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Turbulent expansion flow of low molecular weight shear-thinning solutions

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Abstract

A Laser-Doppler anemometer and a pressure transducer were used to carry out detailed measurements of the mean and root mean square of the velocity and wall-pressure in an axisymmetric sudden expansion flow, with 0.4 and 0.5% by weight shear-thinning aqueous solutions of a low molecular weight polymer (6,000), after appropriate rheological characterisation. In spite of their very low molecular weight, these solutions still exhibited elongational elastic effects through drag reduction of up to 35% relative to Newtonian turbulent pipe flow, as shown by Pereira and Pinho (1994).

The results showed small variations of the recirculation bubble length with polymer concentration and Reynolds number and reductions of the normal Reynolds stresses of up to 30%, especially in the tangential and radial directions. The reduction in normal Reynolds stresses within the shear layer is an elongational elastic effect, but this elasticity needs to be considerably more intense, such as with high molecular weight polymers, in order to strongly affect the mean flow characteristics. The observed mean flow patterns with these low molecular weight polymer solutions were indeed similar to those exhibited by Newtonian and inelastic fluids.

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Abbreviations

D :

diameter of pipe downstream of sudden expansion

d :

diameter of pipe upstream of sudden expansion

ER :

expansion ratio

h :

step height

K :

consistency index in power law model

k :

turbulent kinetic energy

L :

recirculation bubble length

n :

power law index in power law and Carreau viscosity models

R :

radius of pipe downstream of sudden expansion

Re :

Reynolds number

Re a :

Reynolds number based on wall viscosity in the upstream pipe

Re gen :

generalised Reynolds number (Eq. 4)

r :

local radius

U :

axial bulk velocity

U in :

axial bulk velocity at inlet

u :

local axial mean velocity

u 0 :

axial centreline velocity

u′ :

local root mean square of axial velocity

v′ :

local root mean square of radial velocity

w′ :

local root mean square of tangential velocity

\(\dot \varepsilon\) :

dissipation rate of turbulence

\(\dot \gamma\) :

shear rate

λ :

time constant of Carreau viscosity model

ϱ :

fluid density

μ :

fluid viscosity

μ a :

viscosity at the wall in the upstream pipe

μ 0 :

zero shear-rate viscosity

ch :

refers to a characteristic value

in :

refers to characteristic values at the inlet pipe

max:

refers to maximum values

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Author information

Authors and Affiliations

  1. Departamento de Engenharia Mecânica, Instituto Superior de Engenharia do Porto, 4200, Rua de S. Tomé, Porto, Portugal

    O. S. Castro

  2. Departamento de Engenharia Mecânica e Gestão Industrial, Faculdade de Engenharia da Universidade do Porto, 4099, Rua dos Bragas, Porto Codex, Portugal

    F. T. Pinho

Authors
  1. O. S. Castro
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  2. F. T. Pinho
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Additional information

This paper is dedicated to the memory of late Professor A.O. Restivo

The authors acknowledge the support of the ex-Instituto Nacional de Investigação Científica — INIC, Instituto de Engenharia Mecânica e Gestão Industrial — INEGI and Laboratório de Hidráulica da Faculdade de Engenharia in helping to finance the rig, lending some equipment and for providing building space for the installation, respectively. We also would like to thank M. Paulo Coelho and Ms. Doris Dobbelman for their contribution to the measurements and Hoechst, Portugal for providing us with some of the polymer additives.

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Castro, O.S., Pinho, F.T. Turbulent expansion flow of low molecular weight shear-thinning solutions. Experiments in Fluids 20, 42–55 (1995). https://doi.org/10.1007/BF00190597

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