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The characteristics of the turbulence in the mixing region of a round jet

Published online by Cambridge University Press:  28 March 2006

P. O. A. L. Davies ,
M. J. Fisher  and
M. J. Barratt
P. O. A. L. Davies
Affiliation:
Department of Aeronautics and Astronautics, University of Southampton
M. J. Fisher
Affiliation:
Department of Aeronautics and Astronautics, University of Southampton
M. J. Barratt
Affiliation:
Department of Aeronautics and Astronautics, University of Southampton
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Abstract

Measurements in the mixing region of a 1 in. diameter cold air jet are described for Mach numbers ranging from 0.2 to 0.55. The statistical characteristics of the turbulence in the first few diameters of the flow may be expressed in terms of simple kinematic similarity relationships. These are based on the jet diameter and the distance downstream from the jet orifice as length-scales, and the inverse of the local shear as a time-scale. The experiments show that the integral time scale of the turbulence in a frame convected with the maximum energy of the turbulent motion is inversely proportional to the local shear.

The most interesting result obtained is that the local intensity of the turbulence is equal to 0.2 times the shear velocity. This velocity is defined as the product of the local integral length-scale of the turbulence with the local shear. The local intensity is defined as the R.M.S. value of the local velocity fluctuations divided by the jet efflux velocity. It was found that the length-scale is proportional to the distance from the jet orifice, while the maximum shear is also related to this distance as well as to the jet efflux velocity. These two similarity relations break down close to the jet orifice and change beyond the first six or so diameters downstream. The convection velocity is not equal to the local mean velocity but varies slowly over the region of maximum shear when it is just over half the jet efflux velocity. The measurements of other observers fit the relationships obtained quite well. From these relationships it is possible to calculate the noise generated by the mixing region of a given jet directly, using expressions derived by Lilley (1958).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 15 , Issue 3 , March 1963 , pp. 337 - 367
Copyright
© 1963 Cambridge University Press

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References

Allcock, G. A., Tanner, P. L. & McLachlan, K. R. 1962 A general purpose alanogue correlator for the analysis of random noise signals. Univ. Southampton Aero. Astr. Rep. 205.Google Scholar
Corrsin, S. 1943 Investigation of the flow in an axially symmetric heated jet of air. NASA, War-time Rep. no. W. 94.Google Scholar
Corrsin, S. & Uberoi, M. S. 1951 Spectra and diffusion in a round turbulent jet. NASA Rep. no. 1040.Google Scholar
Curle, N. 1961 The generation of sound by aerodynamic means. J. Roy. Aero. Soc. 65, 724.Google Scholar
Davies, P. O. A. L. 1957 The behaviour of a Pitot tube in transverse shear. J. Fluid Mech. 3, 441.Google Scholar
Gerrard, J. H. 1956 An investigation of the noise produced by a subsonic air jet. J. Aero. Sci., 23, 855–66.Google Scholar
Howard, J. B. 1959 An investigation into the applicability of Taylor's hypothesis in an open jet of air. Honours Thesis, Univ. Southampton (unpublished).
Laurence, J. C. 1956 Intensity, scale and spectra of turbulence in mixing region of free subsonic jet. NACA Rep. no. 1292.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically. I. General theory. Proc. Roy. Soc. A, 211, 564–87.Google Scholar
Lighthill, M. J. 1954 On sound generated aerodynamically. II. Turbulence as a source of sound. Proc. Roy. Soc. A, 222, 1–32.Google Scholar
Lighthill, M. J. 1962 Sound generated aerodynamically. The Bakerian Lecture, 1961. R.A.E. Tech. Mem. no. DIR 8.Google Scholar
Lilley, G. M. 1958 On the noise from air jets. Aero. Res. Counc., Lond., 20,376-N. 40-F.M. 2724.Google Scholar
Lilley, G. M. & Westley, R. 1952 An investigation of the noise field from a small jet and methods for its reduction. College of Aeronautics Rep. no. 53.Google Scholar
Proudman, J. 1952 The generation of noise by isotropic turbulence. Proc. Roy. Soc. A, 214, 119.Google Scholar
Ribner, H. S. 1958 On the strength distribution of noise sources along a jet. Univ. Toronto, Inst. Aerophys. Rep. no. 51.Google Scholar
Richards, E. J. 1959 Recent developments in jet noise research. Proc. 3rd Int. Congr. on Acoustics.
Sandborn, V. A. & Laurence, J. C. 1955 Heat loss from yawed wires at subsonic Mach numbers. NACA TN, no. 3563.Google Scholar
Taylor, G. I. 1935 The statistical theory of turbulence. I. Proc. Roy. Soc. A, 151, 421.Google Scholar
Townsend, A. A. 1956 The structure of turbulent shear flow, ch. 8. Cambridge University Press.
Webster, C. A. G. 1962 A note on the sensitivity to yaw of a hot-wire anemometer. J. Fluid Mech. 13, 307.Google Scholar
Williams, J. E. Fr. 1961 The noise from turbulence convected at high speed. Aero. Res. Counc., Lond., 23,323-F.M. 3138-N. 184.Google Scholar