On the universality of the velocity profiles of a turbulent flow in an axially rotating pipe |
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Authors: | B Weigand and H Beer |
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Institution: | (1) Institut für Technische Thermodynamik, Technische Hochschule Darmstadt, Petersenstra e 30, 64287 Darmstadt, Germany |
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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.Nomenclature
b
constant, equation (34)
-
D
pipe diameter
-
l
mixing length
-
l
0
mixing length in a non-rotating pipe
-
N
rotation rate,N=Re
/Re
D
-
p
pressure
-
R
pipe radius
- Re
D
flow-rate Reynolds number,
- Re
rotational Reynolds number, Re
=v
w
D/
- Re*
Reynolds number based on the friction velocity, Re*=v*R/
- (Re*)0
Reynolds number based on the friction velocity in a non-rotating pipe
- Ri
Richardson number, equation (10)
-
r
coordinate in radial direction
-
dimensionless coordinate in radial direction,
-
v
r
,v
,v
z
time mean velocity components
-
v
r
,v
,v
z
velocity fluctations
-
v
w
tangential velocity of the pipe wall
-
v*
friction velocity,
-
axial mean velocity
-
v
ZM
maximum axial velocity
-
dimensionless radial distance from pipe wall,
-
y
+
dimensionless radial distance from pipe wall
-
y
1
+
constant
-
Z
rotation parameter,Z =v
w/v
* =N Re
D
/2Re*
-
m
eddy viscosity
- (
m
)0
eddy viscosity in a non-rotating pipe
-
coefficient of friction loss
-
von Karman constant
-
1
constant, equation (31)
-
density
-
dynamic viscosity
-
kinematic viscosity |
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Keywords: | |
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