Design and Analysis of Noise Suppression Exhaust Nozzle Systems

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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

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

Aerospace Corporation.

iv

TABLE OF CONTENTS

Page

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Supersonic Civil Transport . . . . . . . . . . . . . . . . . . . . . . . 21.2 Challenges Associated with Supersonic Transport . . . . . . . . . . 41.3 Noise Suppression Propulsion System . . . . . . . . . . . . . . . . . 51.4 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Noise Suppression and Design Methodology . . . . . . . . . . . . . . . . 82.1 Jet Noise - A Classical Problem . . . . . . . . . . . . . . . . . . . . 82.2 Noise Suppression Exhaust Nozzles . . . . . . . . . . . . . . . . . . 10

2.2.1 Ejector Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.2 Chevrons - Passive Mixers . . . . . . . . . . . . . . . . . . . 15

2.3 Computational Techniques . . . . . . . . . . . . . . . . . . . . . . . 182.3.1 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . 192.3.2 Turbulence Modeling for Jet Flows . . . . . . . . . . . . . . 20

2.4 Design Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3 Chevron Nozzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3 Three-Stream Separate-Flow Axisymmetric Plug Nozzle (3BB) . . . 29

3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.2 Geometry and Mesh Generation . . . . . . . . . . . . . . . . 303.3.3 Boundary Conditions and CFD Methodology . . . . . . . . . 313.3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.4 Three-Stream Separate-Flow Chevron Nozzle (3A12B) . . . . . . . 423.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.4.2 Geometry and Mesh Generation . . . . . . . . . . . . . . . . 423.4.3 Boundary Conditions and CFD Methodology . . . . . . . . . 453.4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

v

Page

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4 Ejector Nozzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.3 2-D Ejector Nozzle Test Case . . . . . . . . . . . . . . . . . . . . . 60

4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.3.2 Geometry and Mesh Generation . . . . . . . . . . . . . . . . 604.3.3 Boundary Conditions and Numerical Computation . . . . . 624.3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.4 3-D Ejector Nozzle with Clamshell Doors . . . . . . . . . . . . . . . 684.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.4.2 Experimental Investigation . . . . . . . . . . . . . . . . . . . 684.4.3 Nozzle Design and CAD Geometry . . . . . . . . . . . . . . 694.4.4 Grid Generation . . . . . . . . . . . . . . . . . . . . . . . . . 714.4.5 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . 744.4.6 Numerical Computation . . . . . . . . . . . . . . . . . . . . 764.4.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5 3-D Ejector Nozzleswith Clamshell Doors and Chevrons . . . . . . . . . . . . . . . . . . . . . 1085.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1085.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1095.3 Ejector Flow with Chevrons . . . . . . . . . . . . . . . . . . . . . . 1095.4 Nozzle Design and CAD Geometry . . . . . . . . . . . . . . . . . . 1105.5 Computational Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . 1145.6 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 1165.7 Numerical Computation . . . . . . . . . . . . . . . . . . . . . . . . 1175.8 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.8.1 Design I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1185.8.2 Design II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195.8.3 Discussion on the centerline statistics . . . . . . . . . . . . . 1205.8.4 Effect on the ejector mass flow . . . . . . . . . . . . . . . . . 120

5.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1285.10 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

6 Conclusions and Recommendations . . . . . . . . . . . . . . . . . . . . . 129

LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

vi

LIST OF TABLES

Table Page

2.1 Thies and Tam’s k-ε turbulence model constants [39]. . . . . . . . . . . 24

3.1 Boundary conditions for the CFD simulation of the three-stream separate-flow axisymmetric plug nozzle (3BB) [20]. . . . . . . . . . . . . . . . . 32

3.2 Boundary conditions for the CFD simulation of the three-stream separate-flow chevron nozzle (3A12B) [24]. . . . . . . . . . . . . . . . . . . . . . 45

4.1 2-D ejector nozzle boundary conditions [46]. . . . . . . . . . . . . . . . 62

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

2.4 LS/∆ = Optimum attached free mixing layer. (Reproduced courtesy of J.Der Jr. [17].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.5 Three-stream separate-flow nozzle with chevrons on the core and fan noz-zle [18]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.6 Mixing of two streams of the chevron nozzle and streamwise vortex for-mation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.7 Methodology for the jet engine exhaust nozzle design and analysis. . . 27

3.1 The CAD geometry of the three-stream separate-flow axisymmetric plugnozzle [20]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2 The computational mesh for the three-stream separate-flow axisymmetricplug nozzle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 3BB axial velocity magnitude contour plot corresponding to PIV experi-ments on the Z=0 plane [20]. . . . . . . . . . . . . . . . . . . . . . . . 37

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

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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

3.19 The computational mesh for the three-stream separate-flow chevron noz-zle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.20 3A12B axial velocity magnitude contour plot corresponding to PIV exper-iments on the Z=0 and inward-facing chevron mid-plane [24]. . . . . . 49

3.21 3A12B axial velocity magnitude contour plot corresponding to WIND-CFD results on the Z=0 and inward-facing chevron mid-plane [24]. . . 49

3.22 3A12B axial velocity magnitude contour plot corresponding to the k-ωSST turbulence model on the Z=0 and inward-facing chevron mid-plane. 49

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Figure Page

3.23 3A12B axial velocity magnitude contour plot corresponding to the stan-dard k-ε turbulence model on the Z=0 and inward-facing chevron mid-plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.24 3A12B axial velocity magnitude contour plot corresponding to the real-izable k-ε turbulence model on the Z=0 and inward-facing chevron mid-plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.25 3A12B axial velocity magnitude contour plot corresponding to Thies andTam’s k-ε turbulence model on the Z=0 and inward-facing chevron mid-plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.26 3A12B axial velocity magnitude contour plot corresponding to PIV exper-iments on the outward-facing chevron mid-plane [24]. . . . . . . . . . . 51

3.27 3A12B axial velocity magnitude contour plot corresponding to WIND-CFD results on the outward-facing chevron mid-plane [24]. . . . . . . . 51

3.28 3A12B axial velocity magnitude contour plot corresponding to the k-ωSST turbulence model on the outward-facing chevron mid-plane. . . . . 51

3.29 3A12B axial velocity magnitude contour plot corresponding to the stan-dard k-ε turbulence model on the outward-facing chevron mid-plane. . 52

3.30 3A12B axial velocity magnitude contour plot corresponding to the realiz-able k-ε turbulence model on the outward-facing chevron mid-plane. . . 52

3.31 3A12B axial velocity magnitude contour plot corresponding to Thies andTam’s k-ε turbulence model on the outward-facing chevron mid plane. . 52

3.32 3A12B turbulent kinetic energy contour plot corresponding to PIV exper-iments on the Z=0 and inward-facing chevron mid-plane [24]. . . . . . 53

3.33 3A12B turbulent kinetic energy contour plot corresponding to WIND-CFDresults on the Z=0 and inward-facing chevron mid-plane [24]. . . . . . 53

3.34 3A12B turbulent kinetic energy contour plot corresponding to the k-ω SSTturbulence model on the Z=0 and inward-facing chevron mid-plane. . . 53

3.35 3A12B turbulent kinetic energy contour plot corresponding to the standardk-ε turbulence model on the Z=0 and inward-facing chevron mid-plane. 54

3.36 3A12B turbulent kinetic energy contour plot corresponding to the real-izable k-ε turbulence model on the Z=0 and inward-facing chevron mid-plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.37 3A12B turbulent kinetic energy contour plot corresponding to Thies andTam’s k-ε turbulence model on the Z=0 and inward-facing chevron mid-plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

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Figure Page

3.38 3A12B turbulent kinetic energy contour plot corresponding to PIV exper-iments on the outward-facing chevron mid-plane [24]. . . . . . . . . . . 55

3.39 3A12B turbulent kinetic energy contour plot corresponding to WIND-CFDresults on the outward-facing chevron mid-plane [24]. . . . . . . . . . . 55

