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The far field of high frequency convected singularities in sheared flows, with an application to jet-noise prediction

Published online by Cambridge University Press:  29 March 2006

Thomas F. Balsa
Thomas F. Balsa
Affiliation:
Power Generation and Propulsion Laboratory, General Electric Company, Corporate Research and Development, Schenectady, New York 12301
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Abstract

The purpose of the present paper is to derive expressions for the pressure fields of various high frequency convected singularities immersed in a unidirectional sheared flow. These expressions include the simultaneous effects of fluid and source convection and refraction. These results are then combined to predict the far-field directivity of cold round jets. It is found that the agreement between experiment and the present theory is quite good at a source Strouhal number of unity but that this agreement deteriorates as the source frequency is increased. Our theoretical results show the explicit form of the ‘refraction integral’ and that convective amplification for the pressure of a quadrupole is increased by a factor of (1 — MJ cos Θ)−1 over the classical results, where MJ is the jet Mach number and Θ is the angle from the jet axis. Thus acoustic/mean-flow interaction not only implies refraction but also additional convective amplification due not to source convection but to fluid motion.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 74 , Issue 2 , 23 March 1976 , pp. 193 - 208
Copyright
© 1976 Cambridge University Press

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References

Ahuja, K. K. & Bushell, K. W. 1973 J. Sound. Vib. 30, 317.
Atvars, J., Schubert, L. K., Grande, E. & Ribner, H. S. 1966 N.A.S.A. Contractor Rep. CR-494.
Balsa, T. F. 1975 J. Fluid Mech. 70, 17.
Carrier, G. F., Krook, M. & Pearson, C. E. 1966 Functions of a Complex Variable. McGraw-Hill.
Csanady, G. T. 1966 J. Fluid Mech. 26, 183.
Davies, P. O. A. L., Fisher, M. J. & Barratt, M. J. 1963 J. Fluid Mech. 15, 337.
Erdélyi, A. 1956 Asymptotic Expansions. Dover.
Ffowcs, Williams, J, E. 1963 Phil. Trans. A, 255, 469.
Ffowcs Williams, J. E. 1974 J. Fluid Mech. 66, 791.
Lighthill, M. J. 1952 Proc. Roy. Soc. A, 211, 564.
Lilley, G. M. 1972 AFAPL-TR-72-53, vol. 4.
Lush, P. A. 1971 J. Fluid Mech. 46, 477.
Mani, R. 1972 J. Sound Vib. 25, 337.
Mani, R. 1973 J. Fluid Mech. 64, 611.
Mani, R. 1976a J. Fluid Mech. 73, 753.
Mani, R. 1976b J. Fluid Mech. 73, 779.
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. McGraw-Hill.
Pao, S. 1973 J. Fluid Mech. 59, 451.
Phillips, O. M. 1960 J. Fluid Mech. 9, 1.
Proudman, I. 1952 Proc. Roy. Soc. A, 214, 119.
Ribner, H. S. 1962 Inst. Aerophys. University of Toronto, Rep. no. 86.
Ribner, H. S. 1969 J. Fluid Mech. 38, 1.
Schubert, L. K. 1972 J. Acoust. Soc. Am. 51, 439, 447.
Seckler, B. D. & Keller, J. B. 1959 J. Acoust. Soc. Am. 31, 192, 206.
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.