Drag Reduction.pdf

DRAG REDUCTION

Introduction

The main objective of drag reduction is to reduce the ﬂuid mechanical force known

as “drag,” which is exerted on an engineering system improving its efﬁciency. There

are passive and active techniques to reduce the drag (1). The passive techniques

do not require any energy input to ﬂow; only installation and maintenance costs

are involved. The riblets and large eddy breakup devices fall into this category.

However, the maximum drag reduction is limited up to 10%. The active techniques

require certain energy input. However, level of drag reduction achieved is up to

80%. Among all the techniques, additions of minute amount of high molecular

weight polymers and surfactants have been very active area of research ever since

Toms reported it in 1949 (2).

The discovery of turbulent drag reduction due to particle suspensions goes

back to the 1930s. Forest and Grierson (3) reported the turbulent drag reduction in

pipe ﬂow of wood-pulp ﬁber suspensions of water. Vanoni (4) observed that water

with suspended sand ﬂowed more rapidly in an open channel. Toms (5) and Mysels

(6) independently observed the striking reduction in turbulent drag in pipe ﬂows

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of solutions of high molecular weight poly(methyl methacrylate) (5–10 ppm by

weight) in monochlorobenzene and of aluminum disoaps in hydrocarbon liquids,

respectively. Since Toms (2,5) was the ﬁrst to publish his results, the phenomenon

of turbulent drag reduction is also known as Toms effect. Ever since the reporting

of these results, there has been extensive research activity in this fascinating

ﬁeld of ﬂuid mechanics and polymer science. Nadolink and Haigh (7) compiled

an exhaustive bibliography on the subject containing over 4900 references dating

from 1931 to 1994.

The soluble polymers are the most potential drag-reducing agents of all the

additives mainly because drag reduction of up to 80% can be obtained with the

addition of a few tens of ppm by weight in a particular solvent. The polymer

solution drag reduction has been investigated in aqueous and hydrocarbon liquids,

and a number of excellent reviews have been written by a number of experts

(8–25). Many state-of-the-art papers have also appeared in number of conference

proceedings (26–31).

Drag-reducing polymers have been successfully applied for potential beneﬁts

in various industrial processes and operations, such as long-distance transporta-

tion of liquids, oil-well operations, sewage and ﬂood water disposal, ﬁre ﬁghting,

transport of suspensions and slurries, irrigation, water-heating and [cooling cir-

cuits, jet cutting, and marine and biomedical operations. The developments in the

above] cited ﬁelds are reviewed in the 1990s by Singh (20), Morgan and McCormick

(21), Den Toonder (22), Gyr and Bewersdorff (23), Moussa (24), and Gad-El-Hak

(25).

10 5 ) are very effective drag reducers, but

get degraded in turbulent ﬂows and lose their effectiveness after a short interval

of time or ﬂow. Aluminum diasops and other surfactants form aggregates or mi-

celles at a critical micellar concentration (CMC). These micelles are responsible

for drag reduction. These micelles also degrade after critical shear stress though

anionic soaps are found to be good and mechanically stable drag reducers (34). But

when shear stress becomes lower than the critical shear stress, the micelles are

reformed and restore the drag reduction effectiveness. Because of their repairabil-

ity and the capability to withstand higher temperatures, the research activity in

surfactant drag reduction has increased appreciably. The anionic, cationic, non-

ionic, and zwitterionic surfactants have been investigated for their drag-reduction

effectiveness (DRE). Though anionic soaps are found to be good and mechanically

stable drag reducers (34), their use is not favoured because of their vulnerability

The most successful application of drag-reduction phenomenon has been in

reducing the drag in crude oil transport through Trans Alaskan Pipelines (TAPS)

and other pipelines in several countries. The ﬁrst large-scale use of hydrocarbon-

soluble drag reducer addition (DRA) in TAPS was accomplished in 1979. The

technology made spectacular advancement since then. Within 10 years, the ef-

fectiveness of additives increased 12 times (32). Because of the effectiveness

of the polymer injection technique, the need of building two delayed pumping

stations disappeared. The 1 ppm of the drag reducer used in the pipeline in-

creased the ﬂow rate by 33%. Several important pipelines such as Tukey-Iraq,

Bas Strait (Australia), Bombay Off Shore (India), etc, have used drag-reducing

additive injection for saving considerable energy. Newer areas are being explored

(23,25,33).