3.40 3A12B turbulent kinetic energy contour plot corresponding to the k-ω SSTturbulence model on the outward-facing chevron mid-plane. . . . . . . 55

3.41 3A12B turbulent kinetic energy contour plot corresponding to the standardk-ε turbulence model on the outward-facing chevron mid-plane. . . . . 56

3.42 3A12B turbulent kinetic energy contour plot corresponding to the realiz-able k-ε turbulence model on the outward-facing chevron mid-plane. . . 56

3.43 3A12B turbulent kinetic energy contour plot corresponding to Thies andTam’s k-ε turbulence model on the outward-facing chevron mid-plane. . 56

3.44 Centerline axial velocity profiles for different turbulence models and com-parison with the experimental result. . . . . . . . . . . . . . . . . . . . 57

3.45 Centerline total temperature profiles for different turbulence models andcomparison with the experimental result. . . . . . . . . . . . . . . . . . 57

4.1 Experimental setup for the 2-D ejector nozzle. (Reproduced courtesyof [46].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.2 Computational mesh for the 2-D ejector nozzle. . . . . . . . . . . . . . 62

4.3 Mach number contour plot of the 2-D ejector nozzle corresponding to thek-ω SST turbulence model. . . . . . . . . . . . . . . . . . . . . . . . . 63

4.4 Mach number contour plot of the 2-D ejector nozzle corresponding to theSpalart-Allmaras turbulence model. . . . . . . . . . . . . . . . . . . . . 63

4.5 2-D ejector nozzle axial velocity profile at X=3.0 in. . . . . . . . . . . 65




4.9 2-D ejector nozzle total temperature profile at X=3.0 in. . . . . . . . . 67

4.10 2-D ejector nozzle total temperature profile at X=10.5 in. . . . . . . . 67

4.11 CAD model of the 3-D ejector nozzle without clamshell doors [44]. . . . 69

4.12 CAD model of the 3-D ejector nozzle with clamshell doors [44]. . . . . 69

xi

Figure Page

4.13 Computational mesh for nozzle walls (a) 3-D ejector nozzle without clamshelldoors (Grid I), and (b) 3-D ejector nozzle with clamshell doors (Grid II). 70

4.14 Computational mesh (Grid II) for the entire flow domain of the 3-D ejec-tor nozzle with clamshell doors for the CFD simulation at experimentalconditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.15 Computational mesh (Grid III) for the entire flow domain of the 3-D ejec-tor nozzle with clamshell doors for the CFD simulation at take-off condi-tions (higher NPR). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.16 Extent of the computational domain for the 3-D ejector nozzle with clamshelldoors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.17 Schematic representation of experimental boundary conditions (Simula-tion I) and their numerical values. . . . . . . . . . . . . . . . . . . . . . 74

4.18 Schematic representation of take-off boundary conditions (Simulation II)and their numerical values. . . . . . . . . . . . . . . . . . . . . . . . . . 75

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






xii

Figure Page


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







4.39 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









xiii

Figure Page













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

5.4 CAD geometry of the ejector nozzle with clamshells and chevrons, DesignI - Isometric view. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

5.5 CAD geometry of the ejector nozzle with clamshells and chevrons, DesignII - Isometric view. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

5.6 Computational mesh for ejector nozzle walls and chevrons - Design I. . 114

5.7 Computational mesh for ejector nozzle walls and chevrons - Design II. . 115

5.8 Contours of Mach number and turbulent kinetic energy corresponding tothe CFD simulation of the baseline nozzle. . . . . . . . . . . . . . . . . 122

5.9 Contours of Mach number and turbulent kinetic energy corresponding tothe CFD simulation of the chevron nozzle (Design II). . . . . . . . . . 122

xiv

Figure Page

5.10 Mach number contour plot Z=0 symmetry plane for the ejector nozzlewithout chevrons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

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

5.18 Centerline axial velocity profiles corresponding to the ejector nozzle withand without chevrons. . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

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

Navier-Stokes (RANS) equations-based computational fluid dynamics (CFD) method-

ology was followed for the analysis of the design. First, the design of a three-stream

separate-flow axisymmetric plug nozzle was studied and its CFD simulation was per-

formed. The mean flow and turbulent kinetic energy flow fields were compared to the

experimental data.

Second, a detailed computational study of the design and analysis of the chevron

nozzle was carried out. A CAD geometry of the nozzle was created and its flow field

was studied using a RANS solver. As a validation task, CFD simulations of the 3-D

ejector nozzle with and without clamshell doors were performed and the results were

compared to the experimental data. A zone of flow separation was found at the inner

surface of clamshell doors. Hence, the design of the ejector nozzle with clamshell

doors was improved by the introduction of chevrons. Chevrons introduce streamwise

7

vortices, which enhance the mixing between the nozzle flow and the atmospheric air.

A detailed CAD design and CFD analysis of this new nozzle design was performed

and documented in this thesis. It was observed that the extent of flow separation was

greatly reduced by the application of chevrons.

The organization of this thesis is as follows. A detailed discussion on the literature

survey of noise suppression exhaust nozzles, jet noise sources and the turbulence

models available in the flow solver are presented in Chapter 2. Chapter 3 covers the

CFD simulation of a baseline three-stream separate-flow axisymmetric plug nozzle

and a chevron nozzle. A comparison between the computations and experiments was

carried out to study the performance of various turbulence models. CFD simulations

of the 3-D ejector nozzle with and without clamshell doors are presented in Chapter 4.

The design and computational analysis of the 3-D ejector nozzle with clamshell doors

and chevron mixers are presented in Chapter 5. Chapter 6 summarizes the key

findings of this work and recommendations for future study.

8

2. Noise Suppression and Design Methodology

In airbreathing propulsion, the main purpose of the exhaust nozzle is to increase the

kinetic energy of the exhaust gases by increasing the exit jet velocity while main-

taining the back pressure for the operation of compressors and turbines. Since the

pressure ratio across the nozzle is the driving force for the operation of any nozzle,

an ideal nozzle should closely match the exit and atmospheric pressures, and thereby

maximize the thrust for a given jet engine. The net thrust is more sensitive to noz-

zle performance than any other engine component. For this reason, it is extremely

important to obtain the highest possible nozzle performance with consideration of

nozzle cost, weight, complexity, reliability and maintainability.

The propulsive efficiency of any jet engine is directly related to the performance

of the exhaust system. Complexities involved in the nozzle design increase for high

speed transport and military aircraft. For supersonic transport, additional consider-

ations such as jet noise, shock-associated noise and better mixing of core and bypass

flow govern the exhaust nozzle design. Afterburner operation, thrust reversal, thrust

vector control and minimization of infrared signature are some of the exhaust noz-

zle design challenges associated with military applications. Design motivations other

than jet noise and better mixing of exhaust streams are beyond the scope of the

present study and will not be discussed.

2.1 Jet Noise - A Classical Problem

One of the critical challenges associated with the performance of the supersonic

cruise propulsion system during take-off conditions is the aerodynamic noise associ-

ated with its jet exhaust. This is referred to as Jet Noise. The three primary sources

of jet noise are as follows [10]:

9

1. The mixing of two or three streams at different velocities (development of shear

layers)

2. Interaction of turbulence with shocks in imperfectly expanded nozzles, and

3. Radiation from the turbulent jet convected at supersonic velocity relative to the

freestream.

Figure 2.1. Jet noise as a result of the shear layer mixing phenomenon.

Figure 2.1 shows the distribution of the noise sources associated with the mixing

of primary and secondary jet exhaust streams. In the case of supersonic exhaust

streams, the jet noise is comprised of jet-mixing noise (broadband noise) and shock-

associated noise. Early theoretical work of Lighthill [11], shows that fluctuations

in the shear stress, as a result of the mixing process behind the nozzle, generate

broadband noise. This theory postulates that the acoustic power varies according to

the eighth power of the exhaust velocity (V ). In practice, most experiments show

a significant departure from the V 8 relationship both at high and low speeds. In

high speed flows, the deviation can be explained in terms of the convection speed

of the turbulent eddies which are comparable to the speed at which acoustic waves

propagate to the far field [12]. As the jet velocity increases and becomes greater than

the speed of sound, source power is dominated by kinematic effects and tends towards

V 3.

