The Connection Between Acoustics and Unsteady Aerodynamics

Transcription

1 National Aeronautics and Space Administration The Connection Between Acoustics and Unsteady Aerodynamics Keynote Address F. Farassat- Fellow of AIAA NASA Langley Research Center 14th AIAA/CEAS Aeroacoustics Conference Vancouver, British Columbia, Canada 5-7 May 2008

2 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 2

3 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 3

4 Some interesting quotations I. Edward Garrick: The addition of the dimension of time to steady aerodynamics has far-reaching effects, both practical and theoretical....apart from the many applications, theoretical nonsteady aerodynamics embraces and sheds light on the realm of steady aerodynamics and introduces interesting new methods. From: Nonsteady Wing Characteristics, in Aerodynamic Components of Aircraft at High Speed,

5 Some interesting quotations Luigi Morino on asking various people if there is a difference between aeroacoustics and aerodynamics: For the man on the street they do not seem to have anything to do with each other For a politician in the Budget Committee for Scientific Research, there is no difference whatsoever.aerodynamicists and Aeroacousticians are one of a kind. They both want a lot of money. 5

6 Some interesting quotations Luigi Morino (Cont d) For an informed environmentalist aerodynamics and aeroacoustics have a lot in common. They are both useful for the environment For the chief executive officer of an aeronautical industry, they have nothing in common.. the director of experimental facility sees the difference in terms of cost: Aeroacoustics is much more expensive.we would have to use anechoic wind tunnel, and you would have to pay us more much, much more. 6

7 Some interesting quotations Luigi Morino (Cont d) Thus, if one were to ask an expert in BIM what is the difference between the evaluation of the pressure on the surface (aerodynamic Problem) and that in the field (aeroacoustic problem), the reply would be: The same difference that there is between a boundary integral equation and a boundary integral representation. From: Is There a Difference Between Aeroacoustics and Aerodynamics? An Aeroelastician s View (AIAA J., 41, 2003) 7

8 An Old Opinion By the Speaker (Since 1970s) Linear aerodynamics, even steady aerodynamics, 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 included compressibility in their aerodynamic work (Küssner, Garrick, Ashley, Lomax, Morino, Atassi, Amiet, Hanson, etc.) were aware of the connection between aerodynamics and acoustics. Only a few treated the two subjects by a unified approach. Acoustics became a hot topic after most linear aerodynamic theories were developed. 8

9 A Look at Some Unsteady Aerodynamic Theories 9

10 When Can We Treat a Problem as Quasi-Steady? A problem is quasi-steady when we can treat the problem as steady at any moment of time t during its motion. 10

11 When Can We Treat a Problem as Quasi-Steady? 11

12 Models of Classical Incompressible Unsteady 2D Airfoil Theories Types of airfoil motions of interest in aeronautics 12

13 A Thin Airfoil in Plunging and Oscillatory Motion 2D Quasi-Steady Incompressible Case The instantaneous lift Coefficient is: 13

14 Models of Classical Incompressible Unsteady 2D Airfoil Theories Theodorsen 1935 (Frequency Domain) 14

15 Models of Classical Incompressible Unsteady 2D Airfoil Theories Theodorsen Function Note the real and imaginary axes scales are not equal. 15

16 Models of Classical Incompressible Unsteady 2D Airfoil Theories von Karman & Sears 16

17 Models of Classical Incompressible Unsteady 2D Airfoil Theories von Karman & Sears 1938 (Frequency Domain) 17

18 Models of Classical Incompressible Unsteady 2D Airfoil Theories Sears Function 18

19 Models of Classical Incompressible Unsteady 2D Airfoil Theories Küssner 1935 (Time Domain) 19

20 Models of Classical Incompressible Unsteady 2D Airfoil Theories Küssner Function Note the real and imaginary axes scales are not equal. Küssner with Garrick, Wittmeyer and Ashley in September

21 Models of Classical Incompressible Unsteady 2D Airfoil Theories All the above models of unsteady airfoil theories are very 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 developed linearized 3D wing theories based on the wave equation. Acoustics and linear aerodynamics theories can then be unified but this has been done since 1970s. 21

22 Unification of Acoustics and Aerodynamics 22

23 The General Approach of Unifying Acoustics and Aerodynamics If the conservation laws can be cast into a wave equation in terms of velocity potential or pressure valid in the exterior of a body in motion, then acoustics and linear aerodynamics can be treated together, e.g., by BEM. Advantages: Important practical problems of engineering can be solved much faster than purely numerical method, much less computer resources are needed than other methods, 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 23

24 The General Approach of Unifying Acoustics and Aerodynamics Morino, students and coworkers have used FW-H equation as well as other wave equations in terms of pressure and velocity potential for both aerodynamics and acoustics. Time and frequency domain methods are used. A frame fixed to the body is preferred. Morino has worked on unsteady aerodynamic theory and code development since 1970s. Later he worked on aeroacoustics. He has used boundary element method in some of the most difficult problems of aerodynamics, aeroacoustics and aeroelasticity such helicopter rotor flow field computation. He has contributed substantially to the mathematics of BEM. See the refs. in Morino AIAA J., 41, 2003,

25 The General Approach of Unifying Acoustics and Aerodynamics 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 medium is preferred. The subsonic solution is called Formulation 1A. From the acoustic point of view, a wing in uniform rectilinear motion is unsteady! Farassat has emphasized the power of generalized functions and analytic methods in solving difficult problems of acoustics. The problem of numerical evaluation of singular integrals of BEM can only be answered by GF theory. New results await discovery. See NASA TP-3428, 1994 and NASA TM ,

26 The General Approach of Unifying Acoustics and Aerodynamics A moving and possibly deformable surface in motion 26

27 The General Approach of Unifying Acoustics and Aerodynamics 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. But there seems to be some clear advantages of using advanced mathematics particularly generalized functions. 27

28 The General Approach of Unifying Acoustics and Aerodynamics The Green s function of the wave equation in unbounded space is In a moving frame, one often needs the emission distance in terms of the visual coordinates of the source and the observer. This can be done analytically for a frame moving at uniform speed or numerically always. 28

29 The General Approach of Unifying Acoustics and Aerodynamics 29

30 Some Problems to Solve For the Young and the Brave 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? 30

31 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 31

32 Dedication This talk is dedicated to William R. Sears, my teacher, mentor and friend. Working with him at Cornell ( ) has been one of the most memorable experiences of my life. High school graduation photograph of W. R. Sears 32

33 Acknowledgements Figures on models of 2D classical unsteady aerodynamic theories are from J. Gordon Leishman Principles of Helicopter Aerodynamics, First Edition, Portrait of Professor H. W. Küssner was kindly provided by Dr. Wolfgang Send of DLR, Germany. Note added after the Conference: The speaker has benefited greatly from the seminal paper of H. Atassi Unsteady Aerodynamics of Vortical Flows: Early and Recent Developments in Symposium on Aerodynamics & Aeroacoustics, K.-Y. Fung (Ed.), World Scientific, 1994,

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