Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-09T21:47:36.876Z Has data issue: false hasContentIssue false
  • English
  • Français

Self-preserving turbulent wall jets over convex surfaces

Published online by Cambridge University Press:  12 April 2006

D. E. Guitton  and
B. G. Newman
D. E. Guitton
Affiliation:
Department of Mechanical Engineering, McGill University, Montreal, Quebec
B. G. Newman
Affiliation:
Department of Mechanical Engineering, McGill University, Montreal, Quebec
Get access Rights & Permissions [Opens in a new window]

Abstract

The flow of an ostensibly two-dimensional wall jet over a logarithmic spiral has been studied both experimentally and theoretically. It is established that, if the skin friction is effectively constant, the flow may be self-preserving, and this is confirmed experimentally for the two spirals studied ($x/R = \frac{2}{3}$ and x/R = 1). The rate of growth has been predicted using the integral momentum equation and the integral equation for the combined mean and turbulent energy. Important assumptions in this theory are that the turbulence structure parameter $\overline{u^{\prime}v^{\prime}}/\overline{q^{\prime 2}}$ and the normalized mean position of the superlayer are invariant with curvature, and the experiments show that this is nearly true. The growth is constant for each spiral and increases with curvature. Using the measured rate of growth, the integral energy equation gives a satisfactory prediction of the turbulent shear stress, but the two-dimensional integral momentum does not. The turbulence is very intense in these flows and the Reynolds stresses were corrected using correlations of up to fourth order. However, the corrections may still have been too small, which would account for some of the difference between the calculated and measured shear stress. The outer flow of a wall jet strongly influences the inner boundary layer and this effect is found to increase with curvature. The conventional logarithmic law of the wall ceases to apply for $x/R >\frac{2}{3}$.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 81 , Issue 1 , 9 June 1977 , pp. 155 - 185
Copyright
© 1977 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alcaraz, E., Guillermet, G. & Mathieu, J. 1968 Mésures de frottement à la paroi à l'aide de tubes de Preston et d'une balance. C.R. Acad. Sci. Paris A 266, 432.Google Scholar
Bellhouse, B. J. & Schultz, O. L. 1966 Determination of mean and dynamic skin friction, separation and transition in low-speed flow with a thin-film heated element. J. Fluid Mech. 24, 379.Google Scholar
Bradshaw, P. 1969 The analogy between streamline curvature and buoyancy in turbulent shear flow. J. Fluid Mech. 36, 177.Google Scholar
Bradshaw, P. 1973 Effects of streamline cúrvature on turbulent flow. AGARDograph no. 169.Google Scholar
Brown, G. L. 1967 Theory and application of heated films for skin friction measurements. Proc. Heat Trans. Fluid Mech. Inst. (ed. D. R. Olfe & W. Van Atta), p. 361. Stanford University Press.
Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aero. Sci. 21, 91.Google Scholar
Escudier, M. P., Nicoll, W. B. & Spalding, D. B. 1966 An explicit drag law for uniform density turbulent boundary layers on smooth impermeable walls. Imperial College Rep. TWF/TN/12.Google Scholar
Fekete, G. I. 1963 Coanda flow of a two-dimensional wall jet on the outside of a circular cylinder. McGill Univ., Mech. Engng Dept. Rep. no. 63–11.Google Scholar
Förthmann, E. 1934 Über turbulente Strahlausbreitung. Ing. Arch. 5, 42. (Trans. N.A.C.A. Tech. Memo. no. 789.)Google Scholar
