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Turbulent flow regions with shear stress and mean velocity gradient of opposite sign

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Abstract

An explanation is given for a phenomenon observed e.g. in a wall jet in a small region near the maximum velocity. The turbulence shear stress is expressed as the sum of two terms, proportional to the first and the second derivative of the mean velocity, respectively. Use is made of the nonsymmetric flow pattern around the maximum velocity, and of the nonuniform distribution of the intensity of the lateral turbulence velocity component. The coefficient of the second derivative of the mean velocity is shown to contain the first derivative of this turbulence velocity component. Since the second derivative of the mean velocity is negative around its maximum, a positive turbulence intensity gradient as observed in the region concerned in the wall jet, results in a negative contribution to the shear stress. Hence, in this region the shear stress can have a sign opposite to the positive — though very small — gradient of the mean velocity. Consequences with respect to the mechanical energy balance of the mean flow and of the turbulence are discussed.

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Abbreviations

P:

mean static pressure

p :

turbulence static pressure

t :

time

Ū i :

mean velocity component in x i direction

u i :

turbulence velocity component in x i direction

u′ i :

root mean square value of u i

u 2− :

negative value of u 2

u 2+ :

positive value of u 2

x i :

Cartesian coordinates, i=1, 2, 3

x 2− :

negative value of distance x 2 to control plane

x 2+ :

positive value of distance x 2 to control plane

(x 2)1/2 :

half value distance

α, β, γ :

numerical constants

ε m :

eddy viscosity

ν :

kinematic viscosity

ρ :

density

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Authors and Affiliations

  1. Laboratory for Aero- and Hydrodynamics, Technological University, Delft, The Netherlands

    J. O. Hinze

Authors
  1. J. O. Hinze
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Hinze, J.O. Turbulent flow regions with shear stress and mean velocity gradient of opposite sign. Appl. Sci. Res. 22, 163–175 (1970). https://doi.org/10.1007/BF00400525

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  • DOI: https://doi.org/10.1007/BF00400525

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