les for acoustics by wei shyy and michael j. rycroft

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LARGE-EDDY SIMULATION FOR ACOUSTICS

Noise pollution around airports, trains, and industries increasingly attracts environmental con-

cern and regulation. Designers and researchers have intensified the use of large-eddy simulation

(LES) for noise-reduced industrial design and acoustical research. This book, written by thirtyexperts, presents the theoretical background of acoustics and LES followed by details about nu-

merical methods such as discretization schemes, boundary conditions, and coupling aspects. In-

dustrially relevant, hybrid Reynolds-averaged NavierStokes/LES techniques for acoustic source

predictions are discussed in detail. Many applications are featured ranging from simple geome-

tries for mixing layers and jet flows to complex wing and car geometries. Selected applications

include recent scientific investigations at industrial and university research institutions. Presently

perfect solution methodologies that address all relevant applications do not exist; however, the

book presents a state-of-the-art collection of methods, tools, and evaluation methodologies. The

advantages and weaknesses of both the commercial and research methodologies are carefully

presented.

Claus Wagner received his Ph.D. in Fluid Dynamics in 1995 at the Technical University of

Munich, Germany. He is Honorary Professor for Industrial Aerodynamics, Ilmenau University

of Technology, Germany. Since 1998, he has been a scientist in and head of the Section of Nu-

merical Simulations for Technical Flows of the Institute for Aerodynamics and Flow Technology,

German Aerospace Center, Gottingen, Germany. Dr. Wagners research includes experimental

investigations of the resonant control of nonlinear dynamic systems, theoretical and numerical

investigations of thermal convection in cylindrical containers, and direct numerical simulation

and large-eddy simulations of turbulent flows in different configurations. He has held visiting

positions in Gainsville, Florida, USA as well as in Bremen, Germany.

Thomas Huttl received his Ph.D. in Fluid Dynamics in 1999 at the Technical University of

Munich, Germany. His academic research included work on the direct numerical simulation of

turbulent flows in curved and coiled pipes, and direct and large-eddy simulations of boundary

layer flows with and without separation, in the framework of a FrenchGerman DFG-CNRS-

Cooperation project. He has held visiting positions in Nantes, France and Bangalore, India.

Between 2000 and 2003, he was a senior engineer for aeroacoustics at MTUAero Engines GmbH,

Germanys leading manufacturer of engine modules and components and of complete aero

engines. Dr. Huttl led MTUs contribution for the European research project TurboNoiseCFD and

contributed to the European research project SILENCER. After some years working as IT quality

manager and internal auditor, he is now Chief Privacy Officer for the entire MTU Aero Engines

concern. Among his many honors, Dr. Huttl was elected a member of the Senate of the DGLR,

Deutsche Gesellschaft fur Luft- und Raumfahrt - Lilienthal - Oberth e.V. in 2003 and 2006.

Pierre Sagaut received his DEA in Mechanics in 1991 and his Ph.D. in Fluid Mechanics in

1995 at Universite Pierre et Marie Curie Paris 6 (Paris, France). He worked as a research

engineer at ONERA (French National Aerospace Research Center) from 1995 to 2002. He has

been a professor in mechanics at University Pierre et Marie Curie Paris 6 since 2002. He is

also part-time Professor at Ecole Polytechnique (France) and scientific consultant at ONERA,

IFP, and CERFACS (France). His main research interests are fluid mechanics, aeroacoustics,

numerical simulation of turbulent flows (both direct and large-eddy simulation), and numerical

methods. He is also involved in uncertainty modeling for computational fluid dynamics (CFD).He has authored and coauthored more than sixty papers in peer-reviewed international journals

and 130 proceedings papers. He is the author of several books dealing with turbulence modeling

and simulation. He is member of several editorial boards:Theoretical and Computational Fluid

Dynamics, Journal of Scientific Computing, and Progress in CFD. He received the ONERA

award three times for the best publication and the John Green Prize (delivered by ICAS, 2002).


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Cambridge Aerospace Series

Editors

Wei Shyy

and

Michael J. Rycroft

1. J. M. Rolfe and K. J. Staples (eds.):Flight Simulation

2. P. Berlin:The Geostationary Applications Satellite3. M. J. T. Smith:Aircraft Noise

4. N. X. Vinh:Flight Mechanics of High-Performance Aircraft

5. W. A. Mair and D. L. Birdsall:Aircraft Performance

6. M. J. Abzug and E. E. Larrabee:Airplane Stability and Control

7. M. J. Sidi:Spacecraft Dynamics and Control

8. J. D. Anderson:A History of Aerodynamics

9. A. M. Cruise, J. A. Bowles, C. V. Goodall, and T. J. Patrick:Principles of Space

Instrument Design

10. G. A. Khoury and J. D. Gillett (eds.):Airship Technology

11. J. Fielding:Introduction to Aircraft Design12. J. G. Leishman:Principles of Helicopter Aerodynamics, 2nd Edition

13. J. Katz and A. Plotkin:Low Speed Aerodynamics, 2nd Edition

14. M. J. Abzug and E. E. Larrabee:Airplane Stability and Control: A History of the

Technologies that Made Aviation Possible, 2nd Edition

15. D. H. Hodges and G. A. Pierce:Introduction to Structural Dynamics and

Aeroelasticity

16. W. Fehse:Automatic Rendezvous and Docking of Spacecraft

17. R. D. Flack:Fundamentals of Jet Propulsion with Applications

18. E. A. Baskharone:Principles of Turbomachinery in Air-Breathing Engines

19. Doyle D. Knight:Elements of Numerical Methods for High-Speed Flows20. C. Wagner, T. Huttl, and P. Sagaut:Large-Eddy Simulation for Acoustics


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Large-Eddy Simulation for

Acoustics

Edited by

CLAUS WAGNERGerman Aerospace Center

THOMAS HUTTL

MTU Aero Engines GmbH

PIERRE SAGAUT

Universit e Pierre et Marie Curie


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CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, So Paulo

Cambridge University PressThe Edinburgh Building, Cambridge CB2 8RU, UK

First published in print format

ISBN-13 978-0-521-87144-0

ISBN-13 978-0-511-29466-2

Cambridge University Press 2007

2006

Information on this title: www.cambridge.org/9780521871440

This publication is in copyright. Subject to statutory exception and to the provision ofrelevant collective licensing agreements, no reproduction of any part may take place

without the written permission of Cambridge University Press.

ISBN-10 0-511-29466-2

ISBN-10 0-521-87144-1

Cambridge University Press has no responsibility for the persistence or accuracy of urlsfor external or third-party internet websites referred to in this publication, and does notguarantee that any content on such websites is, or will remain, accurate or appropriate.

Published in the United States of America by Cambridge University Press, New York

www.cambridge.org

hardback

eBook (EBL)

eBook (EBL)

hardback
http://www.cambridge.org/9780521871440http://www.cambridge.org/http://www.cambridge.org/9780521871440http://www.cambridge.org/


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Contents

List of Figures and Tables pagexiii

Contributors xxi

Preface xxv

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 The importance of acoustic research 1

Thomas H uttl

1.1.1 Health effects 1

1.1.2 Activity effects 2

1.1.3 Annoyance 2

1.1.4 Technical noise sources 3

1.1.5 Political and social reactions to noise 4

1.1.6 Reactions of industry 5

1.1.7 Research on acoustics by LES 5

1.2 Introduction to computational aeroacoustics 7

Manuel Keler

1.2.1 Definition 7

1.2.2 History 7

1.2.3 Aeroacoustics 81.2.4 Conceptual approaches 9

1.2.5 Remaining problem areas for sound computation 13

1.3 State of the art: LES for acoustics 15

Claus Wagner, Oliver Fleig, and Thomas H uttl 15

1.3.1 Broadband noise prediction in general 15

1.3.2 Broadband noise prediction based on LES 17

2 Theoretical Background: Aeroacoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Avraham Hirschberg and Sjoerd Rienstra