Gartshore, I. S. & Hawaleshka, O. 1964 The design of a two-dimensional blowing slot and its application to a turbulent wall jet in still air. McGill Univ., Dept. Mech. Engng Tech. Note no. 64–5.Google Scholar
Gibson, M. M. 1963 Spectra of turbulence in a round jet. J. Fluid Mech. 15, 161.Google Scholar
Giles, J. A., Hays, A. P. & Sawyer, R. A. 1966 Turbulent wall jets on logarithmic spiral surfaces. Aero. Quart. 17, 201.Google Scholar
Glauert, M. B. 1956 The wall jet. J. Fluid Mech. 1, 625.Google Scholar
Goldstein, S. 1938 Modern Developments in Fluid Dynamics, vol. 1. Oxford University Press.
Guitton, D. 1964 Two-dimensional turbulent wall jet over curved surfaces. McGill Univ., Dept. Mech. Engng Rep. no. 64–7.Google Scholar
Guitton, D. 1970 Some contributions to the study of equilibrium and non-equilibrium turbulent wall jets over curved surfaces. Ph.D. thesis, McGill University.
Guitton, D. 1974 The effect of high intensity turbulence on the response of a hot wire. C.A.S.I. Trans. 7, 69.Google Scholar
Head, M. R. & Rechenberg, I. 1962 The Preston tube as a means of measuring skin friction. J. Fluid Mech. 14, 1.Google Scholar
Irwin, H. P. A. H. & Smith, P. A. 1975 Prediction of the effect of streamline curvature on turbulence. Phys. Fluids 18, 624.Google Scholar
Jerome, F. E., Guitton, D. & Patel, R. P. 1971 Experimental study of the thermal wake interference between closely spaced wires of a X-type hot wire probe. Aero. Quart. 22, 119.Google Scholar
Kohan, S. 1968 Studies of the intermittent region and the wall region of a two-dimensional plane wall jet. Ph.D. thesis, Dept. of Chemical Engineering, Stanford University.
Launder, B. E., Reece, G. & Rodi, W. 1973 Development and application of a Reynolds stress turbulence closure. Imperial College, Mech. Engng Dept. Rep. HTS/73/31. (See also J. Fluid Mech. 68, 1975, 537.)Google Scholar
Myers, G. E., Schauer, J. J. & Eustis, R. H. 1961 The plane turbulent wall jet. Part 1. Jet development and friction factor. Dept. Mech. Engng, Stanford Univ. Tech. Rep. no. 1.Google Scholar
Nakaguchi, H. 1961 Jet along a curved wall. Dept. Aeronautics, Univ. Tokyo Res. Memo. no. 4.Google Scholar
Newman, B. G. 1961 The deflection of plane jets by adjacent boundaries — Coanda effect. Boundary Layer and Flow Control. Pergamon.
Parthasarathy, S. P. 1964 Two-dimensional, turbulent wall jets with and without a constant outside stream. M.Sc. thesis, Dept. of Aeronautics, Indian Institute of Science, Bangalore.
Patel, V. C. 1965 Calibration of the Preston tube and limitations on its use in pressure gradients. J. Fluid Mech. 23, 185.Google Scholar
Sawyer, R. A. 1962 Two-dimensional turbulent jets with adjacent boundaries. Ph.D. thesis, University of Cambridge.
Schwarz, W. H. & Cosart, W. P. 1961 The two-dimensional turbulent wall jet. J. Fluid Mech. 10, 481.Google Scholar
Shridhar, K. & Tu, P. K. C. 1969 Experimental investigation of curvature effects on turbulent wall jets. Aero. J. 73, 977.Google Scholar
Sigalla, A. 1958 Measurements of skin friction in a plane turbulent wall jet. J. Roy. Aero. Soc. 62, 873.Google Scholar
Smith, P. A. 1973 A two-dimensional jet with small curvature. Ph.D. thesis, McGill University.
Spetel, F., Mathieu, J. & Brison, J. F. 1972 Tensions de Reynolds et production d'energie cinétique turbulente dans les jets pariétaux sur parois planes et concaves. J. Méc. 11, 403.Google Scholar
Tailland, A. & Mathieu, J. 1967 Jet pariétal. J. Méc. 6, 103.
Townsend, A. A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11, 97.Google Scholar
Townsend, A. A. 1970 Entrainment and the structure of turbulent flow. Boeing Sci. Res. Lab., Symp. on Turbulence, 1969. J. Fluid Mech. 41, 13.Google Scholar