Applied Scientific Research

, Volume 52, Issue 2, pp 115–132

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

• B. Weigand
• H. Beer
Article

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.

Keywords

Rotational Speed Velocity Profile Flow Pattern Velocity Distribution Axial Velocity
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

b

constant, equation (34)

D

pipe diameter

l

mixing length

l0

mixing length in a non-rotating pipe

N

rotation rate,N=Re ϕ /Re D

p

pressure

R

ReD

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

Reϕ

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

$$\tilde r$$

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

vr,vϕ,vz

time mean velocity components

v′r,v′ϕ,v′z

velocity fluctations

vϕw

tangential velocity of the pipe wall

v*

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

$$\bar v_z$$

axial mean velocity

vZM

maximum axial velocity

$$\tilde y$$

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

y+

dimensionless radial distance from pipe wall

y1+

constant

Z

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

εm

eddy viscosity

(εm)0

eddy viscosity in a non-rotating pipe

λ

coefficient of friction loss

κ

von Karman constant

κ1

constant, equation (31)

ρ

density

μ

dynamic viscosity

ν

kinematic viscosity

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