IMECE 2010
Rayleigh Lecture 2010Vancouver, B.C.
Acoustics fromExternal Flow-Structure Interactions
Theodore M. FarabeeFellow, ASME
Theodore M. FarabeeNaval Surface Warfare CenterCarderock Division, Code 7050 [email protected]
Rayleigh Lecture -
Established by Noise Control and Acoustics Division in 1985
The Rayleigh Lecture
is given at the Society's International Mechanical Engineering Congress and Exposition (IMECE) (formerly the Winter
Annual Meeting) by lecturers selected amongst those who have made pioneering contributions to the sciences and applications of noise control and acoustics
This is the 25th
Anniversary of the Lecture Series
ASME NCAD What is the Rayleigh Lecture
Background:
Who was the person -
Lord Rayleigh
History of the NCAD Rayleigh Lecture Series
Brief History of the Noise Control and Acoustics Division
External Flow-Structure Interactions:
Terminology
for this Lecture
Turbulence as source of sound
Sound due to turbulence-surface interactions
Sound from turbulence-edge interactions
Sound due to turbulent flow past Surface Irregularities
Surface Roughness
Surface Steps
Summary
ASME NCAD Rayleigh Lecture -
Outline
John William Strutt
Born 12 November 1842
Died 30 June 1919 (aged 76)
Eldest son of John James Strutt
Father of 3 sons
eldest became Professor at Imperial College
3rd
Lord Rayleigh
Brief Bio (& other items of interest)
Referred to as an unremarkable student
early in life
1861
entered Trinity College in Cambridge (aged 19)
1865
graduated in the Mathematical Tripos as Senior Wrangler and Smiths Prizeman
1866
became a Fellow of Trinity College
1868
after returning from trip to U.S., purchased equipment and set up experimental laboratory at his fathers country estate
1871
married and resigned Fellowship (Fellowship was only for bachelors)
Soon after getting married, became afflicted with rheumatic fever & as part of cure, took a trip up the Nile during which, it is reported, he worked on his seminal book The Theory of Sound
Lord Rayleigh Who was he?
Brief Bio (& other items of interest), contd 1873
Father dies and he assumes family title of Baron Rayleigh 1877
The Theory of Sound
is published (two-volume)According to biography by Rayleighs son, he wrote the book on the back side of pages turned in by candidates for the Mathematical Tripos in 1876
1876-to-1877-
President of London Mathematical Society (LMS)Interestingly, in 1874 Rayleigh made a generous bequest of 1000and the LMS was thus saved from what could have resulted in its early demise1000 amounts to around $110,000 in todays value
1879
Maxwell dies & Rayleigh replaces him as Cavendish Professor at Cambridge University (holds position for 5 years)
1904
Nobel Prize for Physics (co-discovery of argon, with W. Ramsay)
1905-to-1908
President of Royal Society Authored in excess of 446 scientific papers Many other achievements and accolades
a few of which include Order of Merit; thirteen honorary degrees; five government awards; honorary
membership of five learned societies world-wide
Lord Rayleigh Who was he, contd?
This day in history Lord Rayleigh born 12 November 1842
168 years (and 2 days) ago Jean leRond dAlembert is born in 1717
French mathematician/scientistdAlembertian Operator (related to acoustic wave equation)dAlemberts Paradox (drag on body in inviscid fluid is zero)
14 November 1878
Rayleigh presented Presidential lecture to London Mathematical Society
Lecture titled: On the Instability of Jets
Rayleighs interests in flow noise Interest in subject of Aeloian tones
Extensive citing of the work of Helmholtz and Strouhal Chapter XXI
The Theory of Sound
(Volume Two)Vortex Motion and Sensitive JetsDerivation of criterion for stability of shear layers (Rayleigh Criterion)
Inviscid form of Orr-Sommerfled equationShear layer with inflection point in profile is inviscidly unstable
Lord Rayleigh Other historical notes
http://www-history.mcs.st-andrews.ac.uk/PictDisplay/Rayleigh.html http://www.nobel-winners.com/Physics/john_william_strutt.htmlhttp://en.wikipedia.org/wiki/Lord_Rayleighhttp://nobelprize.org/nobel_prizes/physics/laureates/1904/strutt.htmlhttp://www.lms.ac.uk/contact/lms_history.pdfOptics and Photonics News, Vol. 20, Issue 6, pp. 36-41 (200)
J. Howard, "The Rayleigh Notebooks," Appl. Opt. 3, 1129-1129 (1964)
Lord Rayleigh References for material on Lord Rayleigh
History of the NCAD Rayleigh Lecture Series
Lectures & Lecturers
Lectures addressing topic of Flow Noise
Lecturers who have made contributions to
understanding of Flow Noise
ASME NCAD Rayleigh Lecture Series
NCAD Rayleigh
Lecturers; 1985 -
2009Year Lecturer Lecture Title
2009 Scott Sommerfeldt Global Attenuation of Acoustic Fields Using Energy-Based Active Control Techniques
2008 Martin Pollack A History of ASME Noise Control and Acoustics Division (NCAD)
2007 Robert Schlinker Putting it all Together -
The Technology stages in the Design of Propulsion Systems for Noise
2006 Donald Thompson A Systems Approach to Noise Mitigation Strategies
2005 Robert Clark Structural Acoustics from Macro to Micro
2004 Hafiz M. Atassi Fluid-Structure Interaction and Acoustics
2003 Earl G. Williams Fourier Acoustics: Uncovering the Origins of Sound
2002 Ilene Busch-Vishniac The Big Problems Remaining in Transduction
