prediction of mean
flow variables downstream from the nozzle exit plane.
The computational analysis of the 3-D ejector nozzle with and without clamshell
doors at experimental conditions was successfully carried out and the results were
compared with the experiments. Regions of flow separation, observed in the experi-
107
ments were well captured. Menter’s k-ω SST turbulence model predicted the mean
flow field very well within the potential core. However, it deviated from the experi-
mental results away from the nozzle exit because of the overprediction of the potential
core length.
The CFD simulation of the full-scale ejector nozzle was successfully carried out
at take-off conditions with Mthroat ≈ 0.75. A new grid with boundary layer mesh
was created to accurately predict the near wall turbulence. The flow separation and
recirculation zone were also observed at higher nozzle pressure ratios. This proposes
additional challenges in the design and development of a successful noise suppression
exhaust nozzle system. In order to make use of the advantages of ejector nozzle such
as thrust augmentation and noise suppression, it was necessary to remove the flow
separation and recirculation zones. One idea to address this challenge was to make
use of additional passive mixing devices such as tabs or chevrons at the ejector slot
to introduce streamwise vorticity and thereby enhance mixing. This will be discussed
in detail in the next chapter.
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5. 3-D Ejector Nozzles
with Clamshell Doors and Chevrons
5.1 Introduction
The experimental testing of the baseline ejector nozzle with clamshell doors was
documented in the reference [44]. Its detailed CFD analysis, as discussed in Chapter 4,
showed the presence of a zone of separation and recirculation near the inner surface of
the clamshells. This had detrimental effects on the advantages of the ejector nozzle
with clamshell doors, such as reduced thrust augmentation and noise suppression.
The flow was separated because of the inability of the free shear layers, originating
from the primary nozzle surface, to attach to the inner surface of the clamshells. This
phenomenon was studied in detail by Der [17] and is explained briefly in Section 2.2.1.
One of the proposed measures to overcome flow separation and recirculation zones,
as documented in [44], was to introduce streamwise vortices in the ejector flow by
the application of passive mixing devices such as chevrons or tabs, thereby enhancing
the mixing between the ejector flow and the nozzle flow. The concept of chevrons
is not new and has already been used in civil air-transportation powerplants such
as the Rolls-Royce Trent-1000 and the General Electric GE-NX. The application
of chevrons on the ejector nozzle results in the spreading of the jet and forces the
shear layer to attach to the inner surface of the clamshells which can reduce flow
separation. In addition to the ejector nozzle performance improvement, chevrons
have noise suppression capability in the low frequency part of the spectrum.
For the above mentioned reasons, a preliminary design work involving the design
of chevrons on the ejector nozzle with clamshell doors and its detailed CFD simulation
was carried out. This chapter summarizes the work done related to the design and
computational analysis of the ejector nozzle with clamshell doors and chevrons. It was
109
found that the extent of the flow separation was greatly reduced by the application
of chevrons.
5.2 Objectives
The objective of the current task was to modify the existing design of the baseline
ejector nozzle by placing chevrons at the throat of the primary nozzle and perform
computational analysis of the new design. The performance of these passive mixers
was studied with respect to the reduction of the separation zone encountered near the
inner surface of the clamshells and the amount of ejector mass flow. Two nozzle con-
figurations with a different number of chevrons were designed and the computational
analysis of their flow fields is presented.
5.3 Ejector Flow with Chevrons
Figure 5.1. The phenomenon of the ejector flow with chevrons.
110
The ejector nozzle is preferable for subsonic operations of a supersonic cruise jet
engine because of its thrust augmentation (achieved by increasing the nozzle mass
flow through entrainment) and noise suppression (by reducing the exhaust velocity
of the nozzle jet). For these reasons, powerplants of the SR-71 and the Concorde
aircraft use the ejector nozzle concept. The addition of chevrons on the primary
nozzle throat surface results in a complex three-dimensional flow phenomenon as
shown in Figure 5.1.
The ejector nozzle with chevrons introduces counter-rotating streamwise vortices
into the primary nozzle flow. These kidney-shaped vortices interact with the ejector
flow and the primary nozzle flow. This results in an increased mixing and outward
spreading of the shear layer which finally attaches to the inner surface of the clamshell
doors. The design of the chevron is critical from the aeroacoustic point of view. The
enhanced mixing results in additional small-scale eddies which produce high frequency
noise. Hence the design of the chevron should be such that it increases the mixing
with minimum high frequency noise penalty. This can be achieved by the use of
advanced optimization techniques.