2.1 Introduction to aeroacoustics 24

2.2 Fluid dynamics 25

2.2.1 Mass, momentum, and energy equations 25

2.2.2 Constitutive equations 28

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viii CONTENTS

2.2.3 Approximations and alternative forms of the basic

equations 30

2.3 Free-space acoustics of a quiescent fluid 33

2.3.1 Orders of magnitude 33

2.3.2 Wave equation and sources of sound 352.3.3 Greens function and integral formulation 36

2.3.4 Inverse problem and uniqueness of source 38

2.3.5 Elementary solutions of the wave equation 39

2.3.6 Acoustic energy and impedance 44

2.3.7 Free-space Greens function 47

2.3.8 Multipole expansion 47

2.3.9 Doppler effect 49

2.3.10 Uniform mean flow, plane waves, and edge diffraction 52

2.4 Aeroacoustic analogies 55

2.4.1 Lighthills analogy 55

2.4.2 Curles formulation 59

2.4.3 Ffowcs WilliamsHawkings formulation 60

2.4.4 Choice of aeroacoustic variable 62

2.4.5 Vortex sound 65

2.5 Confined flows 68

2.5.1 Wave propagation in a duct 68

2.5.2 Low-frequency Greens function in an infinitely long uniform duct 72

2.5.3 Low-frequency Greens function in a duct with a discontinuity 74

2.5.4 Aeroacoustics of an open pipe termination 76

3 Theoretical Background: Large-Eddy Simulation . . . . . . . . . . . . . . . . . . . . 89Pierre Sagaut

3.1 Introduction to large-eddy simulation 89

3.1.1 General issues 89

3.1.2 Large-eddy simulation: Underlying assumptions 90

3.2 Mathematical models and governing equations 91

3.2.1 The NavierStokes equations 91

3.2.2 The filtering procedure 92

3.2.3 Governing equations for LES 95

3.2.4 Extension for compressible flows 98

3.2.5 Filtering on real-life computational grids 100

3.3 Basic numerical issues in large-eddy simulation 105

3.3.1 Grid resolution requirements 105

3.3.2 Numerical error: Analysis and consequences 109

3.3.3 Time advancement 112

3.4 Subgrid-scale modeling for the incompressible case 112

3.4.1 The closure problem 112

3.4.2 Functional modeling 113

3.4.3 Structural modeling 118

3.4.4 Linear combination models, full deconvolution, and Lerays

regularization 119

3.4.5 Extended deconvolution approach for arbitrary nonlinear terms 120

3.4.6 Multilevel closures 121

3.4.7 The dynamic procedure 121


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CONTENTS ix

3.5 Extension of subgrid models for the compressible case 125

3.5.1 Background 125

3.5.2 Extension of functional models 125

3.5.3 Extension of structural models 126

3.5.4 The MILES concept for compressible flows 126

4 Use of Hybrid RANSLES for Acoustic Source Predictions . . . . . . . . . . . . 128

Paul Batten, Philippe Spalart, and Marc Terracol

4.1 Introduction to hybrid RANSLES methods 128

4.2 Global hybrid approaches 130

4.2.1 The approach of Speziale 130

4.2.2 Detached-eddy simulation 131

4.2.3 LNS 133

4.2.4 The approach of Menter, Kunz, and Bender 138

4.2.5 Defining the filter width 140

4.2.6 Modeling the noise from unresolved scales 142

4.2.7 Synthetic reconstruction of turbulence 143

4.2.8 The NLAS approach of Batten, Goldberg,

and Chakravarthy 145

4.3 Zonal hybrid approaches 148

4.3.1 The approach of Qu em er e and Sagaut 150

4.3.2 The approach of Labourasse and Sagaut 150

4.3.3 Zonal-interface boundary coupling 152

4.4 Examples using hybrid RANSLES formulations 154

4.4.1 Flow in the wake of a car wing mirror 154

4.4.2 Unsteady flow in the slat cove of a high-lift airfoil 158

4.5 Summary of hybrid RANSLES methods 163

5 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

5.1 Spatial and temporal discretization schemes 167

Tim Broeckhoven, Jan Ramboer, Sergey Smirnov, and Chris Lacor

5.1.1 Introduction to discretization schemes 167

5.1.2 Dispersion and dissipation errors 168

5.1.3 Spatial discretization schemes 170

5.1.4 Temporal discretization schemes 197

5.2 Boundary conditions for LES 201

Michael Breuer

5.2.1 Outflow boundary conditions 203

5.2.2 Inflow boundary conditions 204

5.2.3 Boundary conditions for solid walls 208

5.2.4 Far-field boundary conditions for compressible flows 214

5.2.5 Final remark for discretization schemes 215

5.3 Boundary conditions: Acoustics 216

Fang Q. Hu

5.3.1 Characteristic nonreflecting boundary condition 217

5.3.2 Radiation boundary condition 218

5.3.3 Absorbing-zone techniques 218


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List of Figures and Tables

Figures

1.1 Magnetic levitation hover train project Transrapid 4

1.2 Noise prediction methods 12

1.3 Insulator of a high-speed trains pantograph 21

1.4 Sketch of the insulator of a high-speed trains pantograph 22

1.5 Far-field sound-pressure spectra 22

2.1 Monopole, dipole, and quadrupole generating waves on the surface

of the water around a boat 44

2.2 Sketch of scattered plane wave with mean flow 54

2.3 A potential flow through the vocal folds is silent 662.4 Straight duct of arbitrary cross section 68

2.5 (a) Method of images applied to a source aty = (y1,y2,y3) at a distance

y3 from a hard wall x3= 0 has a Greens function: G(x,t|y,) =

G0(x,t|y,) + G0(x,t|y,) withy = (y1,y2,y3). (b) A source between

two parallel hard walls generates an infinite row of images. (c) A source

in a rectangular duct generates an array of sources 73

2.6 The end correction for no flow (Mj = 0) and a little flow (Mj = 0.01) 84

2.7 Plane-wave reflection coefficient |R| and end correction at jet

exhaust without coflow for Mj = 0.01,0.1, . . . , 0.6 85

2.8 Plane-wave reflection coefficient |R| and end correction at jetexhaust with Mj = 0.3 and coflow velocities Mo/Mj = 0,0.25,

0.5,0.75,1 86

2.9 Acoustic flow at a pipe outlet (a) for an unflanged pipe termination

and (b) for a horn 87

3.1 Schematic kinetic energy spectra of resolved and subgrid scales

with spectral overlap (Gaussian filter) 95

3.2 Streaks in the inner layer of the boundary layer 107

3.3 Schematic of kinetic energy transfer in isotropic turbulence 114

3.4 Schematic of the two-level filtering procedure and the Germano identity 122

4.1 Turbulence energy spectrum partitioned into resolvableand unresolvable frequencies 135

4.2 Required near-wall mesh resolutions with DNS, traditional LES, global

hybrid RANSLES, and nonlinear acoustics solvers (NLAS) based on

disturbance equations 147

xiii


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xiv LIST OF FIGURES AND TABLES

4.3 Initial startup transient at probe 111 (cylinder rear face) predicted by

unsteady RANS and hybrid RANSLES (LNS model) using identical

base model, mesh, and time step 155

4.4 Instantaneous streamwise vorticity contours (with streamwise velocity

shading) predicted by hybrid RANSLES model 1554.5 Resolved and unresolved (synthetically generated) signals for probe

111 (cylinder rear face) 156

4.6 Sound-pressure levels determined by resolved, unresolved, and

composite signals for probe 111 (cylinder rear face) 157

4.7 Instantaneous streamwise vorticity contours (with streamwise velocity

shading) predicted by the nonlinear acoustics solver (NLAS) 157

4.8 Sound-pressure levels determined by NLAS method at probe 111

(cylinder rear face) 158

4.9 Location of the LES subdomain (displayed mesh shows every eighth

grid line) 159

4.10 Mean flow streamlines. Left: RANS computation, Right: Hybrid

RANSLES computation 159

4.11 Instantaneous Schlieren-like view 160

4.12 Isovalue contours of the dilatation field 160

4.13 Acoustic pressure spectrum at location S2 161

4.14 Acoustic pressure spectrum in the recirculation bubble (location S3) 162

4.15 Isovalue contours of the dilatation field 162

4.16 Acoustic pressure spectrum at the slats trailing edge (location S4) 163

4.17 Acoustic pressure spectrum in the slats wake 164

5.1 Resolution of different explicit and compact (implicit) schemes 178

5.2 Comparison of the resolution of Taylor and Fourier difference

schemes 180

5.3 Effect of f on a second- and an eighth-order filter 188

5.4 Perturbation pressure of an acoustic wave initiated by a Gaussian

pulse: comparison of solution with smooth and randomly perturbed

mesh 197

5.5 Example for a reasonable choice of the integration domain (inflow

and outflow boundaries) for the flow past a wing in a wind tunnel 202

5.6 Von K arman vortex street past an inclined wing (NACA4415) at

Re= 20,000 and = 12 visualized by streaklines; four different time

instants of a shedding cycle in the vicinity of the outflow boundary

are shown 205

5.7 Sketch of Lund et al.s (1998) procedure for generating appropriate

inflow conditions for a boundary layer flow 206

5.8 Example for the generation of inflow data for a 90 bend using a

second simulation for a straight duct flow with periodic b.c. 207

5.9 Law of the wallu+(y+) in a turbulent boundary layer without or with

only a weak pressure gradient (half-logarithmic plot) 211

5.10 Sketch of the computational domains to determine, for example,

trailing-edge noise with the hybrid approach 224

5.11 Sketch of the rescaling concept 226

5.12 Sketch of the flat-plate boundary layer domain (left) and the

trailing-edge domain (right). The procedure to provide the inlet

distribution to simulate trailing-edge flow is visualized 230


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LIST OF FIGURES AND TABLES xv

5.13 LES of a turbulent boundary layer for Re0 = 1400 and M = 0.4.

Skin-friction coefficientc f versus Refor different rescaling

formulations 232

5.14 Transfer function | F| as a function of wave number scaled by

damping zone thickness d 2355.15 Spurious sound waves and velocity field generated at an artificial

boundary atx= 0 236

5.16 Pressure distribution on y= 35 in Figure 5.15 for several thickness

values dand BiotSavarts law (denoted as compensation) 237

6.1 Simulation of a 2D mixing layer. (a) Snapshot of the dilatation field

= .uon the whole calculation domain, levels in s1. (b) View

of the pairing zone with the vorticity field in the mixing layer and the

dilatation field outside 240

6.2 LES of a ReD = 6.5 104 subsonic jet. Time evolution of the

fluctuating pressure p in Pa as a function oft = tuj/D, atx= 16r

0,

y= 8r0, andz= 0 242

6.3 LES of a ReD = 6.5 104 subsonic jet. Snapshot of the vorticity norm

in the flow field and of the fluctuating pressure outside in the plane

z= 0 att = 7.5 242

6.4 LES of a ReD = 6.5 104 subsonic jet. Snapshots of the vorticity norm

in the planez= 0 at times: (a)t = 2.2, (b)t = 3.5 243

6.5 LES of a ReD = 4 105 subsonic jet. Snapshot of the vorticity norm in

the flow field and of the fluctuating pressure outside in the planez= 0 243

6.6 LES of a ReD = 4 105 subsonic jet. (a) Pressure spectra at

(x= 11r0,r = 15r0). (b) Profiles of v

rms

/uj in the shear layer for r = r0.