10

Shock-associated noise, comprised of both screech and broadband components, is

the result of shocks at high exit jet velocities. The tones are generated through a

feedback mechanism between the shock and the nozzle lip, whereas the broadband

component is a result of turbulent eddies interacting with the shock structure. As far

as community noise is concerned, it is the broadband shock noise that is of concern

unlike the discrete component. The intensity of the broadband shock-associated noise

is reasonably predictable [13]. The intensity of shock-associated noise varies as a

function of pressure ratio and is independent of the jet temperature (and hence the

jet velocity). It is also independent of the observation angle [14].

A typical far field supersonic jet noise spectrum consists of jet mixing noise, shock-

associated screech tones and broadband noise. Traditionally, the idea behind the

reduction of jet noise has been associated with an increase in the mixing rate of

the jet. This can be implemented by the application of various noise suppressors.

Smith et al. [15] summarized various noise suppressors used in the powerplant of the

Concorde for noise reduction.

2.2 Noise Suppression Exhaust Nozzles

The performance of modern aircraft depends heavily on improved and appropri-

ately installed propulsion systems. This dependency is strongly coupled in the field

of supersonic transport. Of all the design challenges, the most critical is to have an

optimized propulsion system for supersonic transport, giving the required design and

off-design performance, while following various airport regulations of the international

civil aviation organization (ICAO) for community noise, emissions and sonic boom.

Before discussing the flow physics involved in various mixing enhancement devices, it

is necessary to have a general discussion on jet engine exhaust nozzles.

The exhaust nozzle system, also referred to as a part of jet engine installation, is

an integral part of the gas turbine jet engine, critical to the overall performance of

the propulsion system during all the phases of flight. It may consists of components

11

such as the nozzle, the jet pipe, active or passive mixers, the thrust reverser, ejectors

and thrust vectoring mechanisms depending upon the specific requirements of the

propulsion system and overall aircraft performance requirements.

The exhaust nozzle serves two primary functions. First, it controls the back pres-

sure for the overall operation of the jet engine and second, it converts the thermal

energy from the combustion of fuel and potential energy in the form of pressure

into kinetic energy in the form of exhaust jet velocity, thereby accelerating the ex-

haust gases to produce thrust. The performance of the exhaust nozzle is significantly

different when installed with the aircraft as part of the entire propulsion system.

Additional design challenges are introduced by the requirements for features such as

reverse thrust, thrust vectoring and variable area throat to facilitate the application

of afterburners in military aircraft.

A supersonic cruise propulsion system requires a noise suppressing, economically

viable, light weight and simple-to-maintain exhaust nozzle system. One of the critical

challenges associated with the design of a supersonic exhaust system during take-off

and landing is its noise suppression. The nozzle should comply with the FAR noise reg-

ulations and produce minimum community noise. During take-off, the aerodynamic

performance of the nozzle is less critical compared to the acoustic characteristics [7].

In the past forty years, research has been done in the field of supersonic noz-

zle design. The primary motivation for the design of low noise jet engine nozzle is

the stringent noise regulations for the community noise. In the past, Rolls-Royce

conducted studies to understand the powerplant noise sources associated with the

supersonic transport and reduce the noise levels associated with the Olympus-593

powerplant. The nozzle design (ejector nozzle with clamshell doors) corresponding

to the Olympus-593 powerplant of the Concorde serves as the primary motivation for

the present work. At this point, it is necessary to discuss the operation of the ejector

nozzle before going into detailed analysis. Since the present work also involves the

design of chevrons, the flow physics of chevrons is discussed.

12

2.2.1 Ejector Nozzle

Variable nozzle exit area is a requirement for the operation of the nozzle at off-

design nozzle pressure ratios when the aircraft speed increases beyond the transonic

regime. During supersonic cruise, as the Mach number increases, the nozzle pressure

ratio and the exhaust nozzle area ratio varies such that(Ptpe

)=

(1 +

γ − 1

2M2

e

) γ(γ−1)

and (2.1)

(AeA∗

)=

1

Me

(1 + γ−1

2M2

eγ+1

2

) γ+12(γ−1)

. (2.2)

Beyond Mach 1.2 ∼ 1.5, nozzle pressure ratios increase rapidly beyond 3.0, as

shown in Figure 2.2, requiring further expansion of the exhaust flow to keep the nozzle

perfectly expanded (pe=patm); increase its velocity and improve nozzle performance.

When exhaust gases are not adequately expanded to near ambient pressures, they

suffer from overexpansion or underexpansion losses. These losses can be avoided

by selecting an area ratio corresponding to the nozzle pressure ratio. The required

area ratio increases with the nozzle pressure ratio as a function of flight altitude and

Mach number. In order to provide optimum thrust, the exhaust nozzle area ratio

should be varied as a function of the nozzle pressure ratio. However, weight, cost

and performance goals must be balanced to provide the best nozzle to meet aircraft

requirements.

Modern supersonic cruise aircraft use different techniques to achieve the variable

exit area capability to operate at off-design conditions. Some of the techniques involve

geometrically scheduled (F-14 and F-18 fighter aircrafts), passively controlled (F-

15 and F-16 fighter aircrafts) and fully variable area ratios (F-22 fifth generation

fighter aircraft) [16]. These techniques involve addition of divergent flaps and an

actuation mechanism to schedule the area variation of the throat (A∗) and the exit

(Ae) either independently or with respect to each other. These techniques suffer from

disadvantages such as increased weight, complexity, cost, and difficulty to maintain.

13

10−1

100

101

10−1

100

101

102

103

Nozzle Exit Mach Number, Me

Noz

zle

Pre

ssur

e R

atio

, Pt e/p

e

10−1

100

10110

−1

100

101

102

103

Noz

zle

Are

a R

atio

, Ae/A

t

Figure 2.2. Requirements for the pressure ratio and the area ratio asMach number increases [16].

The use of ejectors is another concept to address the above-mentioned challenge.

Aerodynamic control of the nozzle exit area ratio can be achieved using ejector nozzles.

Ejectors are used to vary the Ae by allowing the ambient (external) air to fill the

overexpanded portion of the divergent nozzle, reducing its effective expansion ratio.

In addition to thrust augmentation, as a consequence of the increased mass flow

rate and noise suppression because of the reduction in the effective jet velocity, the

clamshell-based ejector nozzle serves other key nozzle operational functions such as

the independent variation of the exit and throat area and reverse thrust operation.

During take-off at subsonic speed, the clamshell angles are scheduled as per the exit

area requirement for optimum performance. During supersonic cruise, the clamshells

are completely closed, thereby representing a conventional convergent-divergent (C-

D) nozzle and giving high efficiency. After landing, clamshells can be deployed for

the application of reverse thrust. These three operations are shown in Figure 2.3.

14

As studied by Der [17] in detail and shown in Figure 2.4, the ejector performance

can be deduced from the behavior of the associated shear layer and its relation to

the ejector shroud walls. For instance, if the mixing duct length (LS) is too small,

the shear layer will not attach to the shroud wall, leaving the secondary flow open

to a stronger influence from external conditions and susceptible to separation and

recirculation. On the other hand, if LS is long and extends beyond the attachment

point of the shear layer with the shroud walls, frictional losses will result.

Nozzle Flow

Ejector Flow Reverse Flow

(a) (b) (c)

Nozzle Flow

Figure 2.3. Operational modes of the ejector nozzle with clamshelldoors (1) Subsonic take-off, (2) Supersonic cruise and (3) Subsonicapproach.

Figure 2.4. LS/∆ = Optimum attached free mixing layer. (Repro-duced courtesy of J. Der Jr. [17].)