5.4 Nozzle Design and CAD Geometry
The baseline ejector nozzle geometry used in the current design task was the
same as used in Section 2.2.1 which was scaled up (8.13 : 1) to represent the full-
scale flight geometry. The baseline CAD geometry, parametrically defined using the
CATIA CAD package was exported as a STEP file for better compatibility with the
Pro/Engineer CAD package. Chevrons were designed based on the dimensions from
the previous study of Janardan et al. and documented in reference [21]. Various
dimensional variables used in the design of the chevron are shown in Figure 3.17 and
their numerical values are given in Table 5.1.
The chevron on the nozzle surface was created using the Pro/Engineer Wildfire
4.0 CAD package. Solid modeling operations such as extrusion and subtraction were
111
used to cut the nozzle throat surface in the form of chevrons. In the current study,
two designs were implemented which differs from each other in the total number of
chevrons and their dimensions. Design I consisted of 12 chevrons resulting in the
chevron-crest on the ejector nozzle Z=0 symmetry plane. Design II was based on the
dimensions corresponding to 14 chevrons and resulted in the chevron-trough on the
ejector nozzle Z=0 symmetry plane. The chevron-crest is defined as the peak of the
chevron and the chevron-trough is defined as the middle point in between the two
chevron peaks.
Table 5.1 Dimensions of the chevron on the 3-D ejector nozzle withclamshell doors for Design I and Design II.
Variable Design I Design II
Nozzle circumference (C = πD) 17.93 in. 17.93 in.
Total number of chevrons (N) 12 14
Actual number of chevrons (Na) 8 10
Chevron arc length (s=C/N) 1.4941 in. 1.280714
Length of the chevron (l) 1.00 in 0.92 in
Chevron angle at the throat center (θ=360◦/N) 30◦ 25.714◦
Included angle at chevron tip (Φ) 90◦ 90◦
The presence of the clamshell door-support allowed only 8 and 10 chevrons for
Design I and Design II, respectively. Figure 5.2 shows the X-sectional view of the
ejector nozzle at the throat with 8 chevrons (Design I). The clamshell doors were hid-
den in this view for better visualization. Similarly, Figure 5.3 shows the X-sectional
view of the ejector nozzle with 10 chevrons configuration (Design II). The isometric
views of the ejector nozzle with 8 chevrons and 10 chevrons are shown in Figures 5.4
and 5.5, respectively.
112
Figure 5.2. CAD geometry of the ejector nozzle with clamshells andchevrons, Design I - X-section at the throat.
Figure 5.3. CAD geometry of the ejector nozzle with clamshells andchevrons, Design II - X-section at the throat.
113
Figure 5.4. CAD geometry of the ejector nozzle with clamshells andchevrons, Design I - Isometric view.
Figure 5.5. CAD geometry of the ejector nozzle with clamshells andchevrons, Design II - Isometric view.
114
5.5 Computational Mesh
Grids for the computational analysis of two designs described above were created
using the Pointwise GRIDGEN version 15.10 grid generation code. The nozzle ge-
ometry was exported in the IGES format from the Pro/Engineer CAD package with
edges and surfaces as the required entities. Edges are required for the creation of con-
nectors and surfaces are required for creating databases on which GRIDGEN projects
the computational mesh.
Figure 5.6. Computational mesh for ejector nozzle walls and chevrons - Design I.
A 3-D, multiblock, nonoverlapping hybrid grid, similar to the one used in Chap-
ter 4, was created. An unstructured mesh was used on chevron surfaces which were
extruded as prisms for the boundary layer mesh. Structured blocks were used for the
far field and shear layer region. The nozzle geometry was symmetric about the Y=0
and Z=0 plane. Hence a quadrant of the geometry was used for grid generation and
CFD simulation.
115
In order to capture the streamwise vortices introduced by the chevrons, additional
grid points were placed inside the unstructured block in the form of a structured block.
The interface between the structured and unstructured blocks consisted of pyramid
cells. The present CFD simulation involved high subsonic Mach numbers inside the
nozzle (flight or take-off conditions) and hence a refined wall resolution was required
to capture the thin boundary layers near the inviscid walls. A variable wall-normal
spacing was used to keep the y+ values within the range of 30 ∼ 300 and hence wall
functions were used for the near wall turbulence.