2001 Jerry H. Ginsberg Variational Solutions: What Rayleigh and Ritz Did Not Tell Us
2000 William K. Blake Quiet Flow: Emerging Design Methods
1999 Adnan Akay Acoustics of Friction
1998 Gary H. Koopmann Designing Quiet Structures -
Virtually
1997 Michael S. Howe Rayleigh Conductivity
1996 Peter A. Nelson Controlled Interference of Acoustic Fields
1995 Maurice M. Sevik Information Extraction from the Scattered Acoustic Field of Waterborne Structures
1994 C. Dan Mote, Jr. Surprises in Axially Moving Material Dynamics
1993 David G. Crighton The High-Speed Many-Bladed Propeller: Asymptotic Theory for its Acoustic Field
1992 Alan D. Pierce Progressive Waves: The Modern Evolution and Refinement of One of
the Most Basic Concepts in Acoustics
1991 David Feit Structural Acoustics from Lord Rayleigh to the Present
1990 David T. Blackstock Nonlinear Acoustics
1989 Sir Michael James Lighthill Biomechanics of Hearing Sensitivity
1988 Allan Powell Elements of Flow Noise from Rayleigh to Today
1987 Miguel C. Junger From the Finite to the Boundless: Acoustics of Very Large Systems
1986 J. E. Ffowcs Williams Computer Aided Silence
1985 K. Uno Ingard Acoustics in Physics and Mechanical Engineering
Rayleigh Lectures Lectures on topic of Flow Noise
Year Lecturer Lecture Title
2007 Robert SchlinkerPutting it all Together The Technology stages in the Design of Propulsion Systems for Noise
2004 Hafiz M. Atassi Fluid-Structure Interaction and Acoustics
2000 William K. Blake Quiet Flow: Emerging Design Methods
1993 David G. CrightonThe High-Speed Many-Bladed Propeller: Asymptotic Theory for its Acoustic Field
1988 Allan Powell Elements of Flow Noise from Rayleigh to Today
1986 J. E. Ffowcs Williams Computer Aided Silence
Rayleigh Lectures
Year Lecturer Lecture Title2008 Martin Pollack A History of ASME Noise Control and Acoustics Division (NCAD)
2007 Robert SchlinkerPutting it all Together The Technology stages in the Design of Propulsion Systems for Noise
2006 Donald Thompson A Systems Approach to Noise Mitigation Strategies
2004 Hafiz M. Atassi Fluid-Structure Interaction and Acoustics
2000 William K. Blake Quiet Flow: Emerging Design Methods
1997 Michael S. Howe Rayleigh Conductivity
1996 Peter A. Nelson Controlled Interference of Acoustic Fields
1995 Maurice M. Sevik Information Extraction from the Scattered Acoustic Field of Waterborne Structures
1993 David G. Crighton The High-Speed Many-Bladed Propeller: Asymptotic Theory for its Acoustic Field
1989 Sir M. James Lighthill Biomechanics of Hearing Sensitivity
1988 Allan Powell Elements of Flow Noise from Rayleigh to Today
1986 J. E. Ffowcs Williams Computer Aided Silence
Lecturers who have made contributions to understanding of Flow Noise
(with apologies to anyone who I might have missed)
Rayleigh Lectures (Grandstanding)
Year Lecturer Lecture Title2000 William K. Blake Quiet Flow: Emerging Design Methods
1995 Maurice M. Sevik Information Extraction from the Scattered Acoustic Field of Waterborne Structures
1991 David Feit Structural Acoustics from Lord Rayleigh to the Present
1988 Allan PowellElements of Flow Noise from Rayleigh to Today
(After retiring from NSWC)
Lecturers from my host organizationDavid Taylor Model Basin
DT Naval Ship Research & Development CenterDavid Taylor Research Center
Naval Surface Warfare Center, Carderock Division
Honorable Mention: Naval Research Laboratory
Year Lecturer Lecture Title2003 Earl G. Williams Fourier Acoustics: Uncovering the Origins of Sound
Noise Control and Acoustics Division (and other Historical Notes)
Noise Control and Acoustics Division (NCAD) established in 1979 with formation of the Noise Control and Acoustics (NCA) National Group
National Group -
an ASME probationary group established prior to becoming a DivisionSee the 2004 NCAD Newsletter article by Dr. A. Akay (one of founding members of NCAD)
Division technical structure has changed over the years, but current structure consists of three Technical Committees
Active & Passive Noise Control (A. Smith, Chair)
Structural Acoustics (S. Sung, Chair)
Aero/Hydro Acoustics (B. Paul, Chair)
Notably, NCAD sponsors
Per Bruel Gold Medal -
Society Award
Rayleigh Lecture -
Division Sponsored Lecture Series
Best Paper Award -
Presented at Annual Meeting
Student Paper Competition -
Presented for Best Student Paper given at Annual Meeting
Side Notes
1880 -
ASME is founded
1880 -
Lord Rayleigh published On the stability, or instability, of certain fluid motions, Proc. Lond. Math. Soc.,
11, 57-70
1998
David Taylor Model Basin (DTMB) is recognized by ASME as Mechanical Engineering Landmark -
ASME Historical Landmark #197 (more Grandstanding)
http://divisions.asme.org/NCAD/
Year Location Symposia Sponsored by Aero/Hydro Acoustics Technical Committee
2009 Disney World (Orlando, FL) Flow-Induced Phenomena
2008 Dearborn, MI (w/NoiseCon) Noise from Flow over External Features; Fan Noise
General Mechanisms; Active & Passive Control of Fan Noise
2007 Seattle, WA External Flow Acoustics; Turbomachinery Noise
2006 Chicago, IL Transportation Noise; Flow-Induced Noise
2005 Disney World (Orlando, FL) External Body Flow Noise; Turbomachinery Noise
2004 Anaheim, CA Prediction of Acoustics from Canonical Flows; Acoustic Treatments for Flow Noise
2003 Washington, D.C. Flow Noise Modeling, Measurement & Control