Different simulations: LESac (- -), LESampl (. . . . . . ), LESshear (- - -),

LESmode ( ) 244

6.7 Schematic of a turbulent jet issuing into a still fluid 247

6.8 OASPL directivity at a distance of 30Djfrom the unheated, Mach 0.9

jet exit 249

6.9 Centerline distribution of streamwise root-mean-square fluctuations 254

6.10 Centerline distribution of density root-mean-square fluctuations

normalized by the difference (j ) 255

6.11 Far-field OASPL taken at a distance of 30Dj from the nozzle exit 256

6.12 Integral Lagrangian time scale of streamwise fluctuations near the end

of the potential core 257

6.13 One-thirdoctave spectral comparisons of an unheated, Mach 0.5 jet

of Bodony and Lele (2004) with the 195 m/s data of Lush (1971) 258

6.14 Azimuthal correlation of the far-field sound field of LES data from

Bogey, Bailly, and Juv e (2003) ( ) and Bodony and Lele (2004) () 258

6.15 Far-field OASPL taken at a distance of 30Dj from the nozzle exit 260

6.16 Far-field acoustic spectra taken at a distance of 30Dj from the

nozzle exit 260

6.17 Transition toward a wake mode for large L/ratio (2D DNS of the

flow over an L/D = 4 cavity, at M = 0.5, and ReD = 4800) 265

6.18 LES of a deep cavity. 268

6.19 Influence of the boundary layer turbulence on cavity noise 270

6.20 Mode switching 271

6.21 The plate model 275


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xvi LIST OF FIGURES AND TABLES

6.22 Sketch of the experimental setup 278

6.23 Wall-pressure transducer positions on the elastic steel plate 279

6.24 Vibroacoustics measurements: (+) accelerometers and ()

microphones positions 280

6.25 General mesh dimensions 2806.26 General sizes of the mesh 281

6.27 Detailed mesh around the obstacle 281

6.28 Contours of the streamwise mean velocityU1/U0 near the ruler in the

median plane 283

6.29 Streamwise velocity fluctuationsurms/U0 near the ruler in the

median plane 283

6.30 Velocity profiles at the origin of the reference: (- -) measurement;

(+ + +) simulation 284

6.31 Pressure coefficient 285

6.32 Wall-pressure fluctuation rms levels calculated at various positions

along the median plane 285

6.33 Comparison of calculated ( ) and measured (+ + +) wall-pressure

fluctuation rms levels on the plate 286

6.34 PSD of wall-pressure fluctuations measured on the flat plate 287

6.35 Coherence2 of wall-pressure fluctuations measured on the flat plate

for streamwise points using the same notation as in Figure 6.34 288

6.36 Coherence2 of wall-pressure fluctuations measured on the flat plate

for spanwise points using the same notation as in Figure 6.34 289

6.37 Phase velocityUp of wall-pressure fluctuations measured on the flat

plate for streamwise points using the same notation as in Figure 6.34 290

6.38 Acceleration PSDaa channel 26 291

6.39 Acoustic pressure PSDpp channel 30 (Pref= 2 105 Pa) using the

same notation as in Figure 6.38 291

6.40 First mesh: detailed mesh around the obstacle 292

6.41 Comparison of the two simulations wall-pressure fluctuations DSP

on the plate 292

6.42 Comparison of the two simulations acoustic pressure in cavity

using the same notation as in Figure 6.41 293

6.43 Numerical simulation of airfoil aerodynamic noise: possible hybrid

strategies 295

6.44 Sketch of the computational domains to determine trailing-edge noise

with the hybrid approach 297

6.45 Coordinate system and nomenclature used to determine corrections

for a 2D acoustic simulation 301

6.46 LES subdomain at the trailing edge (left) and horizontal weighting

function (right) 304

6.47 Damping function |F(d)| over vortical wavenumber in x1-direction

= 2/vscaled with the damping zone on- and offset width

d= (l2 l1)/2 305

6.48 LES grid with partially resolved plate and every second grid point

shown 305

6.49 Acoustic grid scaled with the plate lengthl 306

6.50 Enlargement of the leading- (left) and trailing-edge region (right) 307

6.51 Visualization of the instantaneous flow field 307


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LIST OF FIGURES AND TABLES xvii

6.52 APE source terms L = [ u] = (L x,Ly)

T, L x (left), Ly(right), and

CAA grid 308

6.53 Pressure contours of the trailing-edge problemM = 0.15,

Re= 7 105, at time level T = 3.0 with APE solution

equations (6.32, 6.33) 3096.54 Pressure contours of the trailing-edge problemM = 0.15,

Re= 7 105 at time level T = 3.0 310

6.55 Directivity1/2(,r, f) with = nondimensional power spectral

density (PSD) of p2(,r)/c

2

2, i.e.,

0 (,r, f)df = p2(,r)/

c

2

2310

6.56 Comparison of the trailing-edge noise directivities1/2(,r, f) for

r = 1.5 applying Equations (6.32, 6.33) ( = PSD of p2) and M ohrings

(1999) acoustic analogy ( = PSD of B2), Equations (6.43. 6.44) 311

6.57 Sound-pressure level (SPL) versus frequency for a receiving point in

r = 1.5 above the trailing edge for various directions (see Figure 6.45) 3116.58 Generation of a periodical source term via window weighting 313

6.59 CAA grid 313

6.60 A harmonic test source over the trailing edge (left) and directivities

obtained for M= 0,0.088 with LEE and APE (right) applied 314

6.61 APE source term ( u)y(left) and sound radiation from the trailing

edge (right) 315

6.62 Computational grid 319

6.63 Contours of instantaneous Mach-number isovalues 320

6.64 Flow streamlines at the trailing edge: instantaneous (above) and

time-averaged (below) 3216.65 Wall-pressure fluctuations on pressure and suction sides near the TE 322

6.66 Evolution of the wall-pressure PSD along the chord 323

6.67 Evolution of the wall-pressure PSD along the chord 324

6.68 Wave-numberfrequency spectrum of wall-pressure fluctuations

on the airfoil suction side at x/C= 0.9 324

6.69 Wave-numberfrequency spectrum of wall-pressure fluctuations

on the airfoil suction side at x/C= 0.5 325

6.70 Instantaneous isovalues of pressure fluctuations obtained from

LES data 326

6.71 Evolution of the wall-pressure spectra along the vertical gridline x= C(starting from the TE upper corner) with respect to the

vertical distancez 326

6.72 Spanwise evolution of the coherence of the surface-pressure field on

the suction side near the TE (x/C= 0.9958). The frequency

bandwidths are integrated 327

6.73 Spanwise evolution of the coherence of the pressure field at distance

z0 = 37.9 mm from the TE at x/C= 1 328

6.74 Final problem-adapted acoustic grid 328

6.75 Final problem-adapted acoustic grid (closer view) 330

6.76 Isovalue contours of instantaneous pressure fluctuation field(range 2 Pa, black and white) computed from (i) LES inside the

injection interface and (ii) E3P (from LES data injection) outside the

injection interface 331


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xviii LIST OF FIGURES AND TABLES