Figure 5.7. Computational mesh for ejector nozzle walls and chevrons - Design II.
The computational domain for Design I consisted of a total of 29 blocks resulting
in a total of 3.36 million cells. The total number of blocks included one unstructured
block enclosing the region of the clamshell doors and chevrons. Figure 5.6 shows the
computational mesh for the Design I nozzle. Similarly, the computational mesh for
116
Table 5.2 Boundary conditions for the CFD simulation of the ejectornozzle with clamshell doors and chevrons.
Variables Nozzle flow Freestream flow
Total pressure (kPa) 173.97 107.53
Total temperature (K) 877.5 307.5
Freestream static pressure (kPa) 101.325
Freestream total temperature (K) 303
Freestream Mach number 0.3
Turbulent intensity (%) 10.0 0.1
Turbulent length scale (m) 0.016 NA
Turbulent viscosity ratio NA 1.0
Design II consisted of 31 blocks resulting in a total of 3.56 million cells. This mesh is
shown in Figure 5.7.
5.6 Boundary Conditions
The boundary conditions for the present CFD simulation were the take-off con-
ditions with a NPR of 1.7, as discussed in Section 4.4.5. The ANSYS FLUENT
flow solver recommends the use of pressure-based boundary conditions for high NPR
and Mach numbers for numerical stability and faster convergence. Moreover, in the
ANSYS FLUENT version 6.3.26 flow solver, the ideal gas equation (required for the
definition of density) can be used only with pressure-based boundary conditions.
For the above mentioned reasons, pressure-based boundary conditions were used
for various inlets, far field and outlet boundaries. The boundary conditions were
pressure-inlet at the inflow boundary, inviscid-wall along symmetry planes, pressure
far field along the outer freestream boundary, and pressure-outlet at the exit. The
numerical values of the boundary conditions are shown in Table 5.2.
117
Turbulence quantities were also required as boundary conditions for the simulation
of the turbulent flow. The ANSYS FLUENT flow solver allowed the use of any two of
the turbulent variables viz. the turbulent kinetic energy (k), turbulent intensity (I),
turbulent viscosity ratio (β), turbulent length scale (l), and the secondary variable.
The secondary variable depended upon the turbulence model used, such as νt, ε, l,
and ω for various two-equation turbulence models. In this simulation, the turbulent
intensity and the turbulence length scale were used as the turbulent inlet boundary
condition for the nozzle inlet. The turbulent intensity and the viscosity ratio values
were used for the freestream inlet and the pressure far field.
5.7 Numerical Computation
The ANSYS FLUENT version 6.3.26 flow solver was used for the 3-D, steady CFD
simulation. The solver settings were similar for the CFD simulation of both Design
I and Design II. A NPR of 1.7 results in a throat Mach number on the order of 0.8
and hence the computational simulation of compressible RANS equations mandate
a coupled solver. For this reason, the density-based explicit coupled solver was used
for the numerical stability and better convergence. In general, the explicit coupled
solver requires less computational time compared to the implicit coupled solver. The
system of RANS equations was closed using the Menter’s k-ω SST turbulence model
with wall functions.
The operating conditions were based on the absolute pressure (instead of the
gauge pressure) and the ideal gas equation was used for the definition of the density.
The viscosity of the air was calculated using Sutherland’s three coefficient method
and the temperature dependent thermal conductivity was implemented in the current
simulation. The computational solution was initiated using the freestream primary
flow variables. The first-order solution was obtained after 5000 iterations and then
the discretization schemes were changed to second-order upwind for all the primary
variables to obtain the final second-order converged solution.
118
The converged solution was obtained by using the underrelaxation values of 0.5
for the turbulent kinetic energy, 0.7 for the specific dissipation rate and 0.7 for the
turbulent viscosity. A CFL value of 1.0 was used because of the numerical stability
issues associated with the hybrid grid. The convergence was monitored using residuals
of flow variables, the iteration history of the velocity magnitude at X/DEQ=3.0, and
the mass-balance between the inflow and outflow. When the velocity magnitude
reached a steady state value, the solution was considered to be converged. In this
case, the iteration history of the velocity magnitude oscillated about a mean converged
value because of the presence of a separation bubble on the clamshells.
