COMPUTATIONAL AND ASYMPTOTIC METHODS IN AEROACOUSTICS WITH APPLICATIONS

Abstract

In this article the computational and asymptotic methods used in aeroacoustics are reviewed. In particular, two different aeroacoustic applications are demonstrated. In the first problem we investigate the first and second order asymptotic predictions of the thickness and loading noise of a subsonic B-bladed helicopter rotor in the far field and compare the SPL noise results with those of full numerical computations. The results of the second order asymptotic formula seem to be in better agreement with full numerical computations than the first order asymptotic formula. In the second problem, the effect of acoustic wave propagation in transonic nozzle flow is investigated by solving the unsteady quasi-one-dimensional transonic nozzle equations in conservative form using high order computational aeroacoustic schemes, where a novel non-reflecting boundary condition is implemented in addition to the standard non-reflecting boundary condition using characteristics. Excellent agreement with the exact solution is obtained in each case

Keywords

• Aeroacoustics, Acoustic Analogy, Helicopter Rotor Noise, Acoustic Disturbances, Transonic Nozzle Flows

References

1. [1] Brentner, K. S., (1994), Helicopter Noise Prediction: The Current Status and Future Direction, J. Sound Vibration, 170, 79-96.
2. [2] Gutin, L., (1936), On the sound field of a rotating propeller, Zh. Tekh. Fiz., 6, 899-909.
3. [3] Ernsthausen, W., (1936), The source of propeller noise, Luftfahrtforschung, 8, 433-440.
4. [4] Deming, A. F., (1938), Noise from propellers with symmetrical sections at zero blade angle II, NACA TM, 679.
5. [5] Garrick, I. E., (1954), A theoretical study of the effect of forward speed on the free-space soundpressure field around propellers, NACA Report, 1198.
6. [6] Arnoldi, R. A., (1956), Propeller noise caused by blade thickness, Unite Aircraft Corporation Research Department Report, R-896.
7. [7] Lighthill, M. J., (1952), On sound generated aerodynamically. I. General theory, Proc. Roy. Soc. London A, 211, 564-587.
8. [8] Farassat, F., (1981), Linear Acoustic Formulas for Calculation of Rotating Blade Noise, AIAA J., 19, 1122-1130.