6.77 Isovalue contours of instantaneous pressure fluctuation field

(range 2 Pa, black and white) computed from (i) LES inside the

injection interface and (ii) E3P (from LES data injection) outside the

injection interface (closer view) 331

6.78 Isovalue contours (range 3 Pa black and white) of instantaneouspressure fluctuation field computed from (i) LES data inside the

injection interface, (ii) Euler data (from LES data injection) between the

injection interface and the Kirchhoff control surface, and (iii) from

Kirchhoff integration data beyond the Kirchhoff control surface 333

6.79 Numerical mesh (2D plane) 335

6.80 Sound-pressure level of LES 337

6.81 Sound-pressure level of 3D URANS 337

6.82 Experimental setup 338

6.83 Instantaneous streamlines in 2D URANS simulation 339

6.84 Instantaneous streamlines in LES with adaptive model 340

6.85 Lift and drag coefficients of the cylinder in the third-finest grid 340

6.86 Lift and drag coefficients of the cylinder in the second-finest grid 341

6.87 Lift and drag coefficients of the cylinder in the finest grid 341

6.88 Acoustic density fluctuations of 2D URANS simulation in the finest grid 341

6.89 Sound-pressure level of 2D URANS simulation in finest grid 342

6.90 Acoustic density fluctuations of LES with adaptive model in

second-finest grid 342

6.91 Sound-pressure level of LES with adaptive model in second-finest grid 343

6.92 Acoustic density fluctuations of 3D LES simulation in finest grid 343

6.93 Sound pressure level of LES with adaptive model in finest grid 343

6.94 Sound pressure level of LES in finest grid with Smagorinsky and Lilley

model 344

6.95 The Ahmed body from Ahmed et al. (1984) (isosurface of zero

streamwise velocity from Kapadia et al. 2003) 345

6.96 Mesh for the CFD model from Volkswagen 346

6.97 Streamlines in the wake of the CFD model 347

6.98 Vorticity in the wake of the CFD model 347

6.99 Pressure coefficient in the symmetry plane of the CFD model 348

6.100 Sound-pressure level at an observer point ofx= 10m, y= 10m,

andz= 1 m 348

6.101 Aerodynamic computational domain 351

6.102 Acoustic computational domain 351

6.103 LES velocity field; longitudinal component (U = 14ms1,

t= 6.6 102 s) 352

6.104 Acoustic results: acoustic power radiated by the diaphragm with

respect to the mean velocity (top) and acoustic power spectrum for

U = 14ms1 (bottom) 352

6.105 Geometry of the cavity duct system 353

6.106 Snapshots of the pressure in the duct (left) and the vorticity in the

cavity (right) during a period of the oscillation 354

6.107 Geometry of the sudden enlargment 355

6.108 Snapshots of the Mach number for1= 5.5 355

6.109 Snapshots of the Mach number for2= 2.65 356

6.110 Opel 2004 Astra 360


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LIST OF FIGURES AND TABLES xix

6.111 Lilley turbulence shear-source distribution illustrated by isosurfaces for

the idealized wing-mirror example of Siegert et al. (1999) 361

6.112 Mesh frequency cutoff (MFC) estimate; idealized wing-mirror example

of Siegert et al. (1999) 362

6.113 Predicted versus measured pressure spectra; idealized wing-mirrorexample of Siegert et al. (1999) 363

6.114 Mach 0.85 cavity: symmetry-plane snapshot att= 0.3 s; DES/k

(top) and URANS/k (bottom) 365

6.115 Overall (a) and band-limited (b)Prms along cavity ceiling centerline 366

6.116 PSD (kPa2/Hz) at locationx/L = 0.45 367

6.117 Diesel injector primary liquid spray breakup; liquid-free surface with

synthetic inlet perturbation (top) and without inlet perturbation (bottom) 367

6.118 Audi A2 full-vehicle geometry with localized domain shown in dark 368

6.119 Instantaneous velocity magnitude field 368

6.120 SPL against frequency at Microphone 4 369

6.121 Experimental (top) and simulated (bottom) pressure trace to 0.3 s at

x/L = 0.95 369

6.122 Sampling effects on overall Prms (kPa) along the cavity ceiling for

M219 experimental data 370

6.123 Sampling effects on overall Prms (kPa) along the cavity ceiling for

CFD data 370

6.124 Resonator geometry: application challenge from BEHR GmbH in the

DESTINY-AAC project 372

6.125 Velocity contours (top), pressuretime traces (bottom left), and spectral

magnitude (bottom right) at three bulk velocities (4, 8, and 12 m/s)

taken at the neck of the resonator 373

6.126 Acoustic response for 8 m/s case at the microphone 374

6.127 Experimental prototype with inlet cylinder and outlet filter removed

and locations of far-field monitors 374

6.128 Comparison of steady-state RANS and snapshots from the DES

calculation 375

6.129 Surface acoustic pressure (Pa) on the exterior model (a) and acoustic

pressure in the far-field (b) 375

6.130 Computed and measured dB(A) levels at the nine microphone

locations at the blade-passing frequency (BPF) 376

Tables

1.1 Sound-pressure levels for common sounds 2

3.1 Examples of usual spatial convolution filters 94

3.2 Various decompositions for the nonlinear terms 97

3.3 Resolution requirements referred to Kolmogorov length scale used in

DNS based on spectral methods of some incompressible

homogeneous and wall-bounded flows 105

3.4 Typical mesh size (expressed in wall units) for DNS and LES of

boundary layer flow 107

3.5 Definition of simulation types for compressible flows 109

3.6 Modified wave-number analysis of some classical centered finite

difference schemes 109


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xx LIST OF FIGURES AND TABLES

5.1 Coefficients for the DRP scheme of Equation (5.27) 174

5.2 Coefficients for filter formula 5.72 188

5.3 Optimized coefficients of the amplification factor for the LDDRK schemes 200

5.4 Typical mesh sizes (expressed in wall units) for a boundary layer flow

using DNS, wall-resolved LES, and LES with an appropriate wall model 2096.1 LES of a ReD = 4 105 subsonic jet. Sideline sound levels and

vrms-maxima in the shear layer for the different simulations 244


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Contributors

Jean-Marc Auger

PSA Peugeot Citroen

1 route de Gisy

F-78943 Velizy-Villacoublay Cedex

FRANCE

e-mail: [email protected]

Dr. Christophe Bailly

Centre Acoustique LMFA & UMR CNRS

5509

Ecole Centrale de Lyon36, avenue Guy de Collongue

F-69134 Ecully

FRANCE


Dr. Paul Batten

Metacomp Technologies, Inc.

28632-B Roadside Drive Suite 255

Agoura Hills, CA 91301

USA


Dr. Daniel J. Bodony

Stanford University

Department of Aeronautics and

Astronautics

Stanford, CA 94305-4035

USA


Dr. Christophe Bogey

Centre Acoustique LMFA & UMR CNRS

5509

Ecole Centrale de Lyon

36, avenue Guy de Collongue

F-69134 Ecully

FRANCE


Priv.-Doz. Dr.-Ing. Michael Breuer

Lehrstuhl fur Stromungsmechanik

(LSTM)

Universitat Erlangen-Nurnberg

Cauerstr. 4

D-91058 Erlangen

GERMANY


Ir. Tim Broeckhoven

Vrije Universiteit Brussel Department of

Mechanical Engineering

Fluid Mechanics and Thermodynamics

Research Group

Pleinlaan 2

B-1050 Brussels

BELGIUM


xxi


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xxii CONTRIBUTORS

Fabien Crouzet

Electricite de France

Analysis in Mechanics and Acoustics

Department

1 avenue du General de GaulleF-92141 Clamart Cedex

FRANCE


Jean Paul Devos

Electricite de France

Analysis in Mechanics and Acoustics

Department

1 avenue du General de Gaulle

F-92141 Clamart Cedex

FRANCEe-mail: [email protected]

Dr.-Ing. Roland Ewert

DLR Institute of Aerodynamics and Flow

Technology

Technical Acoustics

Lilienthalplatz 7

D-38108 Braunschweig

GERMANY


Oliver Fleig

The University of Tokyo

Graduate School of Engineering

Department of Mechanical Engineering

7-3-1 Hongo, Bunkyo-Ku

Tokyo 113-8656

JAPAN


Xavier Gloerfelt

Laboratoire SINUMEFENSAM (Ecole Nationale Superieure

dArts et Metiers)

151, boulevard de lHopital

F-75013 Paris

FRANCE


Prof. Dr. Ir. Avraham Hirschberg

Faculteit Technische Natuurkunde

Technische Universiteit EindhovenCC 2.24, Postbus 513

NL-5600 MB Eindhoven

THE NETHERLANDS


Prof. Fang Q. Hu

Department of Mathematics and Statistics

Old Dominion University

Norfolk, VA 23529

USAe-mail: [email protected]

Dr. Thomas Huttl

MTU Aero Engines GmbH

Dachauer Str. 665

D-80995 Munchen

GERMANY


Andre Jacques

Mcube

54, Rue Montgrand - BP 232

F-13178 Marseille Cedex 20

FRANCE


Dr. Manuel Keler, Dipl.-Phys.