15

2.2.2 Chevrons - Passive Mixers

The term Chevron literally means a V-shaped pattern. In the context of jet en-

gines, a chevron nozzle features triangular serrated trailing edge as shown in Figure

2.5. When compared with a baseline axisymmetric nozzle, this additional feature

promotes streamwise vortices, which, along with the naturally occurring toroidal vor-

tices, accelerate the mixing between the jet exhaust and the surrounding atmospheric

air. Enhanced mixing results in a reduction of the exhaust velocity and therefore the

jet noise, in accordance with the Lighthill’s eighth power law (U8) [11].

Figure 2.5. Three-stream separate-flow nozzle with chevrons on thecore and fan nozzle [18].

Other passive mixers include corrugated mixers and tabs. Corrugated mixers suf-

fer from additional weight, drag and increased specific fuel consumption. Tabs result

in a reduction of the low frequency noise but suffer from considerable high frequency

penalties. When compared with other passive mixers, chevrons offer simplicity in de-

sign, manufacturing and maintenance, with much smaller weight and high frequency

penalties [19]. Because of these advantages, chevrons are finding applications in recent

16

commercial jet engines such as the Rolls-Royce Trent-1000 and the General Electric

GE-NX.

Kenzakowski et al. (2000) [20] studied the effect of passive noise reduction devices

such as chevrons and tabs in plume mixing enhancement. They compared the mean

and turbulent flow fields, obtained using the inhouse Combustion Research and Flow

Technology (CRAFT) flow solver, with experiments conducted at NASA Glenn Re-

search Center (GRC). The main concentration in these simulations was to study the

performance of available turbulence models in predicting the chevron flow, which will

be discussed in more detail in Section 2.3.2. Janardan et al. (2000) [21] documented

the noise reducing performance of various passive mixing enhancing devices with a

three-stream separate-flow axisymmetric plug nozzle. Most of the acoustic measure-

ments presented in the above references were based on microphones alone and hence

a more detailed experimental study of the flow physics involved with chevron nozzles

was required to understand the distribution and nature of the noise sources.

The Particle Image Velocimetry (PIV) emerged as a promising candidate for this

application and is popular in characterizing jet plumes because of its capability of

capturing small turbulence scales. Bridges and Wernet (2002) [18] carried out a com-

prehensive experimental study of the turbulent flow characteristics using various mix-

ing enhancement devices on a three-stream separate-flow axisymmetric plug nozzle

using PIV. The passive mixing device alters the turbulence components significantly

and reduces the turbulent kinetic energy (TKE) magnitude in the jet mixing region

(six to nine fan diameters from the nozzle exit) while increasing it in the fan/core

shear layer near the nozzle exit (around first two fan diameters from the nozzle exit).

Bridges and Brown (2004) [22] conducted a parametric experimental study of

chevron nozzles. They performed flow field measurements using PIV and acoustic

field measurements on single-flow hot and cold jets with chevrons. The effect of

chevron count, penetration length and symmetry on the exhaust jet flow field was

studied in detail. They concluded that the chevron penetration decreases the noise

at low frequency and increases the noise at high frequency. Also, low frequency noise

17

reduction can be achieved by increasing the chevron count. Rask et al. (2007) [23]

recently conducted a detailed investigation into the primary chevron mechanisms

using PIV.

Koch and Bridges (2004) [24] studied a three-stream separate-flow plug nozzle with

chevrons arranged in an alternating fashion on the core nozzle. Chevrons arranged in

alternating fashion consisted of a chevron facing towards the nozzle flow and the other,

facing away from the nozzle flow arranged alternatively around the circumference of

the core nozzle as shown in Figure 2.6. Koch compared the experimental results

obtained with 12 chevrons from the PIV measurements with the WIND and CRAFT

CFD solver results. Kurbatskii (2009) [25] came up with a comprehensive set of

results on using various turbulence models and corrections given for the prediction

of the mean flow field of cold and hot subsonic jets from chevron nozzles using the

ANSYS FLUENT version 12.0 flow solver.

Research shows that the presence of chevrons significantly increases the entrain-

ment of the primary flow into the secondary stream and vice versa. This mixing

results in a reduction of the primary stream velocity and lower levels of turbulent

kinetic energy far downstream in the jet plume. However, increased mixing also

causes increased levels of turbulence immediately downstream of the nozzle resulting

in additional high frequency noise. Therefore, there should be a trade-off between

the mixing of two streams and its acoustics benefits. This trade-off can be controlled

by parameters such as the chevron count, the chevron penetration, and the shear

velocity.

Figure 2.6 shows the mixing between two streams and the formation of streamwise

vortices. Low penetration chevrons cause higher mixing between adjacent streams

compared to the baseline axisymmetric nozzle and results in the jet noise reduction,

particularly at low frequencies. With high penetration chevrons, this mixing is further

enhanced and higher noise reduction of low frequency noise is achieved. This more

aggressive mixing, however causes additional turbulence immediately downstream of

the chevron nozzle, which can result in a high frequency penalty. A similar trend can

18

Secondary Flow (Cold flow) Streamwise vortices formation

Primary Flow (Hot flow)

Figure 2.6. Mixing of two streams of the chevron nozzle and stream-wise vortex formation.

be observed with shear velocity. High shear velocity (high velocity difference between

two streams) results in higher mixing causing higher noise reduction of low frequency

noise, but with a penalty. Further study by Rask et al. (2007) [26] shows that the

reduction on overall noise levels with the application of chevrons on fan and core

nozzle are additive.

2.3 Computational Techniques

There is always a great demand for well-validated computational tools that would

allow aerospace engineers to parametrically design and evaluate new low noise nozzle

concepts. Ideally, these tools should provide accurate aerodynamic and aeroacoustic

predictions for a wide variety of nozzle geometries operating through a range of flow

conditions. Coaxial jets consist of two or more flow streams and therefore may have

more than one potential core length. In general, these lengths can be different. In

the case of a chevron nozzle, if chevrons are fitted only on the primary jet, as shown

in Figure 2.6, the mixing between the primary stream and the secondary stream is

much faster than the mixing between the secondary stream and the atmospheric air.

Therefore, the primary core length is relatively short and the jet centerline velocity

starts to decrease well before the shear layer between the fan stream and the external

flow start to merge.

19

This characteristic of coaxial jets poses additional requirements for turbulence

modeling. Extensive research has been done on the performance of turbulence mod-

els for different classes of jet flows and it has been observed that none of the turbulence

models can accurately predict all characteristics of the jet flows [27]. Several modi-

fications to these turbulence models have been proposed for jet flows. The modified

turbulence models give improved prediction of the mean flow. However, efforts to

accurately predict the turbulent kinetic energy fields have had a limited success [28].

Numerical methods and turbulence models used in the present work are discussed in

the following sections.

2.3.1 Numerical Methods

In the present study, the ANSYS FLUENT [29] version 6.3.26 computational

solver was used to solve Reynolds-averaged Navier-Stokes (RANS) equations and the

system of governing equations was closed using turbulence models. The FLUENT

code is a finite volume numerical solver that can be used with both structured and

unstructured meshes. Both the pressure-based segregated and the density-based cou-

pled solvers are available in the FLUENT code.

In general, flow features of high speed jet flows are predicted using density-based

numerical approaches. In density-based coupled formulations, the continuity, mo-

mentum and energy governing equations are solved simultaneously. Density-based

algorithms are efficient for high subsonic, transonic or supersonic flows. However,

they require modifications, such as the preconditioning in low Mach number flow

regions, to overcome the problem of the system matrix becoming singular in the in-

compressible limit. In the density-based algorithm, convergence is mainly governed

by the Courant number. It should be noted that numerical stability considerations

for large grids mandate a low Courant number, such as 1.0.