2002 New Orleans, LA 5th
Intern. Symp on Fluid-Structure Interact. (FSI), Aeroelasticity (AE), and Flow-Induced Vibration & Noise (FIV&N)
2001 New York, NY Aero-Hydroacoustic Facilities and Techniques; Validation of Computational Methods
2000 Disney World (Orlando, FL) Pump Unsteady Flow & Acoustics (joint with FED)
1999 Nashville, TN Flow-Induced Vibration and Noise of Thin Materials
1998 Anaheim, CA Flow Noise Modeling, Measurement & Control
1997 Dallas, TX 4th
Intern. Symp. On Fluid-Structure Interactions (FSI), Aeroelasticity (AE), and Flow-Induced Vibration (FIV); Coupling of Acoustic Fields and Flows
1996 Atlanta, GA Vehicle Flow/Structure Noises
1995 San Francisco, CA Flow Noise Modeling, Measurement & Control; Turbomachinery Noise
1994 Chicago, IL Active Control of Vibration & Noise: Active/Passive Control of Flow-Induced Noise & Vibration
1993 New Orleans, LA Flow Noise Modeling, Measurement & Control
1992 Anaheim, CA Flow-Induced Vibration and Noise: Flow-Structure and Flow-Sound Interactions
1991 Atlanta, GA Flow Noise Modeling, Measurement & Control; Hydroacoustic Facilities, Instrumentation & Experimental Techniques
1989 San Francisco, CA Flow-Induced Noise Due to Laminar-Turbulence Transition Process
1988 Chicago, IL Flow Induced Vibration & Noise: Non-Linear Interaction Effects and Chaotic Motions
1987 Boston, MA Developments in Transduction for Flow Induced Noise & Vibration
1986 Anaheim, CA Flow-Induced Noise & Vibrations
1985 Miami, FL Shear Flow/Structural Interactions
1983 Boston, MA Turbulence-Induced Vibrations and Noise of Structures
Symposia/Forums Sponsored by Aero/Hydro Acoustics Technical Committee (listed on Division Webpage)
External Flow-Structure Interactions What is meant by this title
Emphasis on flow-structure interactions due to turbulent flow over a vehicle exterior (Turbulent Boundary Layer
TBL)
Focus on flow-structure interactions that:
Result in production of sound (blocked structure)
Result in excitation of flow surface
Surface vibration
Acoustic radiation from flow-excited vibration
Generate unsteady forces that interfere with system functions
Primary flow-structure configurations of interest are those that occur in marine applications
however there are direct extensions to automotive & aeronautical applications
Fully turbulent flow
Typically a wall bounded shear layer (turbulent boundary layer
TBL)
Low Mach number flow (M
External Flow-Structure Interactions Examples of Flow-Structure Interactions
Examples are taken from Aeroacoustic community who have pioneered to use of phased array measurements for the study of flow noise (airframe noise).
Similar techniques and results for the marine and transportation industries
41st
Aerospace Sciences Meeting & Exhibit, 6-9 January 2003, Reno, NVRobert W. Stoker, Using Microphone Phased Arrays to Enable Low Airframe Noise Design
W.D. Fonseca, S.N.Y. Gerges, and R.P. Dougherty, Pass-by noise measurement using beamforming technique
Internoise 2008
External Flow-Structure Interactions Examples of Flow-Structure Interactions
Interesting images of noise resulting from flow-structure interactionsObtained using phased-arrays
Video from Optinav (B. Dougherty) as placed on YouTubeWind Turbine
Video from Optinav (B. Dougherty) as placed on YouTubeMotorboat
AIAA
Short CoursePhased Array Beamforming
for Aeroacoustics
Sound from Turbulence How to begin?
Theory of Aerodynamically Generated Sound given by Sir James Lighthill Sir James Lighthill (1952)M. James Lighthill. On sound generated aerodynamically I. General theory. Proc. Roy. Soc. A, 211:564-87, 1952. M. James Lighthill. On sound generated aerodynamically II. Turbulence as a Source of Sound. Proc. Roy. Soc. A, 222:1-32, 1954.
Lighthills theory (acoustic analogy) derived by manipulating momentum and
continuity equations to form a wave equation
with turbulence as the (inhomogeneous) source term for the wave equation.- Take divergence of momentum equation- Subtract from it the time derivative of the continuity equation- Subtract from both sides to get Lighthills equation220c
( ) ijjiijji
ij cpvvTwherexx
Tc
t 20
222
02
2
, +=
=
Sir James Lighthill Sir James Lighthill
Rayleigh Lecture 1989Rayleigh Lecture 1989Allan Powell Allan Powell
Rayleigh Lecture 1988Rayleigh Lecture 1988
For flows with constant sound speed and density,(Reynolds stress tensor)
Sound is generated by the unsteady Reynolds stresses (quadrupole
distribution) Note: the equation can be written for the pressure realizing that Further Note: Powell provides and alternative derivation based on vorticity
jiij vvT =
20cp =
Sound from Unbounded Turbulent Flows Slight digression
Lighthills analogy is derived assuming only turbulence sourcesConsider a similar derivation for which;
-
Continuity equation contains a mass-source term (q)-
Momentum equation contains an applied forcePerform same manipulation of the equations and express the wave equation in terms of the pressure -
Consider the multipole
character of the source terms as they appear in the equation
The mass source term has the form of a MonopoleThe applied force term has the form of a DipoleThe Reynolds stresses have the form of a Quadrupole (distribution)
What are the acoustic implications of the multipole nature of the source terms?