Institut fur Aerodynamik und Gasdynamik

Universitat Stuttgart

Pfaffenwaldring 21

D-70550 Stuttgart

GERMANY


Prof. Dr. Ir. Chris Lacor

Vrije Universiteit Brussel



Research Group

Pleinlaan 2

B-1050 Brussels

BELGIUM


Philippe Lafon

Laboratoire de Mecanique des Structures

Industrielles Durables

(LaMSID)

UMR CNRS EDF 2832

1 avenue du General de Gaulle

F-92141 Clamart Cedex

FRANCE



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CONTRIBUTORS xxiii

Sanjiva K. Lele

Stanford University

Department of Aeronautics and

Astronautics & Department of

Mechanical EngineeringStanford, CA 94305-4035

USA


Dr.-Ing. Franco Magagnato

Fachgebiet Stromungsmaschinen

Universitat Karlsruhe (TH)

Kaiserstrasse 12

D-76128 Karlsruhe

GERMANY


Eric Manoha

ONERA/DSNA/BREC

BP 72

F-92322 Chatillon Cedex

FRANCE


Fred G. Mendonca

CDadapco

CFD Engineering Services Manager,

London

CD adapco Group, UK

200 Shepherds Bush Road

London W6 7NY

ENGLAND


Dimitri Nicolopoulos

Mcube



FRANCE


Fred Perie

Mcube



FRANCE


Ir. Jan Ramboer




Research GroupPleinlaan 2

B-1050 Brussels

BELGIUM


Dr. Sjoerd W. Rienstra

Department of Mathematics

and Computer Science

Eindhoven University of Technology

P.O. Box 513

NL-5600 MB EindhovenTHE NETHERLANDS


Prof. Pierre Sagaut

LMM - UPMC/CNRS

Laboratoire de modelisation en mecanique

Universite Pierre et Marie Curie

Boite 162, 4 place Jussieu

F-75252 Paris Cedex 05

FRANCE


Univ.-Prof. Dr.-Ing. Wolfgang Schroder

Lehrstuhl fur Stromungslehre und

Aerodynamisches Institut

RWTH Aachen

Wullnerstr. zw. 5 u. 7

D-52062 Aachen

GERMANY


Ir. Sergey Smirnov




Research Group

Pleinlaan 2

B-1050 Brussels

BELGIUM


Philippe Spalart

Boeing Commercial AirplanesP.O. Box 3707

Seattle, WA 98124-2207

USAe-mail: [email protected]


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xxiv CONTRIBUTORS

Marc Terracol

ONERA

29 avenue de la Division Leclerc

F-92320 Chatillon

FRANCEe-mail: [email protected]

Sandrine Vergne

PSA Peugeot Citroen

2 route de Gisy

F-78943 Velizy-Villacoublay Cedex

FRANCE


Dr. Claus Wagner

Deutsches Zentrum fur Luft- und

Raumfahrt e.V., DLR

Institut fur Aerodynamik und

StromungstechnikAbt. Technische Stromungen

Bunsenstrae 10

D-37073 Gottingen

GERMANY



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Preface

Two branches of the same tree are growing together: Acoustics and the large-eddy

simulation (LES) technique are based on the same fundamental equations of fluid

dynamics. In the past, both scientific disciplines developed independently from each

other. Acoustics is one of the classical disciplines of mechanics, having its roots in Greek

and Roman times. LES is a comparatively young field of research that has benefited from

the exponential growth in computational possibilities over the last few decades. Each

scientific community has developed its own methods, definitions, and conventions, and

it sometimes seems that experts and scientists in acoustics and LES techniques speak

different languages. During the last few years, the LES and the acoustics communitiesrealized that LES can be a comprehensive tool for acoustical research and design and

intensified its use.

This book presents the current state of the art for LES used in acoustical inves-

tigations and comprises 19 contributions from 30 authors, each an expert in his field

of research. A general introduction to the subject is followed by descriptions of the

theoretical background of acoustics and of LES. A chapter on hybrid RANSLES for

acoustic source predictions follows. More details are given for numerical methods,

such as discretization schemes, boundary conditions, and coupling aspects. Numerous

applications are discussed ranging from simple geometries for mixing layers and jetflows to complex wing or car geometries. The selected applications deal with recent

scientific investigations at universities and research institutes as well as applied studies

at industrial companies. Side areas of LES for acoustics are addressed in a contribution

on vibroacoustics.

The book is a collection of different methods, tools, and evaluation methodologies.

Currently it is not possible to offer a perfect solution methodology that generally covers

all possible applications. Although interesting results of several commercial codes

are presented, a recommendation for any specific solver cannot be made because a

benchmark of the codes has not been established and several other codes have notbeen considered yet. Each method, both scientific and commercial, has its individual

advantages and weaknesses. It was also not our intention to harmonize the definitions

xxv


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xxvi PREFACE

and conventions in acoustics and LES computing. Therefore, the same nomenclature

is not used by all authors.

The book is intended to be used by students, researchers, engineers, and code

developers willing to become more familiar with the use of the LES technique for

acoustical studies. The limitations of the method have been outlined as well as itsrequirements. The reader should acquire an impression of possible and appropriate

applications for this methodology. The editors would welcome any initiatives motivated

by this book for international cooperation in the development or application of LES for

acoustics.

The idea for this book came from Eric Willner, the former commissioning editor for

engineering at Cambridge University Press, when he read the first call for papers for

the International Workshop on LES for Acoustics organized by Thomas Huttl, Claus

Wagner, and Jan Delfs in Gottingen, 2002. At this time, Cambridge University Press

was actively seeking a book on LES for acoustics for its aerospace series. Thomas Huttl

and Claus Wagner agreed to edit a scientific book based on the contributions of the

workshop in Gottingen. Several speakers and participants of the workshop and other

experts promised to contribute to the book, which was conceived as more of a scientific

handbook than a simple workshop proceedings. Pierre Sagaut separately developed the

idea of a book on LES for acoustics and joined the team of editors.

The book would not exist without the contributions from each of the authors. The

editors are not only grateful for these contributions but also for valuable review com-

ments from several authors during two book reviews as well as interesting scientificdiscussions of review comments and proposals. We would also like to thank Peter

Gordon, Senior Editor of Engineering at Cambridge University Press, for his help in

preparing the book but also for enthusiasm, patience, and confidence during the last 2

years when the progress of the book was sometimes slow but never stopped.

Thomas Huttl gratefully acknowledges the advice and comments of MTU Aero

Engines aeroacoustics specialist Fritz Kennepohl, who introduced him to the secrets of

acoustics during the TurboNoiseCFD research project.

Pierre Sagaut, Thomas Huttl, and Claus WagnerEurope, May 2006

International ERCOFTAC-DGLR-DLR-Workshop on LES for Acoustics organized by T. Huttl, C.

Wagner and J. Delfs, German Aerospace Center (DLR), Gottingen, Germany, 78 October 2002.


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LARGE-EDDY SIMULATION FOR ACOUSTICS


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1 Introduction

1.1 The importance of acoustic research

Thomas H uttl

There are some aspects of acoustics that significantly affect the quality of our daily lives.

By speaking, we transfer information and knowledge from one person to another. The

sound of rain, of wind or anything else gives us orientation and aids optical perceptions.

Music can fascinate us and stimulate our emotions and moods. Pleasant sounds and

music positively affect health by their calming character.The negative side of acoustics is noise. Noise is the most commonly cited form

of environmental pollution. Noise is easily detected by the human hearing system. Its

effects can be cumulative, and it influences our work environment as well as our leisure.

Even the quality of our sleep is reduced if we are exposed to noise. In recent decades,

the effects of noise on people have been studied intensively.

1.1.1 Health effects

There is no doubt that noise has an impact on health. Very loud sounds are clearly highlyinjurious to people as well as animals. Table 1.1 shows sound-pressure levels (dB(A))

for common sounds. At sound-pressure levels of 160165 dB(20 kHz) flies die when

exposed only for a short time. With these exposures levels, human beings become tired,

may experience facial pain, and may develop burned skin. When the sound pressure

is lowered, reactions to the sound decrease. Long-term exposure to high noise levels

of about 90 dB(A) can result in permanent hearing loss. Even for a steady daily noise

level of 75 dB(A) for 8 hours per day, there is a risk of permanent hearing damage after

40 years of exposure. Apart from the auditory effects of noise, nonauditory effects on

health are well known. Noise can induce a range of physiological response reactionssuch as increases in blood pressure, heart rate, and breathing, and these reactions are not

confined to high noise levels and sudden noise events but are also true for noise levels

commonly experienced in noisy environments such as busy streets (Nelson 1987).

1


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2 INTRODUCTION

Table 1.1. Sound-pressure levels for common sounds

(dB(A)) Common sounds

30 whisper

50 rainfall, quiet office, refrigerator60 dishwasher, normal conversation

70 traffic, vacuum cleaner, restaurant

80 alarm clock, subway, factory noise

90 electric razor, lawnmower, heavy truck or road drill at 7 m

100 garbage truck, chain saw, stereo system set above halfway mark

110 rock concert, power saw

120 jet takeoff, nightclub, thunder

130 jack hammer

140 shotgun, air raid system

180 rocket-launching pad

Exposure to excessive noise during pregnancy may result in high-frequency hearing

loss in newborns and may be associated with prematurity and intrauterine growth

retardation (American Academy of Pediatrics 1997).

1.1.2 Activity effects

Noise influences human activities such as sleep, communication, and peoples general

performance. Studies have shown that noise can affect sleep in many ways. Noise may

shorten the length of the sleep period and increase the number or frequency of awaken-

ings, and it may affect the duration of the various stages of sleep. Given the importance

of sleep for individual health, a perturbation of sleep is usually not tolerated by people.