As an alternative, the coupled pressure-based numerical solver [30] can be used

for problems where strong coupling among equations exist. Unlike a segregated al-

20

gorithm, in which momentum equations and pressure correction equations are solved

one after another in a decoupled manner, a pressure-based coupled algorithm solves

a coupled system of equations comprised of momentum equations and the pressure

equation. Since momentum and pressure equations are solved in a strongly coupled

manner, the rate of solution convergence significantly improves when compared to

the segregated solver.

The pressure-based coupled approach can also be used for supersonic and hyper-

sonic problems that cannot be tackled by a segregated approach. In all solvers, the

convergence is determined by the residual drop in mean flow variables. The iteration

history of a flow variable at some location in the computational domain is also used

to check the convergence. When the value of the flow variable reaches a relatively

steady state, the solution is considered to be converged.

The convergence of the pressure-based algorithm is mainly governed by the un-

derrelaxation factors and hence, a high value for the Courant number is preferred.

In general, the pressure-based coupled solver is faster than then the density-based

coupled solver. Because of the above mentioned advantages, the pressure-based seg-

regated numerical solver is used for all low subsonic CFD computations and the

density-based explicit coupled numerical solver is used for transonic or supersonic

CFD simulations.

2.3.2 Turbulence Modeling for Jet Flows

Accurate modeling of turbulence in jet flows is essential for the accurate predic-

tion of mean flow profiles, turbulence quantities and the generated noise. This can be

achieved by two methods. One approach involves solving both the mean and acoustic

field directly in the same transient simulation. Turbulence quantities in this method

can be predicted using different methods such as Unsteady Reynolds-averaged Navier-

Stokes (URANS), detached eddy simulation (DES), large eddy simulation (LES) or

direct numerical simulation (DNS) techniques which are mentioned in order of in-

21

creasing computational cost and accuracy. Another method is to calculate the mean

flow profiles and turbulence fields using RANS and use them as input into a sepa-

rate computational aeroacoustics (CAA) code or semi-empirical noise model for the

prediction of acoustic fields such as the JeNo and MGBK code [31], the Goldstein-

Lieb model [32], and the broadband shock-associated noise (BBSAN) code [33]. Both

approaches have advantages and disadvantages. RANS-based semi-empirical models

require less computational time for the estimation of jet noise. However, they are less

accurate when compared with the time resolved methods or the direct CAA approach.

For jet noise predictions, LES is preferable because it estimates the noise more

accurately by giving a good prediction of small and large scale turbulent eddies when

compared with the RANS-based methods [34]. For LES simulations, the initial wall

boundary layers at the nozzle exit need to be thin as well as turbulent (implies a

considerably high jet Reynolds numbers). Large computational resources and fine

mesh requirement limit the application of LES to research level. RANS has matured

greatly over the last decade and is widely used in the aircraft design process. There-

fore, in the present study, only RANS-based jet flow field prediction using turbulence

models was considered.

Nallasamy (1999) [35] studied the performance of various turbulence models for the

computation of turbulent jet flows and noise in round jets. He concluded that length

and time scales should be predicted accurately for the estimation of sound pressure

levels. He found that the Sarkar’s compressibility correction for supersonic jets and

Pope’s vortex stretching correction for axisymmetric jets give correct spreading rates

for round jets.

Birch et al. (2003) [27] listed the turbulence modeling requirements for a chevron

nozzle flow and proposed a two-equation zonal turbulence model for better mean

and turbulent flow predictions. A zonal turbulence model essentially means that one

model is used for mixing layers upstream of the end of the jet potential core and

a second model is used for the axisymmetric region downstream of the end of the

potential core. He concluded that though the vortex stretching term proposed by

22

Pope (1978) improves the prediction of axisymmetric jets, it is not suitable for jets

emerging from a chevron nozzle or other mixing nozzles. In these cases, the vortex

stretching term becomes large and introduces errors [27].

Georgiadis et al. (2006) [28] did a survey of various two-equation turbulence models

and corrections proposed in predicting the flow fields of heated and unheated jets.

He found that for the round jet flow calculations, all the modified turbulence models

considered in the study such as the Tam-Ganesan k-ε formulation, the standard k-

ε turbulence model with the temperature correction, and the k-ε turbulence model

with variable diffusion offer improved mean flow predictions relative to the unmodified

standard turbulence models viz. the Chien k-ε turbulence model and Menter’s k-ω

SST turbulence model. None of the standard and modified turbulence models is

capable of giving a good estimate of turbulent kinetic energy fields when compared

with the experimental data.

In the following chapters, the CFD simulation results involve the application of

various turbulence models. Hence a brief introduction of various turbulence models is

presented here. Reynolds-averaging of instantaneous Navier-Stokes equations results

in additional unknowns, known as Reynolds stresses. These unknowns are related

to mean velocity gradients using the Boussinesq hypothesis. The advantage of this

approach is a relatively low computational cost associated with the computation

of the turbulent viscosity. Additional transport equations are required to calculate

the turbulent viscosity. In the case of two-equation turbulence models, an accurate

TKE k-equation and an approximate TKE dissipation rate ε-equation are used to

independently determine turbulent length and velocity scales. These scales are used

to calculate the turbulent viscosity. This is the primary motivation for the two-

equation turbulent models discussed below.

23

Launder and Spalding’s k-ε Turbulence Model

The standard k-ε turbulence model was proposed by Launder and Spalding (1972)

[36]. The model has become the workhorse of practical engineering flow calculations.

RANS equations are closed using the k and ε equations. In the past, it was observed

that for jet flows this turbulence model underpredicts the length of the potential core

and turbulence levels.

Shih’s Realizable k-ε Turbulence Model

As the advantages and disadvantages of the standard k-ε turbulence model became

known, several improvements were proposed to further refine the model. One problem

associated with the standard k-ε model is the overprediction of the TKE in high

strain-rate regions. The realizable model differs from the standard k-ε model in two

ways:

1. A new formulation is used for the turbulent eddy viscosity involving variable

Cµ originally proposed by Reynolds [37], and

2. A new transport equation is used for the dissipation rate ε, which has been

derived from the exact equation for the transport of the mean square fluctuating

vorticity.

The term realizable means that the turbulence model satisfies certain mathemati-

cal constraints on Reynolds stresses, consistent with the physics of the turbulent flow.

An immediate benefit of the realizable k-ε turbulence model is that it accurately pre-

dicts the spreading rate of both planar and round jets. The version of the turbulence

model implemented in the FLUENT flow solver corresponds to Shih (1995) [38].

24

Table 2.1 Thies and Tam’s k-ε turbulence model constants [39].

Model Cε1 Cε2 Cµ σκ σε PrT

Thies and Tam 1.4 2.02 0.09 0.324 0.377 0.422

Standard k-ε 1.44 1.92 0.09 1.0 1.3 0.85

Thies and Tam’s k-ε Turbulence Model

This model was proposed by Thies and Tam (1996) [39]. In this model, some of

the coefficients of the standard k-ε turbulence model were changed specifically for

jet flows and correction terms were added to resolve the planar/axisymmetric jet

problem and for compressibility effects. They validated the performance of these

modified constants with a variety of experimental tests involving round, elliptic and

rectangular jets. It was found that the model gives accurate mean flow predictions

for the Mach number range of 0.4 ∼ 2.0. The modified constants are presented in

Table 2.1.

Wilcox’s Standard k-ω Turbulence Model

Wilcox (1988) [40] postulated a new two-equation turbulence model based on his

study of the optimum choice of dependent variables and replaced the scale determining

ε-equation with the specific turbulent kinetic energy dissipation rate ω-equation. This

model shows improvements in the case of boundary layer flows with adverse pressure

gradients. However, it was found that this model is very sensitive to the inflow

turbulence levels and requires an accurate inflow turbulence boundary condition for

an accurate flow prediction. Wilcox has since revised the k-ω model (1998, 2006) [41];

however, the updated models are not available in the FLUENT flow solver.

