Drag reduction by polymer–polymer mixtures

An extensive study on the turbulent drag reduction caused by the various mixtures of polyacrylamide, purified guargum, xanthangum, and their graft copolymers has been conducted at low concentrations and Re = 14,000 using a turbulent flow rheometer. It has been found in most of the cases that the drag reduction caused by mixtures shows a positive deviation from the linearly additive straight line. This effect is more prominent when the drag reduction caused by both the constituents differ appreciably. In most of the cases, the drag reduction caused by the mixtures is higher than the DR caused by either of the constituent polymers; however, the drag reduction caused by the mixture is less than the sum of the drag reduction caused by both the constituents at their respective concentration in the mixture. It has also been noticed that there is no evidence of synergism in these mixtures at low concentrations.     

The turbulent drag reduction by graft copolymers of guargum and polyacrylamide

Commercial guargum is known to be a shear stable drag reducing agent. However, the aqueous solutions of guargum start degrading within 8 hrs. of their preparation and after 65 hrs., they degrade completely. In the present investigation, the graft copolymers of guargum and polyacrylamide have been prepared. It has been shown that the purification and grafting enhance the drag reduction effectiveness and biodegradation resistance considerably in guargum.     

Drag reduction effectiveness,shear stability and biodegradation resistance of guargum-based graft copolymers

Guargum is a seed galactomannan and is known to be a shear stable drag reducing agent. However, the aqueous solutions of guargum are very susceptible to microbial degradation. In the present investigation, seven graft copolymers of guargum and polyacrylamide have been synthesized and their drag reduction effectiveness, shear stability, and biodegradation resistance have been determined. It has been shown that the drag reduction effectiveness and shear stability of the graft copolymer depend upon the length of the graft and number of grafts in the molecule. None of the graft copolymer solutions show any microbial degradation up to 10 days.     

Drag reduction by fibers

Drag reduction in turbulent pipe flow by means of boundary and centerline injection of long hair-like asbestos fibers has been investigated. Pressure drop and mean velocity profiles were measured at various Reynolds numbers and injection rates in order to study some mechanistic aspects of drag reduction in water-fiber and polymer-fiber systems. Drag reduction in a water-fiber system is attributed to a decrease in the momentum transfer in the turbulent-core region, whereas synergism has been found to be a wall phenomenon.     

Drag reduction by fibers

Drag reduction in turbulent pipe flow by means of boundary and centerline injection of long hair-like asbestos fibers has been investigated. Pressure drop and mean velocity profiles were measured at various Reynolds numbers and injection rates in order to study some mechanistic aspects of drag reduction in water-fiber and polymer-fiber systems. Drag reduction in a water-fiber system is attributed to a decrease in the momentum transfer in the turbulent-core region, whereas synergism has been found to be a wall phenomenon.     

Turbulent flow behaviour of dilute polymer solutions in an annulus

An experimental study has been carried out to investigate the turbulent flow behaviour of dilute polymer solutions in an annulus. The polymers used are two grades of Separan, AP30 and MG500, both are known to exhibit drag reduction characteristics in turbulent pipe flow. Similar drag reduction phenomena have been observed in annulus flow. At a given Reynolds number, the friction factor decreases with increase in polymer concentration and appears to reach a minimum (or maximum drag reduction) at certain optimum concentration. An estimate of the critical wall shear stress, which marks the onset of drag reduction, is consistent with pipe flow results, suggesting that the critical value is independent of flow geometry and size. A lower drag reduction, achieved in an annulus in comparison with circular pipes, is attributed mainly to a diameter effect.     

Turbulent friction reduction by aqueous poly(ethylene oxide) polymer solutions as a function of salt concentration

Turbulent friction reduction by high molecular weight poly(ethylene oxide) polymers has been examined in a series of salt solutions ranging from pure water to nearly theta solvent conditions. The effects of polymer homology and solvent character have been successfully analyzed under these conditions and relationships are proposed for the observed effects. The reduction in turbulent friction (drag reduction) has been catalogued through evaluation of the polymer intrinsic concentration—an index of drag reduction effectiveness. Plots of the reciprocal of the polymer intrinsic concentration versus salt molarity are approximately linear and are similar to the plots of intrinsic viscosity versus molarity reported by other workers. An attempt is made to graphically and numerically combine these results. The suggestion is advanced that those solvent properties which bring about decided conformational changes in these polymer molecules (as indexed by intrinsic viscosity effects) also affect, in an apparently analogous fashion, the turbulent friction reduction efficiencies of these molecules. The decreases in turbulent friction reduction resulting from the increasingly collapsed state of the polymer coil suggest the possibility of correlating friction reduction with changes in the polymer expansion factor α. On the basis of the limited data available, the suggestion is also made that drag reduction studies might best be made under theta solvent conditions where different polymer families might be more meaningfully compared in the absence of solvent effects.     