( )F
222
2 20
1 i ji j
Tp qp Fc t t x x
= +
Sound from Unbounded Turbulent Flows Acoustic Scaling of Multipole Source Terms
( )22
22 20
1 ,i ji j
Tp qp F S y tc t t x x
= + =
The following was covered more thoroughly by Prof. Grace in her 2004 NCA Tutorial Lecture on Computational Methods in Aeroacoustics
( ), rS y ty
xAssuming the source terms occupy a limited region, a general solution to the inhomogeneous wave equation can be obtained for locations in the
far field using the free-space Greens function
For a turbulent flow, it is appropriate to assume the following dimensional scaling:
(Without showing the math) consider the scaling of acoustic power for each term
3
0
0
1( , ) ,4
( ); ;
V
r
Rp x t S y t d yR c
x ywhere t t retarded time and for x y R x
c
=
Velocity ~ v (velocity of turbulence)Length ~ l (eddy size of turbulence); which then givesTime ~ l/v, and thus Frequency ~ v/l, with Volume ~ l3
Sound from Unbounded Turbulent Flows Acoustic Efficiency of Source Terms
( )
( )
2 22
00
3 20
; ,Multipolep Area RAcoustic Power giving p andcc
the turbulent kinetic energy is v l
= =
( )( )( )
4 2 3 20 0 0
0
6 2 3 3 2 30 0 0
8 2 5 3 2 50 0 0
~
~
~
Mono
Dipol
Quad
vv l c v l M M c
v l c v l M
v l c v l M
=
3
5
Mono
Dipole
Quad
M
M
M
With the following definitions and approximations,
The acoustic power for each multipole term is approximated to be:
The acoustic efficiency () for each term can then be expressed as:
Celebrated U8 scaling for jet noise
( ) 2 4~ 0.01 ; ~ 10 40DipleQuadrupole
For low Mach number flow M M dB =
Go back to the Lighthill equation (written on pressure)
and examine the solution obtained using a free-space Greens function
222
2 20
1 i ji j
Tp pc t x x
=
Sound from Turbulence Free-field Turbulence
( )
( )
0
23
23
2 3 20
0
1 1( , ) ,4
1( , ) ,4
; ( ); ;
iji jV rt c
i jij
V
i i i
p x t T y d yr y y
application of chain rule and divergence theorem gives
rrp x t T y d y
c r t
x yr x y t retarded time and for x y r x and r x y
c
=
=
= = =
Sound from Turbulence Effect of Flow Surface
Now, consider the solution when there is the presence of a rigid, stationary surfaceA general solution can be given in terms of a Greens function (G) that provides the proper acoustical boundary conditions
( ) ( )2 3 2, ; , , ; ,( , ) ij j ijV Si j i
j
G x t y G x t yp x t T d yd n p d y d
y y y
n surface outward unit normal
=
Curle (1955) used a free-space Greens function in the above to derive
( )2
3 32 3 2 20 0
1 1( , ) ,4 4
i j i jij j ijs
V
r r r rp x t T y d y n p d y
c r t c r t
+
Now the far-field sound now results from:
Original (quadrupole) Reynolds stresses (Lighthills result), & additionally
Dipole term resulting from turbulence interaction with the surface
Sound from Turbulence Effect of Flow Surface
Large & Small
Curles use of a free-space Greens function in elucidating the production of turbulence noise when a surface is present invoked the requirement that the surface be acoustically compact
d
d
Acoustically Compact Acoustically Non-Compact
For the acoustically non-compact case
for example, very large rigid flat plate
the normal force exerted on the flow vanishes and the dipole terms cancel to produce a less efficient surface quadrupole resulting in the only turbulence quadrupole radiation
However, realistic surfaces may be sufficiently
finite, have curvature, or surface features
resulting in the sound generated from the more efficient surface dipoles being a significant contribution to overall turbulence noise
Sound from Turbulence Finite Surfaces
Half Plane Problem
Ffowcs WilliamsFfowcs Williams
& Hall (1970) addressed the issue of sound generated by turbulent flow passing the edge of a finite plate (half plane) -
turbulent eddy convecting past an edge
Ffowcs WilliamsFfowcs Williams
Rayleigh Lecture 1986Rayleigh Lecture 1986
Approach -
obtain solution to Lighthills equation subject to appropriate Greens function on the half-plane
Appropriate Greens function is one for an infinite rigid plane, but weighted by a
Fresnel integral (magnitude varying from approximately 0 to 1)
Any enhancement
of sound over that for an equivalent free-field condition comes from the derivatives of the Fresnel weighted free-space Greens function
Two regimes identified
Turbulence near the edge; 2kr0
Sound from Turbulence Finite Surfaces
Half Plane Problem
Ffowcs Williams & Hall also considered the case for flow past a pressure release
half-plane and concluded results were essentially the same as for a rigid half-planeCrightonCrighton
& Leppington (1970) evaluated flow-noise scattering from a semi-
infinite compliant plate and reached a somewhat differing conclusion
Crighton Crighton
Rayleigh Lecture 1993Rayleigh Lecture 1993
Addressed problem by replacing eddies with volume distribution of quadrupoles
use of reciprocal theorem to transform quadrupole scattering problem into one of the diffraction of plane acoustic wave (solved via Wiener-Hopf technique)
Amplitude of scattered wave (sound) from quadrupoles near the edge are a function of the fluid loading parameter
()
For small
(little fluid loading) the plate is relatively rigid and the results of Ffowcs Williams & Hall are obtained -
sound scales as U5
For high fluid loading the plate appears limp
and strength of scattering is diminished resulting in sound scaling as U6
For aeronautical applications
is small and hence surface is effectively rigid
resulting in scattered sound scaling as U5
For marine applications
can be large (order 1) and hence surface is not effectively rigid
-
resulting in scattered sound scaling as U6
densityareaplateismscalelengthncorrelatioturbulenceisl
densityfluidiswhereml
,
,;2
0
000 =
Flow Noise on Surfaces Turbulent Boundary Layer (TBL)
Infinite Plane
What is the nature of the stresses (forces) generated on an infinite flat surface over which turbulence passes?