25

Menter’s k-ω Shear Stress Transport Turbulence Model

The k-ω shear stress transport (SST) turbulence model was developed by Menter

(1994) [42] to effectively blend the robustness and accurate formulation of the k-ω

model in the near wall region and the free stream independence of the k-ε model

in the far field. In order to achieve this, the k-ε model was converted into a k-ω

formulation. The k-ω SST model is similar to the standard k-ω model, but differs in

the followings aspects:

1. The standard k-ω model and the transformed k-ε model are combined by using

a blending function. The SST model includes a cross-diffusion derivative term

in the ω-equation. This extra term is the difference in the two formulations. It

is turned off near a wall and turned on away from walls.

2. The definition of turbulent viscosity is modified to account for the transport of

turbulent shear stress, and

3. The modeling constants are different.

The above mentioned features make the k-ω SST model more accurate and robust

for a wide class of flows.

Reynold Stress Model

The Reynolds Stress Model (RSM) [43] is a higher level, more elaborate turbulence

model, known as a Second-Order Closure model. RSM deviates from the isotropic

eddy viscosity hypothesis and solves equations for Reynolds stresses, together with an

equation for the dissipation rate. This essentially means that five additional transport

equations for 2-D flows and seven for 3-D flows are required. The RSM is generally

considered to be more accurate compared to one and two-equation turbulence models,

as it accounts for streamline curvature, swirl, rotation and rapid changes in strain-

rate in a more rigorous manner. Hence use of the RSM is suggested when the flow

26

features of interest are the result of anisotropy in the Reynolds stresses such as with

highly swirling and rotating flows.

2.4 Design Methodology

As mentioned in Section 1.4, the present work involved the validation and design

improvement of a new noise suppression nozzle, designed and experimentally tested

by Jones [44]. Hence, there was a requirement to follow a well defined design and

analysis methodology. Figure 2.7 explains the methodology followed in the current

work. The various steps involved were as follows:

1. Design: This step involved brainstorming and performing a literature survey of

previous designs considered during various nozzle design programs, as discussed

earlier. For chevrons, the design work done at the NASA GRC was considered

as the primary inspiration for the designs used in this work. The ejector nozzle

was based on a Rolls-Royce design and is discussed in detail by Jones [44].

2. CAD Modeling: The computer-aided-design of the chevron nozzle geometry

was carried out using the Pro/Engineer Wildfire 4.0 assembly module. The

ejector nozzle was designed parametrically using the CATIA version 6. The

standard for the exchange of product model data (STEP) file format was used

as the primary CAD file exchange format.

3. Grid Generation: The computational meshes necessary for the CFD simula-

tions were created using the Pointwise GRIDGEN version 15.10. Both struc-

tured and unstructured grids were created in the present study. The interface

between the structured and unstructured block consisted of pyramid cells. The

boundary layers consisted of prisms for the unstructured mesh and hexahedral

cells for the structured mesh.

4. CFD Simulation: The ANSYS FLUENT version 6.3.26 flow solver was used

for all the CFD simulations. Both the pressure-based and the density-based

27

Figure 2.7. Methodology for the jet engine exhaust nozzle design and analysis.

coupled solvers were used. The two-equation turbulence models discussed in

Section 2.3.2 were used for the prediction of turbulent quantities.

5. Post-processing: All the post-processing involving contour plots were done

using Tecplot 360 version 2009 and the encapsulated post script (EPS) file

format was used for the data export. In the present work, the post-processing

of the CFD solution involved contour plots of the axial velocity magnitude and

the TKE.

6. Validation: All the data analysis and line plots involved in various validation

studies were done using MATLAB version 2009. The variation of the centerline

velocity magnitude and the total temperature with the axial distance were used

for studying the nozzle jet characteristics.

28

3. Chevron Nozzles

3.1 Introduction

One of the widely used techniques to reduce jet noise from high BPR turbofan

nozzles is to enhance the mixing of the core and the fan jet streams by adding serra-

tions at the trailing edges of the jet nozzle. They are known as Chevrons. Modern

turbofan engines, such as the Trent-1000 on the Boeing-787 and the GE NX-2B67 on

the Boeing 747-800, make use of these chevrons for jet noise reduction. Chevrons are

a viable design feature for the noise suppression of jet engine exhaust nozzle systems

because of their ability to reduce noise with a small percentage of thrust penalty and

easy manufacturability.

The present work served as a preliminary validation task for the design and anal-

ysis of chevron nozzles. We considered the design of chevrons studied by Janardan

et al. [21] and performed the CFD simulations similar to the work of Kenzakowski et

al. [20]. They used a baseline three-stream separate-flow axisymmetric plug nozzle

(3BB) and studied the performance of passive mixing devices such as 12 alternating

chevrons (3A12B) (as explained in Section 2.2.2) and 24 tabs (3T24B).

In the chevron nozzle case, Kenzakowski et al. (2000) found that the inward-facing

chevron enhanced the penetration of the fan stream into the core stream downstream

of the nozzle exit and the outward-facing chevron deflected the core stream into the

fan stream. This resulted in an enhanced mixing and the growth of the shear layer

between the core stream and the fan stream was greatly affected. However, the

growth of the shear layer between the fan stream and freestream did not appear to

be significantly altered by the presence of chevrons.

It was observed that the fan stream and the freestream mixing layer was the dom-

inant turbulent region, but the peaks obtained in the turbulence fields were further

29

upstream compared to the baseline axisymmetric nozzle. CFD simulations using the

WIND-CFD code showed an underprediction of the mixing rate, leading to a longer

potential core compared to the experimental data [20]. As part of the present work, it

was decided to analyze the 3BB and 3A12B nozzle geometries and perform the CFD

simulations using the ANSYS FLUENT flow solver. Since experimental and WIND-

CFD results were available in the literature, this work was beneficial in studying the

potential of the FLUENT flow solver and various turbulence models in the prediction

of the chevron jet flows.

3.2 Objectives

The objective of the present task was to study the performance of the ANSYS

FLUENT flow solver and its available turbulence models in the prediction of three-

stream separate-flow axisymmetric plug and chevron-based jet flows. Results obtained

from the CFD simulations were compared to the WIND-CFD results and validated

using the experimental PIV measurements available in the literature.

3.3 Three-Stream Separate-Flow Axisymmetric Plug Nozzle (3BB)

3.3.1 Introduction

As part of the NASA advanced subsonic transport (AST) program, a series of

experiments were conducted at NASA GRC to study the aeroacoustic characteristics

of three-stream separate-flow axisymmetric plug nozzles for a high BPR turbofan jet

engine. Different passive mixing enhancement devices were implemented on either

core nozzle or fan nozzle or both. Experimental results were compared with the CFD

results in the form of mean and turbulent flow fields.

30

3.3.2 Geometry and Mesh Generation

The baseline nozzle configuration consisted of an axisymmetric, laboratory scale,

three-stream nozzle with an external plug. The geometric details of this nozzle cor-

responded to the 3BB configuration, documented in reference [21]. It had a BPR of

five and consisted of an external plug. The plug angle was approximately 16 degrees.

The core cowl exit radius was 5.156 in. and the core cowl external boat tail angle was

approximately 14 degrees. The core flow exit plane was 4.267 in. downstream of the

fan nozzle exit plane. Figure 3.1 shows the isometric view of the CAD geometry.

Figure 3.1. The CAD geometry of the three-stream separate-flowaxisymmetric plug nozzle [20].

The computational mesh was created using the Pointwise GRIDGEN version

15.10. As the nozzle was axisymmetric, a multiblock 2-D structured mesh, as shown

in Figure 3.2 was created. The grid consisted of a total of 0.115 million cells. A

variable wall-normal grid spacing was used for all viscous wall boundaries to yield a

y+ value in the range of 30 ∼ 300 and hence wall functions were used for the near

wall turbulence.

31

Figure 3.2. The computational mesh for the three-stream separate-flow axisymmetric plug nozzle.

