Pipeline Design for Isothermal, Turbulent Flow of Non-Newtonian Fluids

GBH Enterprises, Ltd.

Process Engineering Guide:
GBHE-PEG-FLO-304

Pipeline Design for Isothermal,
Turbulent Flow of Non-Newtonian
Fluids

Information contained in this publication or as otherwise supplied to Users is
believed to be accurate and correct at time of going to press, and is given in
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Process Engineering Guide:

Pipeline Design for Isothermal,
Turbulent Flow of NonNewtonian Fluids

CONTENTS

SECTION

0

INTRODUCTION/PURPOSE

2

1

SCOPE

2

2

FIELD OF APPLICATION

2

3

DEFINITIONS

2

4

DESCRIPTION OF ANOMALOUS EFFECTS

2

4.1
4.2
4.3
4.4

Wall Slip
Drag Reduction in Polymeric Materials
Transition Delay by Polymeric Materials
Drag Reduction in Suspensions

2
2
3
4

5

DESIGN PROCEDURE FOR PRESSURE DROP
IN TURBULENT PIPE FLOW IN THE ABSENCE
OF DRAG REDUCTION

5

Pressure Drop in the Absence of Wall Slip and
Drag Reduction
Wall Slip
Pipe Roughness
Pipe Fittings

5
5
5
5

DESIGN PROCEDURE FOR DRAG REDUCING
POLYMERIC MATERIALS

7

6.1
6.2
6.3
6.4

General
Transition Delay
Pipe Roughness
Pipe Fittings

7
8
8
9

7

FIBRE SUSPENSIONS

9

5.1
5.2
5.3
5.4

6


8

BIBLIOGRAPHY

9

9

NOMENCLATURE

10

FIGURES
1

DRAG REDUCTION PHENOMENA

3

2

TRANSITION DELAY PHENOMENA

4

3

PROCEDURE FOR THE CALCULATION OF
PRESSURE DROP IN TURBULENT NON-NEWTONIAN
PIPE FLOW

6

TYPICAL RELATIONSHIP FOR Ψ VERSUS ʋ*

8

4

DOCUMENTS REFERRED TO IN THIS PROCESS
ENGINEERING GUIDE

10


0

INTRODUCTION/PURPOSE

This Process Engineering Guide is one of a series of guides on non-Newtonian
flow prepared for GBH Enterprises.
Fluid flow in chemical plants is usually turbulent, and viscosities have to be high
before laminar flow predominates. When viscosities are high, the fluids are often
non-Newtonian in character. In this field of non-Newtonian flow, laminar flow
predominates and this is covered by GBHE-PEG-FLO-303. There are still many
instances when turbulent flow of non-Newtonian fluids is encountered.

1

SCOPE

This guide presents the basis for the prediction of flow rate - pressure drop
relationships for the turbulent flow of non-Newtonian fluid through circular pipes
under isothermal conditions. The Guide also deals with drag reduction by
polymeric materials and fibre suspensions.

2

FIELD OF APPLICATION

This guide applies to the process engineering community in GBH Enterprises
worldwide.

3

DEFINITIONS

For the purposes of this guide, no specific definitions apply.

4

DESCRIPTION OF ANOMALOUS EFFECTS

The fluids which can exhibit non-Newtonian effects are varied, and the flow can
be complicated by the anomalous effects described in 4.1 to 4.4.
4.1

Wall Slip

Wall slip can occur with the flow of slurries. Wall slip is a misnomer, as the liquid
does not, in fact, slip. What occurs is that under the appropriate circumstances, a
layer of fluid is formed next to the wall which has a viscosity appreciably less
than the bulk of the fluid.

This is caused both by the wall affecting packing arrangements of particles and
by the steep velocity gradients near the wall causing hydrodynamic lift effects
which move particles away from the wall. The net effect can be considered as an
effective "slip" at the wall, hence its name.
4.2

Drag Reduction in Polymeric Materials

The addition of very small concentrations of high polymeric substances can
reduce the frictional resistance in turbulent flow to as low as one quarter that of
the pure solvent. This phenomenon, drag reduction, can occur both with fluids
which exhibit Newtonian and non-Newtonian viscous characteristics. Drag
reduction is illustrated in Figure 1.
FIGURE 1

DRAG REDUCTION PHENOMENA


4.3

Transition Delay by Polymeric Materials

The phenomenon of transition delay is closely related to drag reduction and is
illustrated in Figure 2. The behavior shown in Figure 2(a) is typical of soap
solutions (see Ref. [1]) and that in Figure 2(b) is typical of certain types of
polymer solutions, such as polyacrylamide in water (see Ref. [2]).
With transition delayed flow, the flow does not attain turbulent flow
characteristics.
Drag reduction and transition delay are no doubt related but, on the basis of the
available evidence, there appear to be significant differences.
The distinction between the two phenomena is that with drag reduction the flow
attains non-drag reducing fully-developed turbulent flow before it is affected by
the polymer.