5.8 Results
The results from the CFD simulation of the ejector nozzle with clamshell doors and
chevrons are discussed in this section. These results are compared with the ejector
nozzle without chevrons. The CFD post-processing of the flow field showing contours
of the TKE and the Mach number corresponding to the case of 14 chevrons (Design
II) is shown in Figure 5.9. Earlier in Section 4.4.7, we found that the baseline ejector
nozzle with clamshell doors resulted in a zone of separation at take-off conditions as
shown in Figure 5.10. Mach number contours of the cross-section of the nozzle jet,
inside the clamshell doors at about X/DEQ=0.5 is shown in Figure 5.11.
5.8.1 Design I
Design I consisted of 8 actual chevrons, with the chevron-crest on the Z=0 sym-
metry plane as shown in Figure 5.2. In the chevron-trough plane, the high speed
nozzle flow entrained into the shear layer and resulted in its attachment on the inner
surface of the clamshell doors. Figure 5.12 shows the contours of the Mach number
and the attachment of the shear layers in the chevron-trough plane.
In the chevron-crest plane, which is aligned with the axis of the kidney vortex
and Z=0 symmetry plane, there is not much entrainment of the high speed flow.
119
Hence the flow separated from the clamshell doors after a certain distance along the
nozzle axis. Figure 5.13 shows the contours of the Mach number in the chevron-
crest plane. It is evident that the separation near the inner surface of the clamshells
decreased in size when compared to the baseline ejector nozzle case without chevrons
(Figure 5.10). Figure 5.14 shows the jet cross-sectional contours inside the clamshell
doors at X/DEQ = 0.5.
5.8.2 Design II
Design II was based on the dimensions for 14 chevrons. The presence of the
clamshell door-supports allowed the placement of only 10 actual chevrons. Design II
was different from Design I in the sense that the chevron-trough was aligned with the
nozzle Z=0 symmetry plane. This resulted in a clocking of the vortices so that high
speed flow was entrained into the shear layer on the plane where the maximum flow
separation was present.
Figure 5.15 shows the contours of the Mach number on the Z=0 symmetry plane
which coincides with the chevron-trough plane. It is apparent that the flow separation,
observed in the case of the baseline nozzle and Design I, is completely removed in the
chevron-trough plane because of the attachment of the shear layers.
On the chevron-crest plane, a region of flow separation is observed as shown in
Figure 5.16. Therefore, the flow separation zone observed in Design I is redistributed
and divided into two smaller zones by increasing the number of chevrons from 12 to 14.
These two zones are evident in Figure 5.17 which shows the nozzle jet cross-sectional
contours of the Mach number at X/DEQ = 0.5.
Therefore, it is observed that the extent of flow separation and the recirculation
zones is decreased considerably with the application of chevrons. Each chevron results
in the formation of a counter-rotating vortex in the streamwise direction which are
of the shape of a kidney. This causes an enhanced mixing between the nozzle flow
and the ejector flow and the shear layer spreads more outwards. This results in
120
an improvement on the nozzle performance. The nozzle flow stays attached to the
clamshell’s inner surface entirely on the chevron-trough plane and until around half
the axial length of the clamshell doors on the chevron-crest plane. The recirculation
zone is still present at the rear end of the clamshells.
5.8.3 Discussion on the centerline statistics
Nozzle flow variables along the nozzle-axis are of utmost importance in under-
standing the characteristics of the jet. Figure 5.18 shows the distribution of the
centerline velocity magnitude with respect to the normalized axial distance along the
streamwise direction. The fundamental characteristics of jet flows such as the con-
stant velocity potential core and inverse-spreading of the jet with respect to axial
distance are well captured. The oscillations in the potential core region shows the
presence of weak Mach waves. It was observed that the length of the potential core
was longer for the chevron nozzle when compared with the baseline nozzle. This may
be because of the reason that the separated jet flow in the baseline case pushes the
streamlines closer creating a smaller jet; and therefore a shorter jet potential core
length. In conclusion, this issue of longer potential core length in the case of chevrons
when compared with the baseline design is not well understood.
The variation of the total temperature with respect to the axial distance is shown
in Figure 5.19. Increasing the number of chevrons from 12 in Design I to 14 in Design
II resulted in enhanced mixing. This is evident from the decrease in the length of the
potential core for Design II when compared with Design I.
