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On the universality of the velocity profiles of a turbulent flow in an axially rotating pipe

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Abstract

If a fluid enters an axially rotating pipe, it receives a tangential component of velocity from the moving wall, and the flow pattern change according to the rotational speed. A flow relaminarization is set up by an increase in the rotational speed of the pipe. It will be shown that the tangential- and the axial velocity distribution adopt a quite universal shape in the case of fully developed flow for a fixed value of a new defined rotation parameter. By taking into account the universal character of the velocity profiles, a formula is derived for describing the velocity distribution in an axially rotating pipe. The resulting velocity profiles are compared with measurements of Reich [10] and generally good agreement is found.

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Abbreviations

b :

constant, equation (34)

D :

pipe diameter

l :

mixing length

l 0 :

mixing length in a non-rotating pipe

N :

rotation rate,N=Re ϕ /Re D

p :

pressure

R :

pipe radius

Re D :

flow-rate Reynolds number,\(\operatorname{Re} _D = \bar v_z D/v\)

Re ϕ :

rotational Reynolds number, Re ϕ =v ϕw D/ν

Re*:

Reynolds number based on the friction velocity, Re*=v*R/ν

(Re*)0 :

Reynolds number based on the friction velocity in a non-rotating pipe

Ri:

Richardson number, equation (10)

r :

coordinate in radial direction

\(\tilde r\) :

dimensionless coordinate in radial direction,\(\tilde r = r/R\)

v r ,v ϕ,v z :

time mean velocity components

v′ r ,v′ ϕ ,v′ z :

velocity fluctations

v ϕw :

tangential velocity of the pipe wall

v*:

friction velocity,\(v_* = \sqrt {\left| {\tau _{rz} } \right|w/\rho } \)

\(\bar v_z \) :

axial mean velocity

v ZM :

maximum axial velocity

\(\tilde y\) :

dimensionless radial distance from pipe wall,\(\tilde y = 1 - \tilde r\)

y + :

dimensionless radial distance from pipe wall

y +1 :

constant

Z :

rotation parameter,Z =v ϕw/v * =N Re D /2Re*

ε m :

eddy viscosity

(ε m )0 :

eddy viscosity in a non-rotating pipe

λ :

coefficient of friction loss

κ :

von Karman constant

κ 1 :

constant, equation (31)

ρ :

density

μ :

dynamic viscosity

ν :

kinematic viscosity

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Authors and Affiliations

  1. Institut für Technische Thermodynamik, Technische Hochschule Darmstadt, Petersenstraβe 30, 64287, Darmstadt, Germany

    B. Weigand & H. Beer

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  1. B. Weigand
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  2. H. Beer
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Weigand, B., Beer, H. On the universality of the velocity profiles of a turbulent flow in an axially rotating pipe. Appl. Sci. Res. 52, 115–132 (1994). https://doi.org/10.1007/BF00868054

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  • DOI: https://doi.org/10.1007/BF00868054

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