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 stream-wise 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.
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Abbreviations
- c f :
-
skin friction coefficient 2 τw/ϱ U pw 2
- H :
-
boundary layer shape factor δ1/δ2
- K :
-
von Karman constant (= 0.41)
- k 1 :
-
wavenumber
- l :
-
turbulence scale defined by Eq. (6)
- P :
-
stagnation pressure
- p :
-
mean static pressure
- p′:
-
fluctuating component of static pressure
- \(\overline {q^2 } \) :
-
\(\overline {u^2 } + \overline {v^2 } + \overline {w^2 } \)
- R :
-
radius of curvature of wall
- r :
-
local radius of curvature ≅ R + y
- Re 2 :
-
momentum thickness Reynolds number U pw°2/v
- U, V :
-
mean velocity components in x, y directions
- u τ :
-
friction velocity (τ w /ϱ)0.5
- u, v, w :
-
fluctuating velocity components in x, y, z directions
- x, y, z :
-
spatial co-ordinates, x measured along and y measured normal to the wall
- δ:
-
boundary layer thickness
- δ1 :
-
displacement thickness \(\frac{1}{{{\text{U}}_{{\text{pw}}} }}\int\limits_0^\infty {\left( {U_p - U} \right)} dy\)
- δ2 :
-
momentum thickness \(\frac{1}{{{\text{U}}_{_{{\text{pw}}} }^2 }}\int\limits_0^\infty {\left[ {\left( {U_{_p }^2 - U^2 } \right) - U_{pw} \left( {U_p - U} \right)} \right]} dy\)
- ε:
-
turbulent energy dissipation rate
- ϱ:
-
fluid density
- τ w :
-
wall shear stress
- p :
-
potential flow
- ref:
-
reference conditions
- w :
-
wall values
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Gibson, M.M., Verriopoulos, C.A. & Vlachos, N.S. Turbulent boundary layer on a mildly curved convex surface. Experiments in Fluids 2, 17–24 (1984). https://doi.org/10.1007/BF00266314
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DOI: https://doi.org/10.1007/BF00266314