Flow configuration is typically a high Reynolds number Turbulent
Boundary Layer which develops over an infinite flat plate
Stresses that are of interest are:Normal stress or pressureShear stress
From an engineering interest, these stresses are:
Source of surface excitation
leading to unwanted vibration & noise
Noise field for surface mounted sensors (fathometers, etc.)
A general solution for the pressure at a wall is given by
Recall Lighthills Equation ( )22
22 20
1 i jij i j
i j
Tp p with T u uc t x x
= =
( )( )2
2
0
1 1,0, ,2
i jSurface
i jV y
Tp x z t d y
x y x x
=
Assuming flow is homogeneous in planes parallel with surface, take surface-time Fourier-Transform to get,( ) ( ),,,, 31 kktzx
22 2 2 2 2
0 1 3 1 1 2 3 320
; ; ;where k k k k k k and d k d and d kc = = = + = = =
( ) ( ) 21 3 1 2 3 20
2, , , , ,i j i ySurface ij
d dP k k T k y k e dy
i
= y2
Flow Noise on Surfaces Turbulent Boundary Layer (TBL)
Infinite Plane
1 3( , , )ijT k y k
y2i ye
Flow Noise on Surfaces Turbulent Boundary Layer (TBL)
Infinite Plane
( ) ( ) 21 3 1 2 3 20
2, , , , ,i j i ySurface ij
d dP k k T k y k e dy
i
=
While the above is easy
to write ---There is currently insufficient information regarding the Reynolds stress term to provide a complete solutionOver the years, numerous models
have been proposed with varying degrees of validation against (also) limited empirical information, for example:
Kraichnan (1956); Corcos (1963); Chase (1980); BlakeBlake (1986); Goody (2004)
Blake Blake
Rayleigh Lecture 2000Rayleigh Lecture 2000
mm-1
k=/c0 k=/Uc(Uc
0.7U0
)
( ),1k
Wills (1971)
k1
p(
k 1,k 3
, )
/c0 /uc
Chase (1980)
k1
()
,0,
31
=
kk
p
Flow Noise on Surfaces Turbulent Boundary Layer (TBL)
Infinite Plane
Sub-ConvectiveWavenumbers:
k0
< k >k0
SupersonicWavenumbers:
k
Consider Lighthills equation (sound from free-field turbulence)
Now, consider the M = 0 limit (c0
), which represents incompressible flow
(Sound)22
22 20
1 i ji j
Tp pc t x x
=
(Pseudo-Sound) (p
satisfies a Poisson equation)
2 22 i j i j
i j i j
T u up
x x x x
= =
Small amplitude, irrotational fluctuations that satisfy the wave
equation
(propagate from disturbance region at speed of sound, c0)
Pressure fluctuations are directly coupled to density fluctuations (p=c2)
No propagation; hydrodynamic pressures are convected by flow
Incompressible (no change in density with pressure change)
Pressures resulting from turbulence activity
Pressures related to velocity by Bernoulli equation
Far-field is composed of only Sound.
Low Mach Number flows are dominantly incompressible and are thus
essentially silent
In vicinity of turbulence pressures are dominantly pseudo-sound
Flow Noise on Surfaces Sound (Acoustics) vs. Pseudo-Sound (Hydrodynamics)
Slight Digression
Stick-man #1 is riding at 60 mph and there is turbulent flow over his head/ears
' 'turbp u vTypically for a turbulent flow the turbulence intensity (TI) ~10% (TI=u/Ux100%)
( )( ) 2' ' 0.1 0.1 0.01turbp u v U U U =360 26.8 / ; 1.3 / ; 20ref in airmph m s kg m p Pa = = =
3 2
10
0.01 (1.3 / ) (26.8 / ) 1020 log ( / ) 113
turb
ref
p x kg m x m s PaSPL x p p dB
= =
60 mph
-
Biker hears
a pressure level equivalent to sound by a rock band
-
Walker hears nothing from flow over stick-man #1s hears
~ 2x10-4
atm
Sound (Acoustics) vs. Pseudo-Sound (Hydrodynamic) Illustrative Example
http://dir.coolclips.com/People/Body_Parts/Ears/Ears_cart1162.htmlhttp://dir.coolclips.com/People/Body_Parts/Ears/Ears_cart1162.html
Flow Noise on Surfaces Excitation of Surface
Consider turbulent flow (Turbulent Boundary Layer) excitation of
a plate(Chandiramani [1977], Hwang [1990], Hambric [2004], for reference)-
What is the significance of the wavenumber content of the turbulence-
What is the significance of plate boundary conditions
The modal force spectral density
(mn
) response of a structure excited by turbulent flow is given by,
( ) ( ) ( ) ( ) ( )2 2 2, ik xmn p mn mn mnA
k F k d k where F k x e d x
= =
Hwang (1990)The figure displays typical plots of;(a)
the wavenumber response function for large structures typical of marine applications, and
(b)
streamwise TBL pressure spectrum
Of particular note is the mismatch between peak structural response and flow excitation functions
Flow Noise on Surfaces Excitation of Surface
For large structures it is tempting to assume strongest coupling
between flow-and-structure occurs at low wavenumbers where the structure is most responsiveTo evaluate whether this is true consider the high-wavenumber response of a plate for various plate-edge boundary conditions (evaluation of )( )mnF k
Free rectangular panel:
Simply supported rectangular panel:
Clamped rectangular panel:
( ) 22 kkFmn( ) 2 4mnF k k ( ) 2 6mnF k k
Simply supported ClampedFree
For the case considered, largest contribution to vibration for the Simply Supported and Clamped panels comes from the low-wavenumber pressuresFor the Free panel, vibration is dominated by contribution from high-wavenumber pressures -
significance excitation due to turbulence when there are free edges