5.8.4 Effect on the ejector mass flow
One of the effects of the ejector nozzle is the thrust augmentation. This is because
of the addition mass flow introduced into the primary nozzle flow through the ejector
slots. Therefore, the thrust performance of the ejector nozzle is dependent on the
ejector flow. One of the objectives of this design study was to analyze the effect of
121
Table 5.3 The effect of chevrons on the ejector mass flow.
Variables mej,min mej/min
Inlet mass flow for the baseline nozzle (kg/s) 57.7370.1697
Ejector mass flow for the baseline nozzle (kg/s) 9.802
Inlet mass flow for 12 chevrons nozzle (kg/s) 63.8930.1381
Ejector mass flow for 12 chevrons nozzle (kg/s) 8.829
Inlet mass flow for the 14 chevrons nozzle (kg/s) 63.1580.1559
Ejector mass flow for 14 chevrons nozzle (kg/s) 9.844
chevrons on the ejector flow. It is observed that the addition of chevrons resulted in
an increased nozzle-inlet mass flow by 10.7% for Design I and 9.4% for Design II. The
increased nozzle inlet mass flow is also evident in Figure 5.18 showing the centerline
variation of the velocity magnitude.
Table 5.3 shows a quantitative measure of the secondary flow, entrained into the
primary nozzle flow for the baseline ejector nozzle, the ejector nozzle with 12 chevrons
and the ejector nozzle with 14 chevrons. The ejector performance is represented by
the ratio of the secondary mass flow entrained through the ejector slot (mej) to the
primary nozzle mass flow (min). It was observed that the increase in the number
of chevrons from 12 to 14 resulted in an improved mass entrainment because of the
enhanced mixing. However, the mass entrainment was diminished in the case of
12 chevrons when compared with the baseline design. The reason behind this flow
phenomenon was not well understood.
122
Figure 5.8. Contours of Mach number and turbulent kinetic energycorresponding to the CFD simulation of the baseline nozzle.
Figure 5.9. Contours of Mach number and turbulent kinetic energycorresponding to the CFD simulation of the chevron nozzle (DesignII).
123
Figure 5.10. Mach number contour plot Z=0 symmetry plane for theejector nozzle without chevrons.
Figure 5.11. Mach number contours on Y Z-plane at X/DEQ = 0.5for the ejector nozzle without chevrons.
124
Figure 5.12. Mach number contours on the plane in between twochevrons for the ejector nozzle with chevrons - Design I.
Figure 5.13. Mach number contours on Z=0 symmetry plane for theejector nozzle with chevrons - Design I.
125
Figure 5.14. Mach number contours on Y Z-plane at X/DEQ = 0.5for the ejector nozzle with chevrons - Design I.
Figure 5.15. Mach number contours on Z=0 symmetry plane for theejector nozzle with chevrons - Design II.
126
Figure 5.16. Mach number contours on the plane in between twochevrons for the ejector nozzle with chevrons - Design II.
Figure 5.17. Mach number contours on Y Z-plane at X/DEQ = 0.5for the ejector nozzle with chevrons - Design II.
127
−5 0 5 10 15 20 25 30 35150
200
250
300
350
400
450
500
550
Axial Length X/Deff
Cen
terli
ne V
eloc
ity m
/s
Without chevronsWith 12 chevronsWith 14 chevrons
Figure 5.18. Centerline axial velocity profiles corresponding to theejector nozzle with and without chevrons.
−5 0 5 10 15 20 25 30 35300
400
500
600
700
800
900
Axial Length X/Deff
Tot
al T
empe
ratu
re K
Without chevronsWith 12 chevronsWith 14 chevrons
Figure 5.19. Centerline total temperature profiles corresponding tothe ejector nozzle with and without chevrons.
128
5.9 Conclusion
The preliminary design of the ejector nozzle with clamshells and chevrons was
completed and the computational results obtained by CFD simulation were discussed.
The zone of flow separation, observed on the inner surface of the clamshells in the
case of the baseline ejector nozzle, was greatly reduced by the application of chevrons
on the nozzle throat surface.
Two configurations with a different number of chevrons were designed and their
computational simulations were performed. Design I consisted of 12 chevrons which
resulted in the alignment of the chevron-crest plane with the Z=0 symmetry plane.