FIGURE 2

TRANSITION DELAY PHENOMENA


4.4

Drag Reduction in Suspensions

Drag reduction can also occur with the flow of suspensions of rigid, elongated
particles. The shape of the particles is all important, as Kerekes and Douglas
(see Ref. [3]) observed that drag reduction did not occur with suspensions of
spherical particles but did with suspensions of particles having an elongated
shape.
Vaseleski and Metzner (see Ref. [4]) have reviewed the work which has been
carried out into pressure drop in fibre suspensions and have drawn a number of
important conclusions; viz drag reduction in fibre suspensions:
(a)

Increases for a particular fibre as the fibre concentration is increased.

(b)

Increases as the aspect ratio (length to diameter ratio) of the fibers is
increased at constant fibre concentration.

(c)

Is not dependent upon the pipe diameter.

Much less work has been carried out on drag reduction in fibre suspensions than
polymeric materials; this makes design procedures less reliable.

5

DESIGN PROCEDURE FOR PRESSURE DROP IN TURBULENT PIPE
FLOW IN THE ABSENCE OF DRAG REDUCTION

5.1

Pressure Drop in the Absence of Wall Slip and Drag Reduction

Both slurries of approximately spherical particles and polymer solutions can,
under certain circumstances, flow turbulently without exhibiting any of the
anomalous effects described in Clause 4. In the absence of these effects,
Newtonian friction factor correlations can be used to calculate the pressure drop
in turbulent non-Newtonian pipe flow if Reynolds numbers are based on the
apparent viscosity at the wall (see Ref. [5]). Unfortunately, we cannot calculate
the apparent viscosity at the wall until we know the shear stress at the wall (and
hence the pressure drop); consequently an iterative calculation is required.
Figure 3 shows a flow chart for the calculation of pressure drop in turbulent nonNewtonian pipe flow in the absence of any wall effects.


Any departure of experimental data from the Newtonian friction factor correlation
indicates the presence of anomalous effects. Without experimental data under
turbulent conditions it is impossible to predict how a polymeric material or fibre
suspension will behave under turbulent flow conditions.
5.2

Wall Slip

No procedures are currently available for estimating the effect of wall slip under
turbulent flow conditions. If it is neglected in design calculations and does occur
then it is likely to lead to pressure drop predictions which are high and hence, in
most instances, a conservative design. This does not mean to say that wall slip
can also be ignored in the laminar regime. The viscometric measurements
required to characterize the fluid are described in GBHE-PEG-FLO-302.
5.3

Pipe Roughness

All of the experimental work which has been carried out on the turbulent flow of
non-Newtonian fluids in the absence of wall effects has involved hydraulically
smooth pipes. Wall roughness will no doubt affect the turbulent flow of nonNewtonian fluids as it does with Newtonian fluids. In the absence of any
information, it is recommended that the calculation procedure given in Figure 3
still be followed and wall roughness be included in the calculations in the same
way as it would be for a Newtonian fluid but of course using a Reynolds number
based on the apparent viscosity at the wall.
5.4

Pipe Fittings

In turbulent Newtonian flow through pipe fittings, viscous effects are not normally
significant and pressure drops are based on a number of velocity heads lost. It is
thus recommended that pressure losses for the flow of non-Newtonian fluids be
calculated in the same way as for Newtonian fluids. Some data for laminar
pressure drop in pipe fittings have been given in GBHE-PEG-FLO-303.

FIGURE 3

PROCEDURE FOR THE CALCULATION OF PRESSURE DROP
IN TURBULENT NON-NEWTONIAN PIPE FLOW (provided wall
effects are not present)


6

POLYMERIC MATERIALS

6.1

General

Numerous studies have been undertaken to characterize drag reduction
phenomena in polymeric materials and these have been reviewed by Hoyt,
Lumley and Virk (see Refs. [6], [7] and [8] respectively). The evidence which is
available suggests that the presence of the polymer in drag reducing flows alters
the structure of the turbulence in a complex manner. These complexities,
coupled with the difficulty of defining physical properties which characterize
drag reduction, make a scaling procedure attractive for design work, i.e. being
able to scale pressure-drop measurements from one diameter of pipe to another.
This would require turbulent viscometric measurements to be made, in addition
to the normal laminar flow viscometric measurements required to characterize
the fluid.
In order to scale drag reduction from one flow situation to another, it is first
necessary to define the degree of drag reduction in some way. As drag reduction
can at maximum reduce to laminar flow, it would seem logical to define it with
respect to this maximum effect. In fact, Metzner and Park (see Ref. [2])
suggested a ratio of the form:


flow and found that for a particular fluid the value Ψ was a unique function of
the observed friction velocity and independent of pipe diameter. Thus, for a
particular fluid:

Thus, given the fluid density, the purely viscous laminar flow properties of the
fluid, the pipe diameter and bulk velocity, then v* can be calculated (hence t w
and ΔP) if f(v*) is known. This function f(v*) should be determined
experimentally for each fluid. A typical curve is shown in Figure 4. It should be
noted, however, that this method of correlation does not work with transition
delay phenomena.
If a particular design problem does not warrant experimental measurements,
then an over prediction of the pressure drop will be obtained by following the
calculation procedure shown in Figure 3. It is important to note, however, that a
friction factor obtained in this manner (i.e. from Figure 3) should not be used in
heat transfer calculations otherwise this could lead to a gross over-prediction of
the heat transfer coefficient.