Hwang (1990)
Flow Noise on Surfaces Surface Irregularities
Not all flow surfaces of engineering interest are smooth flat platesOr, more to the point - the cost and impact of making surfaces smooth is potentially prohibitive
What is acoustic impact of Surface Irregularities?Perturbations to flow resulting in increases in flow turbulence
Increased flow-structure interactionsScattering of turbulence
Scatter convective pressures (high amplitude) to sound
For discussion purposes, two canonical Surface Irregularities will be consideredSurface roughness
Range of roughness types and heights are possibleSurface steps
Simple forward-facing and backward-facing steps
From Wikipedia
Surface Roughness
(with selected modifications/edits)
Surface roughness, often shortened to roughness, is a measure of the texture of a surface. It is quantified by the vertical deviations of a real surface from its
ideal form. If these deviations are large, the surface is rough; if they are small the surface is smooth. Roughness is typically considered to be the high frequency, short wavelength component of a measured surface.
Roughness plays an important role in determining how a real object will interact with its environment. Rough surfaces usually wear more quickly and have higher friction coefficients than smooth surfaces.
Although roughness is usually undesirable, it is difficult and expensive to control in manufacturing. Decreasing the roughness of a surface will usually increase exponentially its manufacturing costs. This often results in a trade-off between the manufacturing cost of a component and its performance in application.
Flow Noise on Surfaces Surface Roughness
yuln
( )u yu
log-law
outer-flow
overlapviscoussublayer
yuy
+ =
5y + 60y +
5
10
0
15
ks
Flow Noise on Surfaces Roughness Scaling
Boundary Layer impact
For boundary layer flows
surface roughness is quantified in terms the viscous length scale
of the flow;
0 5
5 7 0
7 0
s
s
s
k u
k u
k u
>
Hydraulically Smooth
Transitionally Rough
Hydraulically Rough
( )
uklk
lscalelengthviscousu
ss =
=
+
+
http://mae.ucdavis.edu/~wind/facilities/ablwt.html
Flow Noise on Surfaces Surface Roughness
Modifications to TBL Pressures
How does surface roughness modify TBL pressures?1)
Increases in turbulence and hence surface pressures2)
Scattering (high amplitude) convective pressure (k~/Uc
)
Empirical Approach:-
Assume same scaling as Smooth Wall flows
accounting for changes to flow parameters results from the rough wall (u
& )
-
Adopt scaling similar to Smooth Wall but use roughness-related length scale
-
Or, something different ------
(seems no single approach is fully successful)
However, these approaches do not provide insight to full spectral description (wavenumber & frequency) of pressures:
( ) ( )
( ) ( )
2
2
2 2
p
w
p
w
uouter variable scaling
u
uinner variable scaling
u
=
=
( ) ( )( )2p g g sw g
u kk k
k u
= =
( ),p k
Flow Noise on Surfaces Surface Roughness
Modifications to TBL Pressures
HoweHowe
Rayleigh Lecture 1997Rayleigh Lecture 1997
( ) ( ) ( )0, , ,Rough wall Diffractedk k k = +
HoweHowe proposed an approach to modeling the rough-wall turbulent boundary layer which provides a description at both subconvective
and acoustic
wavenumbersAssumed the high wavenumber-convective portion of the frequency spectrum could be modeled as previously described (modify existing models for TBL pressures by incorporating adjusted rough wall parameters) Include to the above the scattered pressure resulting from diffraction of the near-field pressures convecting over the rough wall ( ),Diffracted k
( )0 ,k
5=U 40
U
= For M=0.005, U=7.5m/s, =5cm
5 ~ 120
40 ~ 960
f HzU
f HzU
=
=
( ) ( ) ( )0 , , , , ,D iffracted R ough w allk k k
Flow Noise on Surfaces Surface Roughness
Sound
(far-field pressure)
( ) ( ) ( ) ( ) ( ) ( )00
000
0
0 |,|,, xdSn
xxGxpxxGnxpxp h
S
hScattered
=
( ) ( ) ( ) 31212122
0 ,,,,2, dkdkkkkkAhxkx hrmsScattered
=
Glegg & Devenport derived relationships for how sound
is generated by TBL flow over rough surfaces which separates the scaling of the sound from the scaling for the TBLApproach is similar to Howe in that a scattering problem is solvedFollowed Mores & IngardIngards acoustic scattering from a rough surfaceIncident field scattered by surface is the hydrodynamic pressure field of TBL
Roughness is acoustically compactHydrodynamic pressure field is homogeneous Wall is taken to be the surface of the roughness
IngardIngard
Rayleigh Lecture 1985Rayleigh Lecture 1985
wavenumber spectrum of surface slopehrms
rms
of roughness height
( )1 2, ,k k
For randomly distributed roughness characterized by relatively discontinuous surfacesTypical of sandpaper roughness and wide range of natural and other man-made roughnesses
Giving ( ) ( ) ( )( )2 2 2 2 2 20 0
2 2
,cos cos, pppp hh
xk h k hx C S or C Sx x
= =
( )( )
22
11 2 0 2, , 2
xk k kx
=
Flow Noise on Surfaces Surface Roughness
Sound
(far-field pressure)
80 grit20 grit 180 grit
Figures from Alexander (2009; MS-thesis, Virginia Tech.)
