Turbulent mixing of fluids with different densities flowing through a pipe |
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Authors: | V I Maron |
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Affiliation: | (1) I. M. Gubkin Institute of the Petrochemical and Natural Gas Industry, Moscow |
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Abstract: | A one-dimensional model of a disperse mixture in a turbulent stream is constructed, with the mutual effect of mixture concentration and turbulence intensity taken into account.Notation
0
mean-over-the-section density
- p
pressure
-
t
turbulent viscosity
- U
average longitudinal velocity
- g
acceleration of gravity
-
angle of pipe inclination from the horizontal
- x, r
cylindrical coordinates
- t
time
- V
average radial velocity
- C
average concentration
- Dt
turbulent diffusivity
- c0
mean-over-the-section concentration
- K
effective turbulent diffusivity
- U0
mean flow velocity
- X
distance, in the moving system of coordinates
-
a
pipe radius
-
0
frictional stress at the inside surface of the pipe
- u*
transient turbulent velocity
- b
turbulence intensity
-
l
linear scale factor
-
chemical potential of mixture
-
density of mixture
- d1, d2
densities of homogeneous fluids
- y+
thickness of laminar layer
- y
distance from the inside pipe surface
- +
derivative of velocity at the layer boundary on the turbulent side
-
hydraulic drag
- Gr
Grashof number
- Re
Reynolds number
- 1, 2,
coefficients in the equation for K*
- K*
dimensionless effective diffusivity
-
=U0t/2a
dimensionless time
-
=X/2a
dimensionless distance
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 6, pp. 992–998, June, 1972. |
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Keywords: | |
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