First- and second-grade school children chronically exposed to aircraft noise have

significant deficits in reading as indexed by standardized reading tests administered

under quiet conditions. Chronic noise may also lead to deficits in childrens speech ac-

quisition (Evans and Maxwell 1997). Other studies show the impact of noise from

aircraft, road traffic, and trains on long-term recall and recognition (Hygge 1993;

Groll-Knapp and Stidl 1999). Mood and behavioral abnormalities can also be relatedto noise exposure.

1.1.3 Annoyance

In addition to the direct effects of noise on sleep, communication, and performance there

are also indirect consequences of annoyance or disturbance that are related to the way

a person feels about noise. Annoyance is a very complex psychological phenomenon,

and it is scarcely possible to define or measure it here. For physically loud sounds the

perceived annoyance is often equivalent to the perceived loudness. For physically softsounds (rustling papers at the movies, people talking while watching television), the

perceived annoyance deviates greatly from perceived loudness. Thus, for physically soft

sounds, more attention is paid to other aspects of the sound than to the loudness-related


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1.1 THE IMPORTANCE OF ACOUSTIC RESEARCH 3

sound-pressure level (Berglund, Preis, and Rankin 1990). Nevertheless, annoyance

effects can also influence mood and behavior and can ultimately cause even severe

health problems.

1.1.4 Technical noise sources

Many noise sources are man-made especially transportation noise from road traffic,

aircraft, and trains. Other technical noise sources can also be annoying such as wind

turbines or cooling and climate systems. Noise can be produced by several physical

interaction mechanisms:

Solid-body friction noise (e.g., gearbox), Solid-body vibration (e.g., unbalanced rotating machines),

Combustion noise (e.g., piston engines), Shocks (e.g., explosions or pneumatic hammer), and Aerodynamic noise (e.g., vortexstructure interaction)

In this book we concentrate on aerodynamic, flow-induced noise.

Aerodynamic noise is one of the major contributors to external vehicle noise emis-

sion as well as of internal vehicle noise due to the transmission of the externally

generated noise through structure and window surfaces into the cabin. Aerodynamic

noise becomes dominant at driving speeds exceeding 100 km/h when compared with

structure-borne, power train, and tire noise, for which substantial noise reduction hasbeen achieved. The interaction of the flow with the geometrical singularities of the vehi-

cle body produces unsteady turbulent flows often detached resulting in an increased

aerodynamic noise radiation (Vergne et al. 2002).

Aircraft noise is dominant for residents near airports when planes fly at low altitudes

such as during departure and landing. The engines, especially their free-jet flow but

also flaps, wings, airbrakes, landing gear, or openings contribute significantly to the

total sound emission. When an aircraft is flying at cruising altitude, the aerodynamic

noise of the aircraft body and propeller, or engine noise, can be annoying for passengers

and crew.For trains, the bow collector and the wheelrail interaction are dominant noise

sources. For high-speed trains, especially unconventional concepts like the magnetic

levitation hover train project Transrapid (Figure 1.1), the relevance of aerodynamic

noise is increased.

Wind turbines in operation emit aerodynamic noise that can be perceived by humans.

With respect to large wind turbines with low rotational speed, the main contribution to

aerodynamic noise is the narrow-band noise caused by bladetower interaction. Smaller,

fast-rotating wind turbines, on the other hand, emit broadband noise, which is mostly

caused by vortexblade interaction (Fleig, Iida, and Arakawa 2002).Cooling and climate systems are designed to regulate temperature and filter out pol-

lution. Their power units often emit tonal noise at constant frequency that is transported

through the duct system. Furthermore, tonal noise due to aeroacoustic resonance can


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4 INTRODUCTION

Figure 1.1. Magnetic levitation hover train project Transrapid.

be activated (Hein, Hohage, and Koch 2004). Although the noise level of cooling and

climate systems is usually very low, it is annoying and should be considered by the

designer.

1.1.5 Political and social reactions to noise

Noise is becoming generally accepted as an environmental and even health hazard to

the population. Public reaction to noise problems is causing governments to adopt laws,regulations, and guidelines for the certification of noise-emitting vehicles and machines

as well as for temporal or spatial limitations on their use. Aircraft and jet engine man-

ufacturers face increasingly stringent noise requirements for near-airport operations

worldwide (Bodony and Lele 2002a). Old-fashioned and noisy aircraft may not be oper-

ated from an increasing number of airports or their operators must pay additional fees for

noise emission. Some aircraft may not be operated during the night if their noise emis-

sion is too high. Airlines have to consider the noise-related airport fees in their operating

costs or reduce the noise emissions by adding new or additional noise-reducing devices

to their planes and jet engines. A sociocultural aspect of traffic noise is that the pricesfor houses and apartments are lower if they are close to highways and roads, railways,

or flying routes near the airports. Costly noise-reduction measures like fences, walls,

and special windows are required to compensate for the increased traffic noise.


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1.1 THE IMPORTANCE OF ACOUSTIC RESEARCH 5

Butterworth-Hayes (2004) describes the European Union (EU) plans to overtake

the United States as the largest aerospace power in the world by 2020. The 2001 re-

port European Aeronautics: A Vision for 2020, which was drawn up by a group of

wise men to advise the European Commission (EC) on the future of the continents

aerospace industry, laid out a series of research objectives that Europes civil aircraftmanufacturers must achieve to ensure dominance of the market. One of the key objec-

tives of Vision 2020 research is the halving of perceived aircraft noise. This means,

in particular, reducing external noise by 45 dB and 10 dB per operation in the short

and long terms, respectively. For rotorcraft, the objective is to reduce the noise foot-

print area by 50% and external noise by 6 dB and 10 dB over the short and long terms,

respectively.

1.1.6 Reactions of industry

The aircraft industry projects a growth in passenger kilometers of 100% or more in the

next 15 years. Satisfying the resulting demand for larger or faster airplanes, or both,

requires that new airplanes be designed. The same is true for future high-speed trains,

which, in order to be able to compete with air traffic, have to become faster as well.

This would boost the emitted noise levels tremendously if these trains were built based

on todays technology because the emitted aerodynamic noise increases approximately

with the fifth to sixth power of the vehicle speed (Schreiber 1995).

After having achieved significant progress in reducing the level of other primary

noise sources such as piston engine noise or road-contact noise, the automotive industry

is now contending with the major problem of interior and exterior noise related to

aerodynamic effects. Aeroacoustics is becomimg increasingly important in many other

fields such as the energy industry or personal computer manufacturing industry.

Sensitivity to noise is increasing all over the world. Therefore, significant noise

reduction in new airplanes, trains, and cars is mandatory if this growth in the trans-

portation system is to be accepted by the population and their political representatives.

This noise reduction can only be realized if the design process is guided by robust and

fast computational aeroacoustic methods. Owing to the lack of commercial software,

many companies and research institutes are using their specialized, self-developed,

in-house codes for solving engineering problems. Remarkable progress has also been

made by designers of commercial codes for aeroacoustic applications, although these

codes are currently still under development (Wagner and Huttl 2002).

1.1.7

Research on acoustics by LESAeroacoustics is the scientific discipline between fluid mechanics and classical acous-

tics. It considers sound generated by aerodynamic forces or motions originating from

(turbulent) flows (Ihme and Breuer 2002). Initially, experimental investigations were


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6 INTRODUCTION

used to derive some empirical relations for estimating the noise emission of new tech-

nical products. However, owing to strongly increased computer performance, the nu-

merical simulation of acoustic fields generated by fluid flow, called computational

aeroacoustics (CAA), has become very attractive. At this time no unique solution pro-

cedure exists for all acoustic problems. Instead, various strategies have been developed,each with individual advantages and disadvantages (Ihme and Breuer 2002).

For applications with complex, inhomogeneous flows and flow-induced noise

radiation, the most promising and commonly used numerical technique is to adopt

a hybrid approach. In such an approach, the sound-generation and sound-propagation

processes are considered separately. A nonlinear aerodynamic near field in which the

aerodynamic perturbations are generating the sound is matched to a linear acoustic

far field in which no flow or homogeneous flow exists and the sound waves are only

propagating. The underlying assumption is that there is no feedback of the acoustic

waves on the flow.