3.3.3 Boundary Conditions and CFD Methodology

The experimental conditions corresponded to the take-off conditions with a NPR

of 1.7. The pressure-based boundary conditions were used in the CFD analysis. The

boundary conditions were pressure-inlet at the inflow boundary, axis along the cen-

terline, pressure far field along the outer freestream boundary and pressure-outlet at

the exit. Table 3.1 shows the numerical values used for various boundary conditions.

The ANSYS FLUENT version 6.3.26 flow solver was used for all the CFD sim-

ulations. Since the flow conditions were high subsonic, the pressure-based explicit

coupled solver was used to solve the continuity and momentum equations. As dis-

cussed in Section 2.3.1, the convergence of the pressure-based coupled algorithm was

governed by the underrelaxation factors. Hence a high underrelaxation factor of 1.0

was used for the density, pressure, and momentum equations and 0.8 was used for the

turbulence equations. A high value of 5.0 was used for the Courant-Friedrich-Lewy

32

Table 3.1 Boundary conditions for the CFD simulation of the three-stream separate-flow axisymmetric plug nozzle (3BB) [20].

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

(CFL) number. The viscous walls were assumed adiabatic and the inflow boundary

layer effects were not included.

Various turbulence models, discussed in Section 2.3.2, were used with walls func-

tions for near wall resolution. In the current work, the focus was to study the potential

of two-equation turbulence models in predicting jet flows accurately. Hence, CFD sim-

ulation of the nozzle was performed using turbulence models viz. the standard k-ε,

the realizable k-ε, Thies and Tam’s k-ε, the standard k-ω and the k-ω SST turbulence

models. In addition to this, the more accurate, second-order closure RSM was also

used. Convergence was greatly affected in the case of RSM and it took more compu-

tational time to get a converged solution when compared to two-equation turbulence

models.

In order to check the convergence, along with the default solver residual moni-

tor, the iteration history of the mass-balance and velocity magnitude at some axial

location downstream of the nozzle throat was monitored. When the mass-balance

reached 1 x 10−5 and the velocity magnitude reached a steady-value, the solution

was considered to be converged. The solutions presented in the present chapter are

second-order accurate.

33

3.3.4 Results

The CFD simulation of the current three-stream separate-flow axisymmetric plug

nozzle serves as a validation of the ANSYS FLUENT flow solver. CFD results are

compared with the experimental data, obtained using the PIV technique and docu-

mented in the reference [18]. In the turbulent jet class of flows, flow variables along

the centerline (axis) of the jet are of prime interest. This information gives an idea

about the jet characteristics such as shear layers and the potential core. It also helps

in the understanding of the jet spreading. The turbulent kinetic energy distribution

gives an idea about the extent of mixing between the three flow streams. Hence, the

computational results are presented as contours and centerline profiles of the axial

velocity (UCL), TKE and total temperature (Tt).

The axial distance along the nozzle centerline is normalized using the fan diameter

(Dfan) which equals 9.61 in. and the origin is shifted to the nozzle fan exit plane. In

general, a small recirculation zone occurs along the plume axis at the external plug

blunt trailing edge. CFD results obtained by the application of various turbulence

models available in the ANSYS FLUENT solver are discussed in the following subsec-

tions. The experimental axial velocity contours are shown in Figure 3.3 while those

from the CFD using turbulence models are shown in Figures 3.4-3.8. The experimen-

tal turbulent kinetic energy contours are shown in Figure 3.9, while the corresponding

CFD result with different turbulence models are given in Figures 3.10-3.14.


Contours of the axial velocity and turbulent kinetic energy for the baseline three-

stream separate-flow axisymmetric plug nozzle, obtained using the standard k-ε tur-

bulence model, are illustrated in Figures 3.4 and 3.10, respectively. The standard

k-ε turbulence model gives a good prediction of the mean flow variables with better

convergence. However, it fails to predict the turbulence quantities in complex flows

such as jets. When compared with the experiments, it is evident that the standard k-ε

34

turbulence model predicts the mean velocity contours very well but with an under-

prediction of the length of the potential core. The classical problem of the unphysical

overprediction of the turbulent kinetic energy associated with the standard k-ε tur-

bulence model in the high shear region is shown in Figure 3.10. The standard k-ε

turbulence model overpredicts the TKE near the fan stream nozzle exit plane, when

compared with the experimental data.


It has been suggested that the overprediction in the TKE contours associated with

the standard k-ε turbulence model is because of the unphysical values of Cµ in the

definition of turbulent viscosity,

µt =

(ρCµ

k2

ε

). (3.1)

Reynolds [37] proposed a realizability limit on the values of Cµ as a solution to this

problem. Because of this improvement, the realizable k-ε model become the most

recommended turbulence model for external aerodynamic flows [29]. Figures 3.5

and 3.11 show the contours of axial velocity and turbulent kinetic energy, respectively.

It is evident that the abnormally high TKE regions are removed and the results

are in close agreement with the experiments in the shear layers close to the nozzle.

However, the TKE level further downstream is significantly underpredicted. Also,

this turbulence model overpredicts the length of the potential core when compared

with the standard k-ε turbulence model results and experiments.

Wilcox’s k-ω Turbulence Model

Figures 3.6 and 3.12 show the axial velocity and turbulent kinetic energy contours

corresponding to the Wilcox’s k-ω (1988) turbulence model. The mean flow velocity

contour is similar to the realizable k-ε turbulence model with an overprediction of the

length of the potential core. However, the TKE contours are diffusive compared to

35

other two-equation turbulence models. The unphysical overprediction of the TKE,

as discussed in the case of the standard k-ε turbulence model is also observed.

Menter’s k-ω SST Turbulence Model

Menter’s k-ω SST turbulence model is an effort to make use of the robustness of

the standard k-ε turbulence model and the accuracy of the standard k-ω turbulence

model for flows with boundary layers using blending functions. Because of the com-

bined advantages, the k-ω SST turbulence model gives a very good prediction of the

turbulent kinetic energy and the mean axial velocity. Figure 3.7 shows the contours

of the mean axial velocity and Figure 3.13 shows the contours of the turbulent ki-

netic energy. The contours are in close agreement with the results obtained using

the realizable k-ε turbulence model. But as with the case of realizable k-ε turbulence

model, the k-ω SST turbulence model overpredicts the length of the potential core

and underpredicts the levels of TKE when compared with the experiment data.

Reynolds Stress Turbulence Model (RSM)

The RSM belongs to the second-order closure class of turbulence models and is

considered to be more accurate than most of the two-equation turbulence models for

strongly swirling and rotational flows. However, as we observed, the improvement in

the accurate prediction of the three-stream separate-flow axisymmetric plug nozzle

jet mean flow is not considerable when compared with the realizable k-ε and the k-ω

SST turbulence model. Figure 3.8 shows the contours of the mean axial velocity. The

contours of the turbulent kinetic energy are shown in Figure 3.14.

It is evident that the contours match closely with the realizable k-ε and the k-ω

SST turbulence model. The potential core is somewhat longer than with the k-ω SST

turbulence model and approximately equal to the one obtained using the realizable

k-ε turbulence model. The contours of the turbulent kinetic energy shows that the

peak TKE regions are shifted downstream in the case of the RSM when compared

36

with the k-ω SST turbulence model. The RSM predicts a higher magnitude of the

peak TKE and are in better comparison with the experiment data when compared

with all the turbulence models used in the present study.

Figure 3.15 shows the variation of the centerline velocity magnitude (UCL) with

axial distance from the nozzle exit. This plot summarizes the findings discussed in

the results for each turbulence model. It is evident that the standard k-ε turbulence

model gives a good prediction of the mean flow, following the trend of the experimental

measurements, but underpredicts the potential core length. Also, it is not accurate

for the prediction of TKE. The realizable k-ε, the k-ω SST and the Reynolds stress

turbulence models perform much better in the prediction of the mean axial velocity

and turbulent kinetic energy. However, they suffer from the overprediction of the jet

potential core length.

Figure 3.16 shows the variation of the total temperature (Tt) along the centerline.

