the connection between acoustics and unsteady aerodynamics

National Aeronautics and Space Administration

www.nasa.gov

The Connection BetweenAcoustics and Unsteady

Aerodynamics

Keynote AddressF. Farassat- Fellow of AIAA

NASA Langley Research Center14th AIAA/CEAS Aeroacoustics Conference

Vancouver, British Columbia, Canada5 - 7 May 2008

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Outline of the Talk

– What this talk is all about– Some interesting quotations– An old opinion by the speaker– A look at some unsteady aerodynamic

theories– Unification of acoustics and aerodynamics– Some problems to solve for the young and

the brave– Concluding remarks

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What This Talk Is All About– Relate linear unsteady aerodynamics to

acoustics– Review briefly some classical unsteady

aerodynamic theories– Show that ideas from acoustics shed light

on aerodynamics– Give some historical tidbits about early

personalities– Present some problems for future research

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Some interesting quotationsI. Edward Garrick:

The addition of the dimension of“time” to steady aerodynamics hasfar-reaching effects, both practicaland theoretical. .......Apart from themany applications, theoreticalnonsteady aerodynamics embracesand sheds light on the realm of steadyaerodynamics and introducesinteresting new methods.From: Nonsteady Wing Characteristics, in AerodynamicComponents of Aircraft at High Speed, 1957

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Some interesting quotationsLuigi Morino on asking various peopleif there is a difference betweenaeroacoustics and aerodynamics:

– For the man on the street they do notseem to have anything to do with eachother……

– For a politician in the Budget Committeefor Scientific Research, there is nodifference whatsoever….Aerodynamicistsand Aeroacousticians are one of a kind.They both want a lot of money.

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Some interesting quotationsLuigi Morino (Cont’d)

– For an informed environmentalist aerodynamicsand aeroacoustics have a lot in common. They areboth useful for the environment……

– For the chief executive officer of an aeronauticalindustry, they have nothing in common…..

– …the director of experimental facility sees thedifference in terms of cost: Aeroacoustics is muchmore expensive….we would have to use anechoicwind tunnel, and you would have to pay us more–much, much more.

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Some interesting quotationsLuigi Morino (Cont’d)

Thus, if one were to ask an expert in BIM what isthe difference between the evaluation of thepressure on the surface (aerodynamic Problem)and that in the field (aeroacoustic problem), thereply would be: The same difference that there isbetween a boundary integral equation and aboundary integral representation.

From: Is There a Difference Between Aeroacousticsand Aerodynamics? An Aeroelastician’s View(AIAA J., 41, 2003)

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An Old Opinion By the Speaker (Since 1970s)Linear aerodynamics, even steadyaerodynamics, is all acoustics. Acoustics sheds light on the subject of aerodynamics and can supply insights and methods not available in classical Aerodynamics.

This idea is not new. All researchers who includedcompressibility in their aerodynamic work (Küssner,Garrick, Ashley, Lomax, Morino, Atassi, Amiet,Hanson, etc.) were aware of the connection betweenaerodynamics and acoustics. Only a few treated thetwo subjects by a unified approach. Acousticsbecame a hot topic after most linear aerodynamictheories were developed.

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A Look at Some UnsteadyAerodynamic Theories

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When Can We Treat a Problem as Quasi-Steady?A problem is quasi-steady when we can treat the problemas steady at any moment of time t during its motion.

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When Can We Treat a Problem as Quasi-Steady?

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Models of Classical Incompressible Unsteady 2D Airfoil Theories

Types of airfoil motions of interest in aeronautics

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A Thin Airfoil in Plunging and Oscillatory Motion2D Quasi-Steady Incompressible Case

The instantaneous lift Coefficient is:

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Models of Classical Incompressible Unsteady 2DAirfoil Theories

Theodorsen 1935 (Frequency Domain)

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Models of Classical Incompressible Unsteady 2DAirfoil Theories

Theodorsen FunctionNote the real and imaginary axes scales are not equal.

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von Karman & Sears

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von Karman & Sears 1938 (Frequency Domain)

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Sears Function

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Küssner 1935 (Time Domain)

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Küssner FunctionNote the real and imaginaryaxes scales are not equal.

Küssner with Garrick,Wittmeyer and Ashleyin September 1980

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All the above models of unsteady airfoil theories arevery ingenious but not satisfactory because

– They are two dimensional and incompressible– They do not incorporate the airfoil geometry– They are independent of speed of sound– They do not start from the first principles, i.e., by starting from conservation laws

Since 1940s many researchers have developedlinearized 3D wing theories based on the waveequation. Acoustics and linear aerodynamics theoriescan then be unified but this has been done since 1970s.

