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Diffusion of macromolecular solutions in the turbulent boundary layer of a cylindrical pipe

IV. Visualization and model of changes occurring at the diffusion boundary layer

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Abstract

A model is presented describing the changes that occur in the diffusion boundary layer upon injection of a macromolecular solution (PEO) into a cylindrical pipe under turbulent flow conditions (Re ≅ 40,000). A shape parameter was introduced to describe the shape of the turbulent plume. The value of this parameter was found to be the same for water and various dilute PEO solutions. The proposed model gives a good approximation at low homogeneous concentrations.

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Abbreviations

x :

downstream distance from the slot

y :

normal distance from the wall

R :

radius of the pipe

C :

concentration

C w :

wall concentration

Q i :

flow rate injection

Q t :

flow rate

C j =C i *Q i /Q t :

equivalent homogeneous polymer concentration

L tf :

characteristic length of the diffusion plume

λ :

characteristic height of the diffusion plume, i.e. the value ofy at whichC/C w = 0.5

δ :

thickness of the diffusion boundary layer

x 0 :

characteristic distance from the slot, i.e. the value ofx at whichδ/R = 1/2

Λ + :

shape parameter of the diffusion boundary layer

δ + —δ/R :

nondimensionalized variables

x + —x/L tf :

nondimensionalized variables

References

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Authors and Affiliations

  1. École Nationale Supérieure des Arts et Industries de Strasbourg, 24, Boulevard de la Victoire, F-67084, Strasbourg Cedex, France

    M. Bues

  2. Institut de Mécanique des Fluides de Strasbourg, ERA CNRS 0594, 2, Rue Boussingault, F-67083, Strasbourg Cedex, France

    H. Reitzer & O. Scrivener

Authors
  1. M. Bues
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  2. H. Reitzer
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  3. O. Scrivener
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Bues, M., Reitzer, H. & Scrivener, O. Diffusion of macromolecular solutions in the turbulent boundary layer of a cylindrical pipe. Rheol Acta 24, 312–316 (1985). https://doi.org/10.1007/BF01332610

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  • DOI: https://doi.org/10.1007/BF01332610

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