The potential core region can be identified by the constant temperature region. It

is observed that the standard k-ε and standard k-ω (1988) turbulence models give a

reasonable prediction of the variation of the total temperature with some underpre-

diction and overprediction, respectively.

37

Figure 3.3. 3BB axial velocity magnitude contour plot correspondingto PIV experiments on the Z=0 plane [20].

Figure 3.4. 3BB axial velocity magnitude contour plot correspondingto the standard k-ε turbulence model on the Z=0 plane.

Figure 3.5. 3BB axial velocity magnitude contour plot correspondingto the realizable k-ε turbulence model on the Z=0 plane.

38

Figure 3.6. 3BB axial velocity magnitude contour plot correspondingto the standard k-ω turbulence model on the Z=0 plane.

Figure 3.7. 3BB axial velocity magnitude contour plot correspondingto the k-ω shear stress transport turbulence model on the Z=0 plane.

Figure 3.8. 3BB axial velocity magnitude contour plot correspondingto the Reynolds stress turbulence model on the Z=0 plane.

39

Figure 3.9. 3BB turbulent kinetic energy contour plot correspondingto PIV experiments on the Z=0 plane [20].

Figure 3.10. 3BB turbulent kinetic energy contour plot correspondingto the standard k-ε turbulence model on the Z=0 plane.

Figure 3.11. 3BB turbulent kinetic energy contour plot correspondingto the realizable k-ε turbulence model on the Z=0 plane.

40

Figure 3.12. 3BB turbulent kinetic energy contour plot correspondingto the standard k-ω turbulence model on the Z=0 plane.

Figure 3.13. 3BB turbulent kinetic energy contour plot correspondingto the k-ω shear stress transport turbulence model on the Z=0 plane.

Figure 3.14. 3BB turbulent kinetic energy contour plot correspondingto the Reynolds stress turbulence model on the Z=0 plane.

41

0 5 10 150

200

400

600

800

1000

1200

1400

1600

X/Dfan

Cen

trel

ine

Vel

ocity

UC

L ft/s

PIV experiment (NASA/CR−2000−210039)WIND k−ω SST (Koch, 2004)Standard k−ε turbulence modelRealizable k−ε turbulence modelStandard k−ω turbulence modelk−ω SST turbulence modelReynolds stress model

Figure 3.15. Centerline axial velocity profiles for different turbulencemodels and comparison with the experimental result.

0 5 10 15300

400

500

600

700

800

900

1000

1100

1200

X/Dfan

Tot

al T

empe

ratu

re T ° K

Experiment (Kenzakowski et al. 2000)Standard k−ε turbulence modelRealizable k−ε turbulence modelStandard k−ω turbulence modelk−ω SST turbulence modelReynolds stress model

Figure 3.16. Centerline total temperature profiles for different turbu-lence models and comparison with the experimental result.

42

3.4 Three-Stream Separate-Flow Chevron Nozzle (3A12B)

3.4.1 Introduction

In addition to the study of the baseline three-stream separate-flow axisymmetric

plug nozzle, the effects of various passive mixing devices such as chevrons and tabs

on the overall aerodynamic and aeroacoustic performances of the nozzle were studied

during the NASA AST program. As discussed in Section 2.2.2, chevrons are passive

mixers which enhance the mixing between the two streams by introducing small

scale eddies near the nozzle exit and thus reduce the jet noise. The chevron nozzle,

designated as 3A12B during the AST program, consisted of an axisymmetric plug

nozzle with twelve alternating chevrons on the primary nozzle, facing in and out of

the core flow. Experimental results are available for comparison in the form of PIV

measurements from reference [24].


The nozzle geometry used in the experimental and computational studies of Koch

and Bridges (2004) [24] was used in the present work. A CAD model was created for

the nozzle geometry using the Pro/Engineer Wildfire 4.0. Dimensions of the baseline

nozzle were the same as the three-stream separate-flow axisymmetric plug nozzle,

discussed in Section 3.3 and were extracted from figures available in the literature [24].

In addition to the baseline nozzle, the core nozzle of this configuration consisted of

12 chevrons arranged in an alternating pattern, facing inward and outward of the

core flow. The fundamental dimensions involved in the chevron design are shown in

Figure 3.17. The alternating chevron arrangement consisted of half of the chevrons

being bent towards the core flow by 4.5◦ and the other half were bent towards the

fan stream by 8◦. A CAD model of the nozzle geometry is shown in Figure 3.18.

The computational mesh for the CFD simulation was created using the Pointwise

GRIDGEN version 15.10 grid generation code. Since the nozzle with chevrons was

43

S. No Parameter Value

1 N = Number of chevrons 12

2 Do = Nozzle ID at baseline nozzle throat plane,

Perimeter Hydraulic Diameter (PHD)

4.827

3 α = Nozzle internal flow path angle at throat

plane. Used to project forward and aft of throat

plane for definition of chevron (degrees)

12.02

4 l = Chevron length along inner flow path; lFWD

and lAFT = split of length forward and aft of

throat plane

1.0

5 Δr = lFWD x sinα 0.1041

6 D = Do+2Δr (internal diameter at chevron base ) 5.0352

Basic Chevron Design Parameters All dimensions in inches unless otherwise specified.

7 C = πD (circumference at the base of chevron) 15.819

8 s = C/N arc length at the base of chevron 1.3182

9 θ = 360o/N (degrees) 30

10 b = D sin (θ/2), Chord length at base of chevron 1.3032

11 lp = l cos α, projected length of chevron 0.9781

12 ф = arc tan[(b/2)/(lp)] half angle of chevron tip 33.67

13 Ф = 2ф (included angle of chevron tip, degrees) 67.34

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


Freestream static pressure (atm) 0.98

Freestream total pressure (atm) 1.04

Freestream total temperature (K) 298.8


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.


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.


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].


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.

62

Table 4.1 2-D ejector nozzle boundary conditions [46].

Variables Value

Primary nozzle total pressure 246 kPa

Primary nozzle total temperature 358 K

Ambient pressure 101 kPa

Ambient temperature 305 K

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



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



0 200 400 600 800 1000 1200−1.5

−1

−0.5

0

0.5

1

1.5

Axial Velocity ft/s

Y/H



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


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


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-

fault values to 0.5 (density), 0.5 (turbulent kinetic energy), 0.8 (specific dissipation

rate), 0.8 (turbulent viscosity) and 0.5 (energy) for numerical stability.

Simulation III was different from the above described two simulations because of

its higher operating nozzle pressure ratio. The density-based coupled explicit solver

was used to solve RANS equations in a coupled manner. This was because of the fact

that the Mthroat ≈ 0.75. Density and viscosity were calculated using the ideal gas

equation and Sutherland’s three coefficient method, respectively. RANS equations

were closed using Menter’s k-ω shear stress transport turbulence model with wall

functions. The flow domain was initiated using freestream conditions and the final

second-order accurate solution was obtained. A CFL value of 1.0 was used for stability

reasons. The underrelaxation factors were reduced from their default values to 0.5

(turbulent kinetic energy), 0.7 (specific dissipation rate) and 0.7 (turbulent viscosity)

for numerical stability.

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



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Figure 4.31. Normalized axial velocity profile at X/DEQ=1.0 and onthe Z=0 plane.

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Figure 4.32. Normalized axial velocity profile at X/DEQ=1.0 and onthe Y=0 plane.

87

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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

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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

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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

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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

in Figures 4.55-4.64.

95

Figure 4.45. Experimental U/UPL contour plot at X/DEQ=0.42 fromthe throat [44].


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Figure 4.55. Normalized axial velocity profile at X/DEQ=0.42 andon the Z=0 plane.

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Figure 4.56. Normalized axial velocity profile at X/DEQ=0.42 andon the Y=0 plane.

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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

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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.

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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

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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


Freestream static pressure (kPa) 101.325

Freestream total temperature (K) 303


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.

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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

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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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Design and Analysis of Noise Suppression Exhaust Nozzle Systems