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Unification of Acousticsand Aerodynamics

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The General Approach of Unifying Acoustics and Aerodynamics

If the conservation laws can be cast into a wave equationin terms of velocity potential or pressure valid in theexterior of a body in motion, then acoustics and linearaerodynamics can be treated together, e.g., by BEM.

Advantages: Important practical problems of engineeringcan be solved much faster than purely numerical method,much less computer resources are needed than othermethods, powerful analytical tools are available

Disadvantages: No closed form solutions are available and one does not gain insights into the behavior of the solution easily, inclusion of nonlinearities is hard

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The General Approach of Unifying Acousticsand Aerodynamics

Morino, students and coworkers have used FW-Hequation as well as other wave equations in terms ofpressure and velocity potential for both aerodynamicsand acoustics. Time and frequency domain methodsare used. A frame fixed to the body is preferred.

Morino has worked on unsteady aerodynamic theoryand code development since 1970s. Later he workedon aeroacoustics. He has used boundary element methodin some of the most difficult problems of aerodynamics,aeroacoustics and aeroelasticity such helicopter rotorflow field computation. He has contributed substantiallyto the mathematics of BEM.

See the refs. in Morino AIAA J., 41, 2003, 1209-1223

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Farassat, students and coworkers have used FW-H equation as the linear wave equation in terms of pressure for both aerodynamics and acoustics. Time domain method and a frame fixed to the mediumis preferred. The subsonic solution is called Formulation1A. From the acoustic point of view, a wing in uniform rectilinear motion is unsteady!

Farassat has emphasized the power of generalizedfunctions and analytic methods in solving difficultproblems of acoustics. The problem of numericalevaluation of singular integrals of BEM can only beanswered by GF theory. New results await discovery.

See NASA TP-3428, 1994 and NASA TM-110285, 1996

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A moving and possibly deformablesurface in motion

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Possible choices one has in solving the problem:– Velocity potential or pressure formulation– Time domain vs frequency domain– The frame of reference

– Fixed to the body (aerodynamics)– Fixed to the medium (acoustics)

– The mathematical approach

The choices one makes often depends on the experience and background of the person. Butthere seems to be some clear advantages of usingadvanced mathematics particularly generalizedfunctions.

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The General Approach of Unifying Acoustics and Aerodynamics

The Green’s function of the wave equation in unboundedspace is

In a moving frame, one often needs the emission distancein terms of the visual coordinates of the source and theobserver. This can be done analytically for a frame movingat uniform speed or numerically always.

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– Can our method be used for blade-vortex and blade-turbulence interaction study?– How can we best regularize divergent integrals of aerodynamics?– What is the fastest method of solving the governing singular integral equations of aerodynamics?– Can we use our method for contra-rotating propfans? – How can we use the new symbolic software (Mathematica, Maple, etc.) to solve aerodynamic and aeroacoustic problems?– How can we use the power of visualization of the symbolic software as an experimental tool in acoustics and aerodynamics?

Some Problems to Solve For the Young and the Brave

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Concluding Remarks– Linear unsteady aerodynamics should be viewed as part of the problem of aeroacoustics– Although a fully numerical approach is more accurate than the proposed linear methods, there are overwhelming advantages of using the latter method.– More analytic work is needed for unsteady aerodynamics useful for aeroacoustics, e.g., in airframe noise prediction– There are still many problems of aeroacoustics to be solved by combined analytic and numerical methods– The available symbolic software (Mathematica, Maple) are opening new possibilities for problem solving, code development and visualization

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This talk is dedicated toWilliam R. Sears, my teacher,mentor and friend. Workingwith him at Cornell (1970-1973) has been one of themost memorableexperiences of my life.

Dedication

High school graduationphotograph of W. R. Sears

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AcknowledgementsFigures on models of 2D classical unsteadyaerodynamic theories are from J. Gordon Leishman“Principles of Helicopter Aerodynamics”, FirstEdition, 2000. Portrait of Professor H. W. Küssnerwas kindly provided by Dr. Wolfgang Send of DLR,Germany.

Note added after the Conference: The speaker has benefitedgreatly from the seminal paper of H. Atassi “UnsteadyAerodynamics of Vortical Flows: Early and RecentDevelopments” in Symposium on Aerodynamics &Aeroacoustics, K.-Y. Fung (Ed.), World Scientific, 1994, 121-171.

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the connection between acoustics and unsteady aerodynamics

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