Coupled or hybrid approaches are currently being created by several research groups

and code developers. Such efforts have also been the focus of two recently finished

European research projects: Application of Large-Eddy Simulation to the Solution of

Industrial Problems (ALESSIA) and TurboNoiseCFD. The primary aim of the EU

ALESSIA project has been to develop software tools for the simulation of fluctuating

flows by large-eddy simulation (LES), with a particular focus on flow-induced acoustics

(Montavon 2002). Commercial computational fluid dynamics (CFD) and CAA codes

have been interfaced within ALESSIA.The aim of the TurboNoiseCFD project was to contribute to the objective of a

10-dB reduction in 10 years in aircraft external perceived noise through new design

technologies. To achieve this objective, the aircraft engine manufacturing industry

significantly enforces to reduce engine noise levels at the source. In response to this

challenge, new methods have been created that will aid in the design of low-noise

turbomachinery components based on the adaptation of existing CFD software and

its integration with propagation and radiation models. Besides other techniques, an

LES methodology has been tested for aeroacoustical evaluations of broadband noise

(Boudet, Grosjean, and Jacob 2003; Jacob et al. 2005).After the successful funding of noise reserach programs under the Fifth Research

Framework Program (19972001), the EC continues to invest money in research

projects aimed at reducing the environmental impact of aviation (fuel consumption,

noise pollution, and emissions of carbon dioxide (CO2), nitrous oxides (NOX), and

other chemical pollutants) in its Sixth Research Framework Program (20022006).

Other coupling methods are also called hybrid methods such as the coupling of the Reynolds-averaged

NavierStokes (RANS) approach and large-eddy simulation (LES) for detached-eddy simulation(DES); see Chapter 4.

Turbomachinery noise-source CFD models for low-noise aircraft designs. This project was funded by

the EC within the GROWTH Fifth Framework Program 19982002. ALESSIA is an ESPRIT Project funded at 50% by the EC.


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1.2 INTRODUCTION TO COMPUTATIONAL AEROACOUSTICS 7

1.2 Introduction to computational aeroacoustics

Manuel Keler

Computational fluid dynamics (CFD) has reached a level of maturity that permits many

industrially relevant problems to be solved routinely using commercially available tools,

although some difficult problems are still out of reach. Consequently, the research in-

terest in the fluid mechanics community has shifted slightly, and there is now a large

and still growing group of experts engaged in the field of acoustics. For a long time

their work was mostly based on analytical and experimental studies, but the astonish-

ing advances in computer technology have made a numerical approach feasible. That

approach is called computational aeroacoustics (CAA).

1.2.1 Definition

Numerous definitions exist for CAA reflecting the many people who have been

attached to this subject. We understand CAA here in the broadest possible sense

that is, as a process using some kind of numerical computation to produce acousti-

cal information for aerodynamic phenomena. That obviously includes all flavors of

acoustical transport techniques (Lighthills acoustic analogy, the Kirchhoff method, the

Ffowcs WilliamsHawkings equation), linearized Euler approaches, combined proce-

dures with CFD, semiempirical treatments like stochastic noise generation (SNGR),and even compressible direct numerical simulation (DNS) admittedly very rarely

used for acoustic analysis these days.

Experimentors evidently use numerical computations for data processing and eval-

uation as well. However, although experimental studies are of substantial significance

in the efforts to find appropriate models, tune constants, and validate computations,

they do not constitute CAA.

1.2.2 History

Even though sufficient computing power has become available only recently, CAA has

quite a long tradition in the fluid mechanics community. Among the earliest efforts was

the paper by Gutin (1948) published first in Russia in 1936. However, modern CAA

rests mostly on the shoulders of Sir James Lighthill (1952, 1954), who published what

are certainly the most influential and therefore the most cited papers in aeroacoustics.

He introduced the idea of representing sound as the difference between the actual flow

and a reference flow usually a quiescent medium at rest. Because sound pressure and

velocities are in general small perturbations around a background flow, approximations

are possible to simplify the problem. In the late 1960s, his acoustic analogyapproachwas extended by Ffowcs Williams and Hawkings (1969) to the case of moving surfaces

immersed in the flow (and acoustic) field, which is second in citations only to the work

of Lighthill. Another classic of its time was Goldsteins (1976) book.


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8 INTRODUCTION

Nevertheless, owing to the highly abstract and mathematical presentation of the

subject and the lack of appropriate aerodynamic simulation data, progress was slow

during the next two decades. Only sound emitted from jets received considerable interest

in the early days of CAA mostly for their simple geometry (because there are no solid

walls) as well as the importance of this sound source for the noise levels of aircraftdeveloped at that time. Many discoveries of basic sound-generation mechanisms and

scaling laws date from this time.

Computers have only recently become powerful enough to tackle other, more dif-

ficult aeroacoustical problems one way or another with sufficient accuracy to provide

results valuable for industry in the design process. Associated with increasing societal

interest in noise reduction, another golden age in aeroacoustics dawned in the late 1980s

and early 1990s. CAA gained momentum since then, and there is still no slowdown in

sight.

1.2.3 Aeroacoustics

Aerodynamic noise occurs because of two basically different phenomena. The first

one isimpulsivenoise, which is a result of moving surfaces or surfaces in nonuniform

flow conditions. The displacement effect of an immersed body in motion and the non-

stationary aerodynamic loads on the body surface generate pressure fluctuations that

are radiated as sound. This kind of noise is deterministic and relatively easy to ex-

tract from aerodynamic simulations because the required resolution in space and timeto predict the acoustics is similar to the demands from the aerodynamic computation.

Aerodynamic noise arises primarily from rotating systems (e.g., helicopter rotors, wind

turbines, turbine engine fans, and ventilators). If the surfaces move at speeds compa-

rable to the speed of sound or there is an interaction between a rotor and a stator wake,

these tonal noise components can be dominant.

The other noise mechanism is the result ofturbulenceand therefore arises in nearly

every engineering application. Turbulence is by its very nature stochastic and therefore

has a broad frequency spectrum. Interestingly enough, turbulent energy is converted

into acoustic energy most efficiently in the vicinity of sharp edges (e.g., at the trailingedge of an aircraft wing). In this case the uncorrelated turbulent eddies flowing over the

upper and lower sides of the edge have to relax with each other, generating locally very

strong equalizing flows that result in highly nonstationary pressure spikes. Another

major source of turbulence sound is jet flows, in which the shear layer in the mixing

zone again radiates into the far field.

A third but here neglected phenomenon is the case of combustion noise, which is

a result of the chemical reactions and the subsequent introduction of energy into the flow.

As previously stated, turbulence noise almost always exists, and as a consequence

aerodynamic noise is usually a broadband noise sometimes augmented by narrow-bandtonal components coming from impulsive noise sources. Impulsive noise can usually

be derived from nonstationary aerodynamic calculations. Like CFD, turbulence noise is


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much more difficult to simulate because the turbulence has to be either simulated fully,

as in DNS, or modeled as in the Reynolds-averaged NavierStokes (RANS) approach,

or something in between, as in large-eddy simulation (LES) or hybrid computations.

1.2.4 Conceptual approaches

In the CFD area, several tools have been developed to a very high level of maturity that

makes them not only useful as a scientific research instrument but also as an industrial

design tool. Some of these tools have reached sufficient reliability to make them helpful

for users not considered experts in their field. However, pushing tools to their limits

can lead to disaster and often to nonobvious paths.

Because CAA is a more recent domain of activity, the situation is much less fa-

vorable. There is not yet a clear path to follow for reliable acoustical information for

each and every application, which may consist of such different things as a cooling fan

for a personal computer or a supersonic jet driving an airplane. Consequently, many

different techniques exist nowadays, each working well in one area and failing totally

in another. We try to classify a few of them in the following paragraphs.

Direct methods can be considered the most exact technology for CAA and are

comparable to the DNS in the CFD field. The complete, fully coupled compressible

Euler or NavierStokes equations are solved in the domain of interest for the unsteady

combined flow and acoustic field from the aerodynamic effective area down to the

far-field observer. They do not include any modeling of the sound (besides, possibly, aturbulence model) and thus do not suffer from modeling or approximation errors. Of

course, they require tremendous computational resources because especially in the

case of small-Mach-number flows flow and acoustics represent a multiscale problem

with its inherent difficulties. The difficulty here is that the small acoustic perturbations

are not drowned out by numerical errors of the much larger aerodynamic forces. Space

and time resolution requirements for the aerodynamic data combined with the large

distances up to an observer in the far field give rise to ridiculously high numbers of cells

and time steps. Even if the necessary computer power were available, the discretization

schemes well known from CFD do not work very well in CAA applications becausethey have dispersion and diffusion errors that are much too high. A plane wave is usually

severely distorted and dampened after being transported for just a few wavelengths,

which is clearly too short for the common case of an observer in the far field.

Direct methods are deceptively attractive because well-known and well-understood

CFD packages promise to provide aerodynamic and aeroacoustic data at the same

time. Sometimes they do work surprisingly well mostly in those cases in which the

differences between aerodynamics and aeroacoustics are negligible as in transonic

problems. However, for many or most other problems they do not because the basic

requirements of CFD and CAA are just too different. Several CFD schemes are tunedspecifically to suppress spurious acoustic waves, which of course is a bad idea when one

is interested in the acoustic properties of a problem at hand. CFD usually is designed


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10 INTRODUCTION

to solve a near-field problem because the perturbations from the mean flow vanish

quickly. Furthermore, the flow in this region is usually highly nonlinear but basically

stationary, or at least changing only slowly (aside from turbulent motions). Acoustics,

on the other hand, is clearly a far-field problem in which sound is generated locally

in the aerodynamic active area and passively radiated outside to an observer with asmaller exponent of decrease. Outside the aerodynamic active area where the sound

is generated the perturbations are small, and a linear description is usually sufficient.

