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Wall shear stress prediction in three-dimensional turbulent boundary layers

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Abstract

A method is developed to infer the wall shear stress for three-dimensional turbulent boundary layers based on the assumption that the resultant surface shear stress and the effective velocity based on Prahlad's model correlates the velocity profile into its two-dimensional form. Existence of the near wall region similarity has been demonstrated for three-dimensional turbulent boundary layers.

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Abbreviations

A and B:

constants connected with log-law, Eq. (1)

\(c_{f_1 } \) :

skin-friction coefficient in the main flow direction

\(F\left( {\frac{y}{\delta }} \right)\)):

QSW or Coles function

\(F_1 \left( {\frac{y}{\delta }} \right)\) :

QSW function

\(F_2 \left( {\frac{y}{\delta }} \right)\) :

Coles function

H :

shape parameter

n :

exponent in power-law profile, Eq. (4)

QSW:

quarter-sine wave function

q :

resultant velocity

q * :

resultant shear velocity

q + :

non-dimensionalised velocity vector = q/q *

U :

free stream velocity

u :

main stream velocity component in the boundary layer

u * :

shear velocity in the main stream direction

V :

effective velocity

w :

cross-flow component in the boundary layer

y :

coordinate normal to the surface of the wall

β :

angle between the velocity vector at any point with velocity vector at y=δ

β 0 :

limiting wall-stream angle

δ :

boundary layer thickness

ϑ 11 :

momentum thickness for velocity profile in main stream direction

ν :

kinematic viscosity

η :

y/δ

η + :

yq */ν

p :

density of fluid

τ wx :

wall shear stress in main stream direction

τ wz :

wall shear stress in cross-flow direction

References

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Authors and Affiliations

  1. Dept. of Appl. Mech., Indian Inst. of Techn., 600 036, Madras, India

    N. V. C. Swamy & P. A. Aswatha Narayana

Authors
  1. N. V. C. Swamy
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  2. P. A. Aswatha Narayana
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Swamy, N.V.C., Aswatha Narayana, P.A. Wall shear stress prediction in three-dimensional turbulent boundary layers. Appl. Sci. Res. 33, 471–480 (1977). https://doi.org/10.1007/BF00411826

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  • DOI: https://doi.org/10.1007/BF00411826

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