SOME MOLECULAR EFFECTS IN DRAG REDUCTION: A SUMMARY†

Dilute solutions of high molecular weight polymers have drawn a great deal of interest in recent years because of their drag reducing characteristics. It is well-known now that a substantial reduction in turbulent frictional drag can be achieved with a very small amount of polymeric additives, usually only a few parts per million by weight (ppmw) in concentration. This unique phenomenon has offered a new dimension in the design development of new marine systems for higher speed, longer range, larger payload as well as possibly quieter machinery. Although the discovery of this turbulent drag reduction phenomenon may be traced back to Toms¹ and Mysels² in the 1940's, the U.S. Navy's exploration of the turbulent drag reduction effect did not begin until the pioneering effort of Hoyt and Fabula in the 1960's. ³ During a period of several years in the early 19707apos;s, an interdisciplinary group at the Naval Research Laboratory undertook an intensive basic research effort to study the effects of polymer molecular structure on turbulent drag reduction. Model compounds were synthesized in the laboratory, and their drag reducing properties characterized. Polymers including polyacrylamide and its derivatives, polyacrylic acid, poiyphosphate and association colloids have been investigated. In this report, an attempt is made to highlight some of the results from that program in a brief summary form.     

Scaling functions of polymer‐induced turbulent drag reduction focusing on the polymer–solvent interaction

Based on turbulent drag reduction characteristics of polystyrene and polyisobutylene in a pipe flow and a rotating‐disk flow, respectively, a relationship between polymer concentration and drag reduction at a given Reynolds number was considered. The universal drag reduction equation of a three‐parameter relationship between drag reduction and polymer concentration was modified using intrinsic concentration and intrinsic viscosity, and it was then found to be the most useful formula for correlating DR data, especially for polymer–solvent interactions in a turbulent flow. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 1836–1839, 2003     

Heat transfer to an immiscible liquid mixture and between liquids in direct contact

Heat transfer to a mixture of two immiscible liquids has been studied in connection with the development of a process for the desalination of sea water. The liquid system consisted of water and refined mineral oil, produced by BP under the trade name of Energol WM-2.Heat transfer to water drops descending through the mineral oil was also investigated. The drag coefficients of the drops in motion were expressed as a function of the Reynolds number. A good correlation was obtained for the heat transfer coefficient expressing the Nusselt number in terms of the Peclet number.Heat transfer to a mixture of two immiscible liquids in co-current turbulent flow without phase change was extensively studied. Friction factor and heat transfer for the oil-in-water type mixtures were theoretically expressed in terms of the volume fraction of oil. The experimental data checked the theoretical derivation quite satisfactorily. No correlations could be obtained for the water-in-oil systems.Similar studies were made for heat transfer in the laminar and turbulent flow with phase change, using a pilot-plant evaporator. Curves were obtained relating the convective heat transfer coefficient to fluid velocity for the liquid mixtures. It was established that, the heat transfer coefficient in evaporation decreased by velocity in the laminar region, but increased in the turbulent region.     

SOME MOLECULAR EFFECTS IN DRAG REDUCTION: A SUMMARY†

Dilute solutions of high molecular weight polymers have drawn a great deal of interest in recent years because of their drag reducing characteristics. It is well-known now that a substantial reduction in turbulent frictional drag can be achieved with a very small amount of polymeric additives, usually only a few parts per million by weight (ppmw) in concentration. This unique phenomenon has offered a new dimension in the design development of new marine systems for higher speed, longer range, larger payload as well as possibly quieter machinery. Although the discovery of this turbulent drag reduction phenomenon may be traced back to Toms¹ and Mysels² in the 1940's, the U.S. Navy's exploration of the turbulent drag reduction effect did not begin until the pioneering effort of Hoyt and Fabula in the 1960's. ³ During a period of several years in the early 19707apos;s, an interdisciplinary group at the Naval Research Laboratory undertook an intensive basic research effort to study the effects of polymer molecular structure on turbulent drag reduction. Model compounds were synthesized in the laboratory, and their drag reducing properties characterized. Polymers including polyacrylamide and its derivatives, polyacrylic acid, poiyphosphate and association colloids have been investigated. In this report, an attempt is made to highlight some of the results from that program in a brief summary form.     