9. [9] Lowson, M. V., (1965), The sound field for singularities in motion, Proc. Roy. Soc. London A, 286, 559-572.
10. [10] Wright, S. E., (1969), Sound radiation from a lifting rotor generated by asymmetric disk loading, J. Sound Vibration, 9, 223-226.
11. [11] Lowson, M. V. and Ollerhead, J. B., (1969), A theoretical study of helicopter rotor noise, J. Sound Vibration, 9, 197-222.
12. [12] Ffowcs Williams, J. E. and Hawkings, D. L., (1969), Sound Generation by Turbulence and Surfaces in Arbitrary Motion, Roy. Soc. London-Philosophical Trans. A, 264, 321-342.
13. [13] Hawkings, D. L. and Lowson, M. V., (1974), Theory of open supersonic rotor noise, J. of Sound and Vibration, 36, 1-20.
14. [14] Farassat, F., (1977), A new capability for predicting helicopter rotor and propeller noise including the effect of forward motion, NASA TM, X-74037.
15. [15] Farassat, F., (1975), Thickness noise of helicopter rotors at high tip speeds, AIAA Paper 75-453.
16. [16] Yu, Y. H., (1978), The influence of the transonic flow field on high-speed helicopter impulsive noise, Fourth European Rotorcraft and Powered Lift Aircraft Forum.
17. [17] Hanson, D. B., (1976), Near field noise of high tip speed propellers in forward flight, AIAA Paper 76-565.
18. [18] Hanson, D. B., (1980), Helicoidal Surface Theory for Harmonic Noise of Propellers in the Far Field, AIAA J., 18, 1213-1220.
19. [19] Leverton, J. W., (1989), Twenty-five years of rotorcraft aeroacoustics: Historical prospective and important issues, J. Sound Vibration, 133, 261-287.
20. [20] Brooks, T. F., (1989), Main rotor broadband noise study in the DNW, J. Am. Heli. Soc., 34, 3-12.
21. [21] Martin, R. M., (1988), Acoustic results of the blade-vortex interaction acoustic test of a 40 percent model rotor in the DNW, J. Am. Heli. Soc., 33, 37-46.
22. [22] Farassat, F., (1983), The prediction of helicopter rotor discrete frequency noise, Vertica, 7, 309-320.
23. [23] Brentner, K. S., (1986), Prediction of helicopter discrete frequency roto”r noise - A computer program incorporating realistic blade motions and advanced acoustic formulation, NASA TM, 87721.
24. [24] Lyrintzis, A. S., (1994), Review: The use of Kirchhoff’s method in computational aeroacoustics, J. Fluids Eng., 116, 665-676.
25. [25] Brentner, K. S., (1998), Analytical comparison of the acoustic analogy and Kirchhoff formulation for moving surfaces, AIAA J., 36, 1379-1386.
26. [26] Brentner, K. S. and Farassat, F., (1998), Supersonic quadrupole noise theory for high-speed helicopter rotors, J. Sound Vibration, 218, 481-500.
27. [27] Howe, M. S., (1999), Trailing edge noise at low Mach numbers, J. Sound Vibration, 225, 211-238.
28. [28] Ianniello, S., (1999), Quadrupole noise predictions through the Ffowcs Williams-Hawkings equation, AIAA J., 37, 1048-1054.
29. [29] Ianniello, S., (2001), Aeroacoustic analysis of high tip-speed rotating blades, Aerospace Science and Technology, 5, 179-192.
30. [30] Tam, C. K. and Webb, J. C., (1993), Dispersion-relation-preserving finite difference schemes for computational acoustics, J. Comp. Phys., 107, 262-281.
31. [31] Lele, S. K., (1992), Compact finite difference schemes with spectral-like resolution, J. Comp. Phys., 103, 16-42.
32. [32] Haras, Z. and Taasan, S., (1994), Finite difference schemes for long-time integration, J. Comput. Phys., 114, 265-279.
33. [33] Kim, J. W. and Lee, D. J., (1996), Optimized compact finite difference schemes with maximum resolution, AIAA J., 34, 887-893.
34. [34] Hixon, R., (2000), Prefactored small-stencil compact schemes, J. Comp. Phys., 165, 522-541. 35. D.
35. W. Zingg 2001 Comparison of high-accuracy finite-difference methods for linear wave propagation, SIAM J. Sci. Comp., 22, 476-502.
36. [35] Hixon, R. and Turkel, E., (2000), Compact implicit MacCormack-type schemes with high accuracy, J. Comp. Phys., 158, 51-70.
37. [36] Zingg, D. W., Lomax, H. and Jurgens, H., (1996), High-Accuracy Finite-Difference Schemes for Linear Wave Propagation, SIAM J. Sci. Comp., 17, 328-346.
38. [37] Hu, F. Q., Hussaini, M. Y. and Manthey, J. L., (1996), Low-dissipation and low-dispersion RungeKutta schemes for computational acoustics, J. Comp. Phys.,124, 177-191.
39. [38] Stanescu, D. and Habashi, W. G., (1998), 2N-storage low dissipation and dispersion Runge-Kutta schemes for computational acoustics, J. Comput. Phys., 143, 674-681.
40. [39] Tam, C. K., (1995), Computational aeroacoustics: Issues and methods, AIAA J., 33, 1788-1796, 1995.
41. [40] Tam, C. K., (2004), Computational Aeroacoustics: An Overview of Computational Challenges and Applications, Int. J. Comp. Fluid Dyn., 18, 547-567.
42. [41] Colonius, T. and Lele, S. K., (2004), Computational aeroacoustics: Progress on nonlinear problems of sound generation, Prog. Aerospace Sci., 40, 345-416.
43. [42] Wells, V. L., (1997), Computing aerodynamically generated noise, Ann. Rev. Fluid Mech., 29, 161-199.
44. [43] Wang, M., Freund, J. B. and Lele, S. K., (2006), Computational Prediction of Flow-Generated Sound, Ann. Rev. Fluid Mech., 38, 483-512.
45. [44] Parry, A. B. and Crighton, D.C., (1989), Asymptotic theory of propeller noise - Part I: Subsonic single-rotation propeller, AIAA J., 27, 1184-1190.
46. [45] Zafer, B., Delale, C. F. and Aslan, A. R., (2005), Second order asymptotics for propeller noise and application to helicopter rotor blades, In Proc. Ankara International Aerosapace Conference (AIAC), 127-135.
47. [46] Zafer, B., Sen, A.L., Delale, C. F. and Aslan, A. R., (2007), Asymptotic prediction and full numerical solution of helicopter rotor noise in the far field, In Proc. Ankara International Aerosapace Conference (AIAC), 87-94.
48. [47] Erdelyi, A., (1956), Asymptotic expansions, Dover publications, New York.
49. [48] Hinch, E. J., (1994), Perturbation methods, Cambridge University Press.
50. [49] Hardin, J. C., Huff, D. and Tam, C. K. W., (2000), Proc. Third Computational Aeroacoustics (CAA) Workshop on Benchmark Problems, NASA/CP-2000-209790.
51. [50] Thompson, K. W., (1987), Time dependent boundary conditions for hyperbolic systems, J. Comp. Phys., 68, 1-24.
52. [51] Abramowitz, M. and Stegun, I. A., (1965), Handbook of mathematical functions, Dover Publications, New York.
53. [52] Ratis, Y. L. and De Cordoba, P. F., (1993), A code to calculate (high order) Bessel functions based on the continued fractions method, Comp. Phys. Com., 76, 381-388.
54. [53] Wake, B. E. and Baeder, J. D., (1996), Evaluation of a Navier-Stokes analysis method for hover performance prediction, J. Am. Heli. Soc., 41, 7-17.
55. [54] Hoffman, J. D., (2001), Numerical Methods for Engineers and Scientists, CRC Press.
56. [55] Hedstrom, G. W., (1979), Nonreflecting boundary conditions for nonlinear hyperbolic systems, J. Comp. Phys., 30, 222-237.
57. [56] Giles, M. B., (1990), Nonreflecting boundary conditions for Euler equation calculations, AIAA J., 28, 2050-2058.
58. [57] Erickson, L. E., (1982), Generation of boundary-conforming grids around wing-body configurations using transfinite interpolation, AIAA Journal, 20, 1313-1320.