M. M. Gibson, C. A. Verriopoulos and N. S. Vlachos. Mechanical Engineering Department, Fluids Section, Imperial ColIege of Science and Technology,.
Experimentsin Fluids
Experiments in Fluids 2, 17-24 (1984)
© Springer-Verlag 1984
Turbulent boundary layer on a mildly curved convex surface Part 1: Mean flow and turbulence measurements M. M. Gibson, C. A. Verriopoulos and N. S. Vlachos Mechanical Engineering Department, Fluids Section, Imperial ColIege of Science and Technology, Exhibition Road, London SW7 2BX, GB
Abstract. Mean flow and turbulence measurements have been made in a boundary layer which grows first on a flat wall and then on a convex wall of radius of curvature approximately 100 times the boundary layer thickness. The turbulence data include profiles of the four non-zero components of the Reynolds stress tensor and three triple velocity products obtained at five streamwise positions. A number of measurements were also made for comparison in the boundary layer on a flat wall under the same conditions. The effects of convex curvature are to reduce turbulent intensities, shear stress and wall friction by approximately 10% of their plane flow values; the triple velocity products are halved in the curved layer. The measurements supplement the small quantity of previously published data available for testing mathematical models of turbulence. The results show the same general trends that have been observed in earlier investigations but there are significant differences in detail, notably in respect of levels of the normal stresses.
List of symbols
9
H K kl l P P p' q2 R F
Re 2
u,v I.lT bl, U, W
x, y, z
gh
skin friction coefficient 2 rw/O U~w boundary layer shape factor 6j/62 von Karman constant (= 0.41) wavenumber turbulence scale defined by Eq. (6) stagnation pressure mean static pressure fluctuating component of static pressure U2 q- V2 q- W2
radius of curvature of wall local radius of curvature ~ R + y momentum thickness Reynolds number Up,, 62/v mean velocity components in x, y directions friction velocity (rw/~) °s fluctuating velocity components in x, y, z directions spatial co-ordinates, x measured along and y measured normal to the wall boundary layer thickness 1 displacement thickness Upw (Up - U) dy
--!
1 momentum thickness ~ 2 - ! [(Up2 - U2) - Upw(Up - U)] dy
yew
8
0 %
turbulent energy dissipation rate fluid density wall shear stress
Subscripts p ref w
potential flow reference conditions wall values
1 Introduction The turbulence in shear layers is highly sensitive to streamline curvature in the plane of the m e a n shear. Turbulent stresses and intensities are reduced by curvature when the angular m o m e n t u m of the m e a n flow increases in the direction of the radius o f curvature, as in the boundary layer on a convex wall, and increased when the angular m o m e n t u m decreases with increasing radius of curvature, as in concave wall flow. Measurements from various sources reviewed by Bradshaw (1973) show that local changes in turbulence quantities are an order of magnitude greater than the ratio of the extra strain rate ~V/Sx~-U/r to the basic mean shear ~ U / ~ y or, in more general a p p r o x i m a t e terms, to the ratio g~/R of the shear layer thickness to the radius of curvature. The effects of prolonged strong stabilizing curvature can be dramatic: the hot-wire measurements of So and Mellor (1973) and Gillis et al. (1980) in convex wall b o u n d a r y layers with 3 / R --- 0.1 revealed extensive regions of low or reversed shear stress in the outer flow where the influence of extra strain in neutralizing turbulence p r o d u c t i o n is dominant. Typical results are shown in Fig. 1 where they are compared with data from more mildly curved convex boundary layers with 3 / R ~ 0.01. The effects of mild curvature are less striking but no less interesting in respect of the basic physics. It has been suggested (Hunt and Joubert 1979) that they m a y be fundamentally different in character. The recent A F O S R - H T I M Stanford Conference on complex turbulent flows has drawn attention to deficiencies in the quantity and quality o f the experimental d a t a currently available for the further d e v e l o p m e n t of calcula-
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Experiments in Fluids 2 (1984)
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