However, noise is inherently unsteady with time scales quite comparable to turbulent

eddies even if the spatial wavelengths are large compared with aerodynamic ones by

an order of the reciprocal of the Mach number.

These different properties (linear versus nonlinear, far-field versus near-field, time-

dependent versus (quasi) stationary, large versus small spatial scale) obviously necessi-

tate different tradeoffs regarding computational schemes. No currently known schemes

score best on all possible requirements of CFD and CAA; therefore, methods espe-

cially adapted for the specific demands of an application will always be superior to

more general ones that necessarily have to balance all their characteristics carefully.

Most of the computational aeroacoustic tools in successful use nowadays are there-

fore of thehybridtype in which sound generation due to aerodynamics is more or less

decoupled from the acoustic transport process to the far field, making it possible for

tailored algorithms to be used for both tasks. This decoupling leads straightforwardly

to an arbitrary combination of a soundgeneration method with another soundtransport

method.

CFD Sources: On the sound-generation side some kind of CFD tool is primarily

in place. If a direct coupling mechanism to the transport method is used it has

to provide sound data in the coupling region (surface or volume). In this case

aeroacoustic applicability is very important; that is, dispersion and diffusion

errors must be at the lowest possible levels. However, the demands are not as high

as for direct methods because an undistorted transport has to be sustained only up

to the coupling regions, which are seldom farther away than a few wavelengths.

A small error in phase and amplitude is therefore acceptable.Semiempirical Sources: Alternatively, the sound sources can be reconstructed

semiempirically from CFD data derived mostly from turbulence quantities. A

straightforward, steady RANS computation provides information about turbu-

lent length and time scales that translate by empirical relations into sound-source

spectra. These spectra are then radiated by one of the transport methods described

in the next paragraph. Of course, this process depends heavily on the soundness of

the empirics and the validation data used to calibrate them. However, the methods

can be very fast and reliable for obtaining a judgment between two close config-

urations (e.g., in the acoustic optimization of an airfoil shape). In such situations,

with a small and well-defined application domain close to the calibration data,

they are fairly useful.


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After identification of the sound sources in the aerodynamic active area, the noise

generated in this near field has to be transported outside to an observer. Again we may

choose between two alternatives:

Computational transport methods are similar to a CFD computation, in the sense

that they solve some partial differential equations(s) in the entire field up to the

observer. In contrast to direct methods, they do not simulate the aerodynamic

area as well but concentrate on the solely acoustic domain. Therefore, several

assumptions and, consequently, approximations are allowable to achieve accu-

rate solutions efficiently. Usually computational transport methods solve simple

equations such as the linearized Euler equations (LEE) or simply the wave equa-

tion. Because these are both linear, many problems encountered with the full

set of equations do not occur, and consequently the discretization schemes canbe highly tuned to reach the desired low level of dispersion and diffusion er-

rors. On the boundary between the CAA domain and the CFD computation, the

CFD solution is used as a boundary condition for the CAA simulation. Owing

to the change in discretization, resolution, and even equations the definition of

proper transmission conditions is a highly nontrivial task. The computational

cost can grow tremendously if the observer is far away because all the space in

between has to be solved for. However, if an entire noise carpet computation is

required in contrast to a single-observer spectrum, this approach may be ben-

eficial inasmuch as the cost is the same regardless of the number of observerpoints.

Analytical transport techniques employ an integrated form of the relevant acous-

tic propagation equation either Kirchhoffs surface integral or the Ffowcs

WilliamsHawkings (FWH) equation. In this case the sound pressure at an

observer at a specific point in time is computed by an integration-of-source term

along a surface either a physical one or surrounding the aerodynamic area and

possibly additional volume integrals outside the surface in the case of the FWH

equation. Owing to the finite speed of sound and the deterministic relationship

between emission and observer time of a signal, there has to be some kind of

interpolation of the data at least on one side. In the case of parts of the integra-

tion surface or volume moving at transonic speeds, the integrals become highly

singular because of the Doppler effect, which leads to difficulties regarding the

numerical stability of the procedure.

Taking all these different techniques together, we end up with a general map of noise

prediction methods shown in Figure 1.2. Given all the different numerical formulations

and specific implementations of each method, there is a plethora of variants to choose

from. In this book we want to delve in more detail into the promising part of this tree

emphasized in bold.


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CAA

Directm

ethods

Hybridmethods

CFD

analysis

Sound

generation

Transport

method

Resolvedsources

(DNS,L

ES,D

ES)

Reconstructedsources

(RANS+SNGR/SATIN)

Acoustic

perturbation

equation(APE)

Comp

utational

transport

Analytical

transport

Linearised

Euler

equation

Wave

eq

uation

Acoustic

analogy

(FWH)

Kirchhoff

integral

Figure

1.2.

Noiseprediction

methods.

12


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1.2.5 Remaining problem areas for sound computation

Despite the progress made in recent years and the substantial number of researchers in

the field, there are still several unsolved issues involving the numerical prediction of

noise. Because CFD still has to struggle with (at least) turbulence modeling, transitionto turbulence, and separation (even more so with relaminarization and reattachment),

the CAA community has not yet reached consensus about the proper treatment of sound

computations in most application areas. Consequently, some remarks concerning these

issues seem to be in order.

Sound is a fundamental nonstationary process. In physical time, the sound waves

generated by some aerodynamic processes in the active region have to be transported

for at least some distance. So that the sound generated (e.g., at a trailing edge) will not

be totally destroyed, it is of paramount importance to perform this transport process as

accurately as possible. This holds especially for two basic features of sound: the wave

speed and the amplitude. Only specifically tuned methods can guarantee that waves will

be supported for a time and distance long enough to be of practical interest, and even

fewer methods can do this for the correct phase speed. Short wavelengths at the edge

of resolvability by the spatial discretization are particularly prone to numerical errors.

They usually encounter totally nonphysical propagation properties possibly up to the

point that the acoustic solution is totally spoiled.

1.2.5.1 DiscretizationThe main problem of CAA is the disparity of energy, length, and time scales between

the aerodynamics and the aeroacoustics especially at smaller Mach numbers. The

ratio of noise energy to mechanical energy is on the order of Pnoise/Pmech 104M5.

For a low-speed case ofM= 0.1 we obtain a ratio of 109, and even for an airliner

at M= 0.7 the number is only 105. In an aerodynamic simulation we of course in-

troduce numerical errors. To be at the same level as the acoustics we are interested

in, these errors have to be five to nine orders of magnitude smaller than the intended

physical values. To obtain acceptable signal-to-noise ratios for sound levels, we have

to add at least one more order of magnitude. In this sense, basically every CFD simu-lation is very loud, counting just the numerical errors that introduce numerical noise.

Common CFD schemes are adapted to stationary simulations and therefore just sup-

press acoustic waves, and so for the aerodynamic community the problem seems to be

solved.

For the purpose of aeroacoustics, on the other hand, the discretization schemes in

both space and time must be specifically tuned. Diffusion and dispersion errors have

to be reduced to the lowest possible level. This noble goal is achieved only partly,

but progress has been made to develop highly accurate discretization techniques to

reach the desired levels. Another problem is the introduction of artifical noise sources

caused by numerical errors that may overwhelm the physical sound sources and thus

generate entirely unreliable noise information. Finally, if we use dimensional splitting


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14 INTRODUCTION

techniques, discontinuities in the metrics of grid lines (e.g., at corners and edges) may

cause spurious noise reflections.

1.2.5.2 Boundary conditionsAt the very heart of CAA lies the proper handling of boundary conditions, which is a

situation not very different from that of CFD. Because acoustics is a radiation problem,

basically all the sound energy will sooner or later try to leave the computational domain.

On solid walls, we obviously get reflections, which we can handle straightforwardly just

as in CFD. However, on artificial far-field boundaries, the physics dictates a straight

pass-through without any spurious reflections. Although this requirement seems to

be obvious, it is indeed very hard to fulfill sufficiently. Several concepts have been

developed for this specific problem and optimized for one application or another, but

the downside is that a generally accepted solution does not yet exist.

Interior boundaries can be problematic as well. If we couple a CFD tool to a com-

putational transport method, there is a difference between the models, and we may

therefore obtain spurious reflections at the interface of the boundaries. The same holds

for other interior interfaces, even in the same code (e.g., in the interpolation region

between Chimera-type overlapping grids). Any difference in modeling, discretization,

or resolution is a potential cause for most unwanted reflections.

1.2.5.3 Coupling

Owing to the fundamental differences between aerodynamics and aeroacoustics in many

applications, a hybrid approach seems to be a sensible way to tackle the sound prediction

problem, as stated before. However, in this case the problem of coupling between the

two different algorithms inevitably arises. There is no theory of backscattering (i.e.,

a feedback from the acoustics to the aerodynamics) because this is not relevant in

any engineering application. Even the sole direction from a flow solution to a sound

computation, however, is difficult enough to handle properly in o

les for acoustics by wei shyy and michael j. rycroft

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