High molecular weight polymers (

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DRAG REDUCTION 521

to calcium and magnesium ions normally present in tap and sea water, and their

foam-forming characteristics (35). Nonionic surfactants have narrow temperature

window of applicability around their cloud points (36). Cationic surfactants show

much broader effective temperature window of applicability, and thus have larger

potential for practical applications (37). The drag-reducing characteristics of zwit-

terionic surfactants are being studied (38–40).

The potential application of surfactants exists in district heating and cooling

systems. The characteristics of surfactant drag reducers differ from polymeric

drag reducers in several aspects particularly having higher level of drag reduction

crossing the Virk’s maximum drag reduction asymptote (41,42).

Several attempts have been made to enhance the DRE and mechanical

stability of polymer drag reducers. In general, homopolymers, alternate copoly-

mers, graft polymers, and polyelectrolytes and polysaccharides from natural and

microbial resources are efﬁcient drag reducers in water, organic solvents, and

crude oil (23,25,43). The extent of drag reduction increases with the molecular

weight and length of the polymers, and so does their susceptibility to ﬂow-induced

degradation.

Recently, three approaches have been put forward to enhance the DRE and

shear stability of polymers. The DRE of polysaccharides can be enhanced by graft-

ing synthetic polyacrylamide branches onto their main chains; the resulting graft

polymers combine efﬁciency of synthetic polymers and robustness of polysaccha-

ride chains (44,45). The reversible intermolecular associations in solution increase

the molecular weight of polymer associates and provide mechanical stability

(46–49).

The third approach is by using cross-linking among the polymer molecules.

The drag-reducing polymers such as guar gum can be cross-linked with concentra-

tion below those required for gel formation. The presence of intermolecular cross-

links leads to increased dimensions of the macromolecules resulting in enhanced

drag reduction though the induced degradation of the polymers is not apprecia-

bly affected by the addition of cross-linking agents (50). The ﬁrst and third ap-

proaches have been pursued for water-soluble systems. It has been observed that

in the ﬁrst approach, the level of DRE is higher, that too at low concentrations

(

100 ppm) of graft copolymers, and that cross-linking is not effective in shear

degradation.

Rheology of polymers and surfactants solutions plays an important part in

drag reduction. Though very dilute drag-reducing solutions have rheological be-

haviors similar to Newtonian solvents except for the anionic polyacrylamide solu-

tions having shear-thinning behaviors at drag-reducing concentration of 50 ppm

(51), their extensional effects may be important. Efforts are still in progress to

measure and correlate the extensional effects to drag reduction (52–60). The

degradation of polymers in turbulent ﬂow needs to be investigated in order

to enhance the effectiveness of polymers by modeling degradation mechanism

(43,61–65).

There are three ways of introducing a polymer solution in the water ﬂow. In

the ﬁrst case of homogeneous drag reduction, the polymer is allowed to mix ho-

mogeneously into the solvent. In the second case of heterogeneous drag reduction,

a highly concentrated polymer solution is injected in the center or at the wall of

the pipe, which disperses completely by turbulent diffusion to yield homogenous

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solution some distance downstream the injector. In the third case, a concentrated

polymer solution is injected into the center line of a turbulent ﬂow at a high

enough concentration that a single coherent unbroken polymer thread forms at

the injector and continuous downstream for several hundred pipe diameters. The

polymer threads have also been injected at the wall or buffer zone of the ﬂow by

Frings (66), who attained highly heterogeneous mixtures downstream. In some

cases (67–69), high concentration strings of polymer develop rather than a single

coherent thread.

All the above forms of drag reduction have been studied in the case of sur-

factant drag reduction as well. The origin of drag reduction in all cases has been

indicated to be similar (70,71). The origin of drag reduction has been extensively

investigated from the very beginning. With the advent of laser Doppler anemome-

try (LDA) (72), and later on with the phase laser anemometry (73), it was possible

to measure and investigate velocity characteristics of ﬂows with precision without

interfering with them. LDA has been extensively used to study various aspects of

drag reduction, particularly in channel ﬂows (74).

Dodge and Metzner (75) developed a correlation between friction factor and

Reynolds number for turbulent pipe ﬂow of purely viscous shear-thinning liquids

based upon a power-law model of shear viscosity. Metzner and Park (76) correlated

the degree of drag reduction in turbulent ﬂow of viscoelastic polymer solutions

with the ratio of elastic to viscous stress, ie with N i /

τ s the corresponding

shear stress. Though the role of extensional viscosity in causing turbulent sup-

pression or drag reduction is being debated till date, there is a persistent view

that the elongational viscosity, possibly in combination with viscoelasticity, is re-

sponsible for drag reduction.