Design II consisted of 14 chevrons and ensured that the chevron-trough plane was
aligned with the Z=0 symmetry plane.
Centerline statistics showed that an increase in the number of chevrons from
12 to 14 resulted in enhanced mixing and a reduction in the potential core length.
However, the phenomenon of the increase in the potential core length for chevrons
when compared with the baseline nozzle was not well understood and is an issue for
future study.
5.10 Future Work
It was found that the application of chevrons resulted in increased effective throat
area in Design I and Design II. The increased throat area caused a mismatch in
the mass inflow between the chevron nozzle and the baseline nozzle. Hence the CFD
simulation of the 3-D ejector nozzle with 14 chevrons (Design II) with a nozzle effective
throat area equal to the baseline nozzle was necessary for the better comparison of
centerline statistics and the ejector performance.
129
6. Conclusions and Recommendations
The computational study of noise suppression exhaust nozzle systems has been suc-
cessfully carried out. Three-dimensional RANS computations were performed on
exhaust nozzles such as the three-stream separate-flow axisymmetric plug nozzle, the
three-stream separate-flow chevron nozzle, the 3-D ejector nozzle with clamshells,
and the 3-D ejector nozzle with clamshells and chevrons. CFD simulations were car-
ried out at low speed wind-tunnel experimental conditions and high NPR take-off
conditions.
The accuracy of the computational prediction of jet flows and the associated noise
depends on the type of the turbulence closure method used. Large computational time
and computing resources associated with high-end turbulence prediction methods
such as DNS, LES, and DES restrict their application in the preliminary design cycle.
Hence there is a need to study the ability of two-equation turbulence models in the
prediction of the mean flow field and turbulence characteristics. CFD simulations
of the baseline three-stream separate-flow axisymmetric plug nozzle with chevrons
(3A12B) and without chevrons (3BB) were performed for this task. It was found
that even though the realizable k-ε turbulence model with Thies and Tam’s jet flow
correction gave better prediction of the mean flow, it failed to predict turbulent flow
quantities. The standard k-ε turbulence model suffered from the conventional problem
of the overprediction of the turbulent kinetic energy. Hence it was concluded that the
k-ω SST turbulence model was the preferred turbulence model for the present study.
However, it was observed that the k-ω SST turbulence model overpredicted the jet
potential core.
The CFD simulation of the 2-D ejector nozzle test case, used for the validation task
showed a good agreement with the experiments. The Spalart-Allmaras one-equation
130
turbulence model performed better than Menter’s k-ω SST turbulence model. The
prediction of the mean flow field improved away from the nozzle exit.
The RANS-based computation of the 3-D ejector nozzle with clamshell doors
using the k-ω SST turbulence model showed good agreement with the wind-tunnel
experiments. The experiments were conducted at low subsonic conditions (M ≤ 0.25).
The computational results compared well with the experiments within the potential
core. However, the overprediction of the potential core resulted in an overprediction
of mean flow quantities at X/DEQ=3.0. Flow features such as the flow separation and
the recirculation zone encountered during the flow visualization were well captured
in computations.
The CFD simulation of the 3-D ejector nozzle with clamshell doors at take-off
conditions (high NPR of the order of 1.7) showed similar flow characteristics, i.e.
flow separation and recirculation zones. This confirmed that the flow separation was
attributed to the nozzle design and not to the flow nozzle pressure ratios.
Application of chevrons on ejectors was examined. The CFD simulation of the 3-D
ejector nozzle with clamshell doors and chevrons showed some improved flow features.
The flow separation zone was decreased significantly. A zone of recirculation remained
at the trailing edge of the clamshell doors. On the chevron plane, the flow separation
was completely removed and the shear layers attached to the clamshell doors giving
improved performance.
It was found that the application of chevrons resulted in an increased effective
throat area in Design I and Design II. This caused a mismatch in the mass inflow
between the chevron nozzle and the baseline nozzle. Hence the CFD simulation of
the 3-D ejector nozzle with 14 chevrons (Design II) with a nozzle effective throat
area equal to the baseline nozzle is necessary for the better comparison of centerline
statistics and the ejector performance. A parametric study on the number of chevrons
will be necessary for further reduction of the extent of the flow separation.
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131
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