HYDRAULIC TRANSPORT OF COAL IN PIPES WITH DRAG REDUCING ADDITIVES†

The aim of the investigations was to determine the drag reduction produced by polymer additives in the hydraulic transport of coal. As no systematic results were available in the literature, experiments were undertaken using a wide range of flow velocities and polymer concentrations (up to 440 ppm) to obtain a clear picture about the processes involved. Special attention was paid to the effects of polymer degradation. The experiments were carried out on two different facilities for hydraulic transport with pipe diameters of 40 and 250 mm

Two criteria were used for selecting the polymer with the most favourable properties. It was to produce the largest possible amount of drag reduction and have the greatest stability against degradation. Six different types of polymers were investigated. Experiments were undertaken to establish the dependence of drag reduction on the polymer concentration for the polymer showing the best results according to the above-mentioned criteria. It was found that the drag reduction on coal-watei mixtures containing polymer was less than in “pure” polymer solutions (not containing any solid particles). Furthermore, for both coal-water mixtures and “pure” polymer solutions there was always found to be a polymer concentration at which drag reduction reached a maximum and this concentration was higher for the coal-water mixtures. The value of drag reduction increased as the flow velocity was increased. In the polymer degradation experiments the decrease in drag reduction as a consequence of polymer degradation was stronger when the polymer concentration was lower for both the coal-water mixtures and the “pure” polymer solutions. Experiments of longer duration showed that even after several hours of transport in the facility, there was still considerable drag reduction. Finally, it was found that for coal-water mixtures polymer degradation was greater at higher flow velocities.     

Drag reduction by polymer threads

A novel type of drag reduction is described which is caused by long polymer threads in turbulent flow. These threads are formed by axial injection of a concentrated, visco-elastic, polymer solution and persis over a distance of more than 200 tube diameters. The observed drag reduction is particularly effective at low Reynolds numbers. Depending on the properties of the injection system, the continuous supply of the polymer solution may change spontaneously into an oscillating supply resulting in periodic pressure drop variations.     

The drag reduction of chrysotile asbestos dispersions

The drag reduction (DR) of dispersions of Chrysotile asbestos fibers in aqueous solutions of Aerosol OT and in ethylene glycol, and of glass microfibers in water at a pH of 3 were studied as a function of concentration and temperature with a rotating disc apparatus. Only the dispersions of asbestos in aqueous Aerosol OT showed DR comparable to poly(ethylene oxide) WSR 35 (～500,000 MW), and these dispersions were more fully studied. As was the case with Polyox WSR 35, the asbestos dispersions achieved maximum DR at a concentration of about 200 ppm. They showed no DR temperature dependence at constant Reynolds number at high concentrations but displayed a decreasing DR with increasing temperatures at low concentrations. However, the temperature effect was much smaller for the asbestos dispersions than for Polyox. The asbestos dispersions also showed a much smaller decrease of DR with time at a given disc rotation than was previously measured for poly(ethylene oxide). Electron microscope evidence indicated that less than 10% of the fibers were fully separated, and it is probable that these were the fibers which were primarily active in DR. Hence, if complete separation and dispersion could be accomplished without breaking the fibers, Chrysotile asbestos would be a most potent, not very shear-degradable DR species.     

Evidence for molecular interactions in drag reduction in turbulent pipe flows

Experiments which test the concentration and molecular weight dependence of turbulent pipe flow drag reduction for random coiling polymers in dilute solutions show correlations with concentration to the one-half power and molecular weight to the 0.8 power for good solvents. This result is not consistent with a model of extension of single1 molecules, but could be related to the increase in bulk viscosity of interacting molecules after some extension. In this work, measurements for very low amounts of drag reduction for rigid rod molecules arc reported, and the effect of tube diameter on the amount of drag reduction is examined for fiexible rod molecules. No diameter effect is observed for the rigid rods, but an increase in drag reduction with increase in pipe diameter is found for the flexible polyeleetrolytes. In all cases, the volume occupied by spheres which circumscribe the molecules is greater than the actual volume when drag reduction is found. The results indicate that combined effects of individual molecule stretching and molecular interactions are present in drag reduction for random coiling or flexible rod molecules.     