Note: for 180 grit @ 60 m/s, k+
~ 6Recall that 0< k+
Flow Noise on Surfaces Surface Roughness
Sound
(far-field pressure)
103
104
105
-110
-100
-90
-80
-70
-60
-50
-40
Frequency [rad/s]
a(
)/ s(
) [dB
re: 1
P
a/H
z]
Cubes
Hemispheres
103 104 105-110
-100
-90
-80
-70
-60
-50
-40
-30
-20
Frequency [rad/s]
a(
)/ s(
) [dB
re: 1
P
a/H
z/N
s/A F
/CD
]
AFF 0.17" Sparse Cuboids
140 fps, 0.17" C92 fps, 0.17" C60 fps, 0.17" C140 fps, 0.17" H92 fps, 0.17" H60 fps, 0.17" H140 fps, 0.118" H92 fps, 0.118" H60 fps, 0.118" H
2
CubesandHemispheresusedasgenericroughnesselements
( )( )
( )22 2 222 2
, cos16
ppD F S
S o
x CC A N
c r
RadiatedRoughnessNoiseasfunction
ofsurfacepressures
( )( )
pressureSurface
Rad
From Anderson, et al., (ASME, IMECE 2009, NCAD 2009)
Scaling for deterministic roughness on roughness element drag coefficient
RadiatedSound
Rayleigh-LikeTurbulence Scattering
More significantfor smaller roughness size
Shed VorticityMore significant
for larger roughness size
Roughness Noise Demonstration
hg
= 3.0 mmh+
u
h/ 200U = 45 m/s
Smooth v. Rough Surface
ForcingFunction
( ) ( ) ( ) ( )2
2 cos cos4 4
= + n n n
nc r r
GreensFunction
Drag -
Force Spectrum
Turbulence ScatteringDrag DipolesShed Vorticity
Flow Noise on Surfaces Surface Roughness
Sound
(far-field pressure)
AudiofilefromDevenport(VT)
Surface Pressures
( ) ( ) ( ) ( )2
22122
cos', " " '4
= S k k f d
k k k
x
RadiatedSound
Greens Function of Surface Roughness
Flow Noise on Surfaces Surface Irregularities -
Steps
HMCS Victoria; December 2000
What is meant by steps?Pillars on automobilesPlating mismatches in streamwise directionInterfaces between streamwise spaced components (wing flaps, rail cars, etc.)
HMCS Windsor; SSK-877
Wind Noise Applications
A. Lauterbach, et. al.Institute of Aerodynamics and Flow Technology
German Aerospace Center DLRBerlin Beamforming Conference, February 2010
S. Oerlemans and P. SijtsmaNLR-TP-2004-320
Flow Noise on Surfaces Surface Steps
Flow Features
Forward-Facing StepBackward-Facing Step
Scaling factor most significant to flow noise
character of Step Flows is;
( ) ( )[ ]hheighSteptothicknesslayerBoundaryh
Flow Noise on Surfaces Surface Steps
Modifications to TBL Pressures
Backward-Facing StepFarabeeFarabee & Casarella (ASME, WAM & Journal
1984)
FarabeeFarabee
Rayleigh Lecture 2010Rayleigh Lecture 2010
For case of /h ~ 1
Highest TBL pressures occur at downstream reattachment location
RMS pressures at reattachment ~ 5 greater than for equilibrium TBL
Spectrum of downstream pressures characterized by enhanced low-frequency content
TBL pressure spectrum has not recovered to equilibrium at most downstream location (x/h = 72)
Flow Noise on Surfaces Surface Steps
Modifications to TBL Pressures
Forward-Facing StepFarabeeFarabee & Casarella (ASME, WAM & Journal
1986)
For case of /h ~ 2.4
Highest TBL pressures occur at reattachment location downstream of step
Highest RMS pressures ~ 10 greater than for equilibrium TBL
Spectrum of downstream pressures characterized by enhanced low-frequency content
TBL pressure spectrum has not recovered to equilibrium at most downstream location (x/h = 36)
Upstream Locations
Downstream Locations
Flow Noise on Surfaces Surface Steps
Sound
(far-field pressure)
Forward-Facing StepFarabeeFarabee & Zoccola (ASME, IMECE
1998)Noise radiated from Forward-facing and Backward-facing steps
Measurements made in Anechoic wind tunnelStep geometries similar to those for Surface pressure measurementsRadiated noise measured using directional-dish microphone positioned normal to step-plate in the acoustic far-field
Measurement approach similar to that pioneered by SchlinkerSchlinker
SchlinkerSchlinker
Rayleigh Lecture 2007Rayleigh Lecture 2007
Could not measure noise from Backward-facing step not measured (lower than background noise)Noise from Forward-facing step
Levels similar for two step heights evaluated
Levels scale as ~ U5
Highest levels at approximately location of step
Prior/OnGoingEffortsinFlowNoise(U)
StepNoise(ONRTurbulenceD&I)
( )
hUp
hUcfvs
Uf
mRad
m
Rad
m
62
52
20.
