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Turbulence measurements in an ‘equilibrium’ axisymmetric wall jet

Published online by Cambridge University Press:  29 March 2006

B. R. Ramaprian
Affiliation:
Department of Aeronautical Engineering, Indian Institute of Science, Bangalore

Abstract

This paper reports measurements of turbulent quantities in an axisymmetric wall jet subjected to an adverse pressure gradient in a conical diffuser, in such a way that a suitably defined pressure-gradient parameter is everywhere small. Self-similarity is observed in the mean velocity profile, as well as the profiles of many turbulent quantities at sufficiently large distances from the injection slot. Autocorrelation measurements indicate that, in the region of turbulent production, the time scale of ν fluctuations is very much smaller than the time scale of u fluctuations. Based on the data on these time scales, a possible model is proposed for the Reynolds stress. One-dimensional energy spectra are obtained for the u, v and w components at several points in the wall jet. It is found that self-similarity is exhibited by the one-dimensional wavenumber spectrum of $\overline{q^2}(=\overline{u^2}+\overline{v^2}+\overline{w^2})$, if the half-width of the wall jet and the local mean velocity are used for forming the non-dimensional wavenumber. Both the autocorrelation curves and the spectra indicate the existence of periodicity in the flow. The rate of dissipation of turbulent energy is estimated from the $\overline{q^2}$ spectra, using a slightly modified version of a previously suggested method.

Type
Research Article
Copyright
© 1975 Cambridge University Press

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References

Blackman, R. B. & Tukey, J. B. 1958 Measurement of Power Spectra from the Point of View of Communication Engineering. Dover.
Bradshaw, P., Ferriss, D. H. & Atwell, N. P. 1967 Calculation of boundary-layer development using the turbulent energy equation. J. Fluid Mech. 28, 593.Google Scholar
Kacker, S. C. & Whitelaw, J. H. 1968 Some properties of the two-dimensional turbulent wall jet in a moving stream. Trans. A.S.M.E., J. Appl. Mech. E 35 (4), 641651.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741773.Google Scholar
Kolmogorov, A. N. 1942 Izv. Akad. Nauk SSSR, Ser. Phys. 1, 2.
Kruka, V. & Eskinazi, S. 1964 The wall jet in a moving stream. J. Fluid Mech. 20, 555579.Google Scholar
Lawn, C. J. 1971 The determination of the rate of dissipation in turbulent pipe flow. J. Fluid Mech. 48, 477505.Google Scholar
Magrab, E. B. & Blomquist, D. S. 1971 The Measurement of Time-Varying Phenomena. Interscience.
Newman, B. G., Patel, R. P., Savage, S. B. & Tjio, H. K. 1972 Three-dimensional wall jet originating from a circular orifice. Aero. Quart. 22, 188200.Google Scholar
Nicoll, W. B. & Ramaprian, B. R. 1970 Performance of conical diffusers with annular injection at inlet. Trans. A.S.M.E., J. Basic Engng, D 92, 827835.Google Scholar
Ramaprian, B. R. 1969 Conical diffusers with annular injection at inlet. Ph.D. thesis, Department of Mechanical Engineering, University of Waterloo, Canada.
Ramaprian, B. R. 1973 Turbulent wall jets in conical diffusers. A.I.A.A. J. 11, 16841690.Google Scholar
Rao, K. N., Narasimha, R. & Badri narayanan, M. A. 1971 The ‘bursting’ phenomena in a turbulent boundary layer. J. Fluid Mech. 48, 339352.Google Scholar
Rotta, J. 1951 Statistiche Theorie nichthomogener Turbulenz. Z. Phys. 129, 547572.(Trans. W. Rodi 1968 Dept. Mech. Engng, Imperial College, Rep. TWF-TN-38.)Google Scholar