FIGURE 4 TYPICAL RELATIONSHIP FOR Ψ VERSUS v*

6.2

Transition Delay

Drag reduction and transition delay behavior are no doubt related. However, the
methods described for dealing with drag reduction do not apply to transition
delay. The small amount of experimental evidence which is available suggests
that the method recommended for correlating pressure drop data in drag
reducing flow (i.e. Ψ against v*) does not work effectively with transition delay.
There are currently no reliable methods available for correlating transition delay
data.
6.3

Pipe Roughness

Polymeric materials are just as effective in reducing drag in rough pipes as they
are in smooth pipes. Virk (see Ref. [10]) carried out an extensive study into the
flow of polymeric materials in roughened pipes. Although his data were
characteristic of transition delay rather than drag reduction, one particularly
important result is worth noting. Virk found that the maximum drag

reduction attainable for a given fluid had the same value for a given Reynolds
number in both smooth and rough pipes.
This implies that the function f(v*) in Equations (2) and (3) should be the same
for both smooth and rough pipes. However, it is recommended that turbulent
pressure drop experiments to determine f(v*) be carried out using pipes with the
same relative roughness (ε/D) envisaged for the design.
6.4

Pipe Fittings

No investigations have been carried out into the flow of polymeric materials
through pipe fittings under turbulent flow conditions. If pressure drops are
calculated in the same way as for Newtonian flow, then this is likely to lead to an
over-prediction of pressure drop.

7

DESIGN PROCEDURE FOR DRAG REDUCING FIBRE SUSPENSIONS

Pressure drop in drag reducing fibre suspensions is less complex to correlate
than in polymeric materials. There is no diameter effect with the flow of fibre
suspensions and thus data for a particular fluid can be represented as a unique
function on a plot of friction factor against Reynolds number. However, the
friction factor vs Reynolds number relationship for a particular fibre suspension
cannot be predicted and can only be determined experimentally.


8

BIBLIOGRAPHY

This Process Engineering Guide makes reference to the following:
[1]

A.White, Flow characteristics of complex soap systems, Nature, London
214, 585-586 (1967)

[2]

A.B.Metzner and M.G.Park, Turbulent flow characteristics of viscoelastic
fluids, J Fluid Mech 20,291-303 (1964)

[3]

R.J.E.Kerekes and W.J.M.Douglas, Viscosity Properties of Suspensions at
the Limiting Conditions for Turbulent Drag Reduction, Can. J Chem. Eng.
SO, 228-231 (1972)

[4]

R.C.Vaseleski and A.B.Metzner, Drag Reduction in the Turbulent Flow of
Fibre Suspensions, A.I.Ch.E.JL 20, 301-306 (1974)

[5]

M.F.Edwards and R.Smith, The turbulent flow of non-Newtonian fluids in
the absence of anomalous wall effects J. Non-Newtonian Fluid Mech.
7,77-90 (1980)

[6]

J.W.Hoyt, The effect of additives on fluid friction, Trans ASME 94D, 258285 (1972)

[7]

J.L.Lumley, Drag reduction in turbulent flow by polymer additives, J.
Polymer Sci Macromol. Rev. 7, 263-290 (1973)

[8]

P.S.Virk, Drag reduction fundamentals, A.I.Ch.JL.21, 625-656 (1975)

[9]

N.F.Whitsitt, L.J.Harrington and H.R.Crawford in C.S. Wells, Viscous Drag
Reduction, Plenum Press (1969)

[10]

P.S.Virk, Drag reduction in Rough Pipes, J.Fluid Mech. 45, 225-246
(1971).


9

NOMENCLATURE


DOCUMENTS REFERRED TO IN THIS PROCESS ENGINEERING GUIDE
This Process Engineering Guide makes reference to the following documents:
PROCESS ENGINEERING GUIDES
GBHE-PEG-FLO-302

Interpretation and Correlation of Viscometric Data
(referred to in 5.2)

GBHE-PEG-FLO-303

Pipeline Design for Isothermal, Laminar Flow of NonNewtonian Fluids (referred to in Clause 0 and 5.4)


Pipeline Design for Isothermal, Turbulent Flow of Non-Newtonian Fluids

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