103
104
-40
-30
-20
-10
0
10
20
30
40
50
freq [Hz]
SPL
[dB
], (d
B re
f. 20
Pa
2 / H
z)
h = 1.5 mmh = 3.0 mmh = 4.6 mmh = 6.1 mmh = 11.7 mmh = 18 mm
Uj = 60 m/s, = 123.5o
103
104
-40
-30
-20
-10
0
10
20
30
40
50
freq [Hz]
SPL
[dB
], (d
B re
f. 20
Pa
2 / H
z)
Uj = 30 m/s
Uj = 45 m/s
Uj = 60 m/s
h = 11.7 mm , = 123.5omU
f
hUc
m52
2
10log10
vs.
Forward Step Far Field Normalization
10-1
100
101
-120
-110
-100
-90
-80
-70
-60
-50
-40
-30
f / Um
10*lo
g 10[
c2
/ 2
U m5 h
]
h = 1.5 mmh = 3.0 mmh = 4.6 mmh = 6.1 mmh = 11.7 mmh = 18.0 mm
Uj = 60 m/s, = 123.5o
10-1
100
101
102
-120
-110
-100
-90
-80
-70
-60
-50
-40
-30
f / Um
10*lo
g 10[
c2
/ 2
U m5 h
]
Uj = 30 m/s
Uj = 45 m/s
Uj = 60 m/s
h = 11.7 mm, = 123.5o
ScalingonVelocity ScalingonStepHeight
Flow Noise on Surfaces Surface Steps
Sound
(far-field pressure)
Forward-Facing StepResults from recent experimental studies of Devenport (VT)
Backward step Forward step
PSD of Greens Function-Weighted Sources
Flow Noise on Surfaces Surface Steps
Sound
(far-field pressure)
Forward-Facing Step
Numerical study of noise from Step Flow
Meng (UND; AIAA & JFM)
Y1 ~ velocity potential for potential flow over step
Flow Noise on Surfaces Surface Steps
Sound
(far-field pressure)
Forward-Facing Step
Numerical study of noise from Step Flow
Meng (UND; AIAA & JFM)
Backward step Forward step
Backward-step sound is dominated by diffraction
Forward-step sound is due to both source generation and diffraction
Flow Noise on Surfaces Surface Steps
Sound
(far-field pressure)
Forward-Facing Step
Numerical study of noise from Step Flow
Slomski (NSWCCD; AIAA)
Uo
surface 1
surface 2
surface 3
surface 4
surface 5
surface 6
surface 7
surface 8
step face
103 10410
20
30
40
50
60
70
Frequency Hz
PSD
dB
re
Pa / H
z at
1 m
CFD DataMeasurement
ASME NCAD Rayleigh Lecture
Thank you for your attention!
Willing to entertain any questions or comments
Very much look forward to seeing everyone at the 50th
Anniversary
of the Rayleigh LectureRayleigh Lecture
at ASMEs IMECE in 2035
Slide Number 1ASME NCADWhat is the Rayleigh LectureASME NCADRayleigh Lecture - OutlineLord RayleighWho was he?Lord RayleighWho was he, contd?Lord RayleighOther historical notesLord RayleighReferences for material on Lord RayleighASME NCADRayleigh Lecture SeriesNCAD Rayleigh Lecturers; 1985 - 2009Rayleigh LecturesLectures on topic of Flow NoiseRayleigh LecturesRayleigh Lectures(Grandstanding)Noise Control and Acoustics Division(and other Historical Notes)Slide Number 14External Flow-Structure InteractionsWhat is meant by this titleExternal Flow-Structure InteractionsExamples of Flow-Structure InteractionsSlide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Sound from TurbulenceFree-field TurbulenceSound from TurbulenceEffect of Flow SurfaceSound from TurbulenceEffect of Flow Surface Large & SmallSound from TurbulenceFinite Surfaces Half Plane ProblemSound from TurbulenceFinite Surfaces Half Plane ProblemFlow Noise on Surfaces Turbulent Boundary Layer (TBL) Infinite PlaneSlide Number 28Flow Noise on Surfaces Turbulent Boundary Layer (TBL) Infinite PlaneFlow Noise on Surfaces Turbulent Boundary Layer (TBL) Infinite PlaneSlide Number 31Slide Number 32Flow Noise on Surfaces Excitation of SurfaceFlow Noise on Surfaces Excitation of SurfaceFlow Noise on Surfaces Surface IrregularitiesFlow Noise on Surfaces Surface RoughnessFlow Noise on Surfaces Roughness Scaling Boundary Layer impactFlow Noise on Surfaces Surface Roughness Modifications to TBL PressuresFlow Noise on Surfaces Surface Roughness Modifications to TBL PressuresFlow Noise on Surfaces Surface Roughness Sound (far-field pressure)Flow Noise on Surfaces Surface Roughness Sound (far-field pressure)Flow Noise on Surfaces Surface Roughness Sound (far-field pressure)Slide Number 43Flow Noise on Surfaces Surface Irregularities - StepsFlow Noise on Surfaces Surface Steps Flow FeaturesFlow Noise on Surfaces Surface Steps Modifications to TBL PressuresBackward-Facing StepFlow Noise on Surfaces Surface Steps Modifications to TBL PressuresForward-Facing StepSlide Number 48Slide Number 49Slide Number 50Slide Number 51Slide Number 52ASME NCADRayleigh Lecture