Gadd (77) was among the ﬁrst to point out that the damping of the turbu-

lence by polymer additives is due to their resistance to elongational strain, which

suppresses shear formation and bursting in near-wall region. Lumley (78,79) sug-

gested that the uncoiling of polymer molecules under ﬂuctuating shear rate in

the buffer region of turbulent ﬂow causes drag reduction because of increase of

extensional viscosity. Gyr (80), Durst and co-workers (81), and Bewersdorff and

Berman (82) provided the extensional viscosity model of drag reduction. Vlas-

sopoulos and Schowalter (51,52) suggested that the origin of DRE is due to the

ﬂuid elasticity inferred from oscillation-induced streaming. Matthys (83) pointed

out the common origin of the extensional viscosity and viscoelasticity. de Gennes

(84) hypothesized that the polymer drag reduction is due to the elastic, rather

than the viscous, phenomenon. Several direct numerical simulations by Orlandi

(85), Den Toonder and co-workers (64,86), and Massah and Hanratty (87) exam-

ined the role of viscoelasticity, extensional viscosity, and stress anisotropy in drag

reduction. Direct numerical simulation (DNS) investigation of Den Toonder and

co-workers (86) points out that drag increases rather than decreases when the

elastic contributions are taken into account.

For the case of viscous anisotropic polymer model, almost all turbulence

statistics and power spectra calculated agree in qualitative sense with experimen-

tal results. Dimitropolous and co-workers (88) did DNS for fully turbulent chan-

nel ﬂow of a polymer solution using the ﬁnitely extensible nonlinear elastic head

spring dumbbell model with Peterlin approximation (FENE-P) and the Giesekus

, and

τ s , where N i is the ﬁrst nor-

mal stress difference for a given wall shear–strain rate

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DRAG REDUCTION 523

model. They demonstrated that the solution extensional viscosity plays the pri-

mary role in turbulent drag reduction. Comparing the mean velocity proﬁles and

statistical features of the turbulent ﬂow showed agreement with well-established

experimental observations, such as enhanced buffer zone, increase in the spacing

of the streamwise streaks, decrease in the streamwise vorticity ﬂuctuations, and

increase in the streamwise velocity ﬂuctuations. This demonstrated the onset of

drag reduction in a turbulent ﬂow at a sufﬁciently high level of viscoelasticity in

the ﬂow and reinforced previously held hypothesis that one of the prerequisites for

the phenomenon of drag reduction is sufﬁciently enhanced extensional viscosity.

However, Sreenivasan and White (89) point out that the connection between

ﬂuctuating strain rates and large extensional viscosity is circumstantial. Further

polymer coils can only be partially stretched in a random ﬁeld of strain rate.

Sreenivasan and White (89) point out that the elastic theory proposed by de

Gennes (84) is compatible with at least two experimental observations; ie, the

dependence of drag reduction onset on polymer concentration and maximum drag

reduction asymptote.

On the other hand, DNS of turbulence in channel ﬂow based on FENE-P

bead-spring chains in the presence of large-enough velocity gradients by Massah

and Hanratty (87) indicates that polymers cause drag reduction by selectively

changing the structures of eddies that produce Reynolds stresses. Their calcula-

tions (87) support the suggestions by Lumley (78) that the polymers can become

unravelled by the turbulence in the buffer region. The calculated unravelling of

a bead-spring chain in the viscous sublayer could explain the increased viscosity

observed by Vismann and Bewersdorff (90) and by James and co-workers (91) in

elongational ﬂow when the solution is presheared in laminar Couette or chan-

nel ﬂow. Thus these investigations point out the basis of further research on the

origin of drag reduction and explanation of its various manifestations in both

polymeric and surfactant drag reduction. A large number of reviews are available

in literature till 1990. In this review, emphasis will be given on the researches

reported since then, with comprehensive accounts of materials, mechanisms, and

applications in the ﬁeld of turbulent drag reduction in liquids.

Characteristics of Turbulent Drag Reduction

Mathematical Description. Lumley’s (92) deﬁnition of drag reduction,

“drag reduction is the reduction of skin friction in turbulent ﬂow below that of

the solvent,” will be followed in this review. Most of the studies on drag reduction

have been conﬁned to hydraulically smooth pipe ﬂows or channels; hence various

physical parameters will be described in terms of smooth pipe ﬂows.

Reynolds was the ﬁrst to ﬁnd out that transition from laminar to turbulent

ﬂow takes place in cylindrical-pipe ﬂows of water at a particular value (

R e =

(1)

2300)

of a dimensionless parameter known as the Reynolds number ( R e ), where R e is

given by the following relation:

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