Turbulent drag effectiveness and shear stability of xanthan-gum-based graft copolymers

A number of graft copolymers of xanthan gum and polyacrylamide have been synthesized by grafting acrylamide onto xanthan gum using the ceric-ion-initiated solution polymerization technique. The effects of various synthesis parameters such as amount of catalyst, reaction time, and ratio of xanthan and acrylamide on drag reduction effectiveness of the graft copolymers have been studied. The scaling up of grafting reaction has been accomplished in 40-L reactor. The drag reduction effectiveness of the graft copolymers is investigated over a wide range of concentrations and Reynolds numbers. It is shown that the maximum drag reduction obtainable in xanthan gum solutions above 300 ppm can be obtained in solutions of graft copolymers at concentrations of 100–150 ppm. The grafting also improves the shear stability at higher Reynolds numbers. The shear stability of the graft copolymers at constant wall stress has been found to be superior to polyacrylamide and the mixtures of polyacrylamide and xanthan gum. In general, the shear stability of graft copolymers and polyacrylamide is shown to increase with concentration. The drag reduction characteristics and shear stability have been discussed in terms of structural features of the graft copolymers. The drag reduction characteristics of the graft copolymers are found to be similar to those of flexible polymers.     

Experimental correlation for pipe flow drag reduction using relaxation time of linear flexible polymers in a dilute solution

In this study, we investigate the drag reduction property of a linear flexible polymer, PEO (polyethylene oxide) in a fully turbulent pipe flow. The aim of this study is to develop a correlation to predict the drag reduction using the Weissenberg number, a dimensionless number related to the relaxation time of the polymer and the polymer concentration in dilute solutions. The physical meaning of the relaxation time of polymers and overlap concentration between the dilute and semi-dilute polymer solution are clarified. A higher polymer concentration, Reynolds number, and Weissenberg number lead to an increasing drag reduction. A semi-empirical correlation to predict the drag reduction with two dimensionless variables mentioned above is established and can predict the experimental data in this work and other previous works well. Previous correlations that use Reynolds number often require high flow velocity or large pipes in the experimental setup to predict drag reduction in large-scale industrial applications, which involves extra cost and potential safety issues. The current new correlation method uses relatively low velocities to avoid the problems mentioned above.     

Characterization of drag reducing guar gum in a rotating disk flow

The turbulent drag reduction characteristics in a rotating disk apparatus were investigated by using polysaccharide guar gum in deionized water. The ultrasonic degradation method was adopted to obtain different molecular weight fractions of guar gum for this study. The stability of guar gum over time was observed to be better than the typical synthetic water‐soluble drag reducers [e.g., poly(ethylene oxide)]. A linear correlation between polymer concentration and the concentration/(drag reduction) for different molecular weights of guar gum was obtained, and the universal drag reduction curve for the guar gum/deionized water system was constructed. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 83: 2938–2944, 2002; DOI 10.1002/app.10300     

Vortex flow of dilute polymer solutions

It has been observed that very d longchain polymers which are effective in turbulent drag reduction inhibit the formation of a vortex or air core as water drains from a tank. This paper considers the fluid mechanical velocity profile measurements have been performed. There appear to be at least two distinct mechanisms for the vortex inhibition—one involving the viscosity enhancement caused by polymer addition, and the other related to the viscoelastic properties of the polymer solutions. This second mechanism is shown to arise due to the generation of high normal stresses as the air core begins to form. The very close correlation between vortex inhibition and turbulent drag reduction suggests that normal stresses may also play an important role in this latter phenomenon.     

The drag reduction of dilute polymer solutions as a function of solvent power,viscosity, and temperature

The frictional drag reduction of high molecular weight poly(ethylene oxide) and polystyrene solutions under turbulent flow conditions has been studied as a function of temperature, solvent power, and solvent viscosity. A rotating-disc apparatus was used to make the drag reduction measurements. For aqueous poly(ethylene oxide) solutions, at concentrations well above that needed to produce maximum drag reduction, all drag reduction data reduced to a common curve when per cent drag reduction was plotted against the Reynolds number for the flow. However, for poly(ethylene oxide) solutions below this optimum concentration, the drag reduction-versus-Reynolds number curves showed decreasing drag reduction with increasing temperature. The data are explained primarily in terms of the inverse temperature solubility characteristics of poly(ethylene oxide) in water. The per cent drag reduction of polystyrene in nonaqueous liquids was found to be greater in good solvents than in poor ones. It was also found that increases in solvent viscosity and decreases in temperature increased the per cent drag reduction. The results are discussed in relation to the current drag reduction theories and are shown to be in opposition to Virk's theory. It is concluded from the data that drag reduction is very likely a function of a relaxation time phenomenon involving the polymer molecules and the flow system. The results also emphasize the importance of considering solvent power, viscosity, and temperature in the design of an efficient drag reduction system.