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.     

黏弹性流体基纳米流体流变学特性

黏弹性流体基纳米流体（viscoelastic fluid based nanofluid,VFBN）是一种具有湍流减阻和对流换热相对强化特性的新型换热工质,其湍流减阻机理与流变学特性关系密切。通过对以2.5×10^-3、5×10^-3、1×10^-2三种质量分数的十六烷基三甲基氯化铵/水杨酸钠水溶液为基液,粒子体积分数为0.1%、0.25%、0.5%、1.0%的铜纳米流体的剪切黏度、零剪切黏度以及松弛时间的测量,实验结果表明VFBN有明显的剪切稀变特性,同时纳米粒子的添加增大了基液的零剪切黏度,并导致基液黏弹性增强。以Giesekus本构模型为理论基础,利用实验参数得到了描述VFBN剪切黏度的实验关联式。     

减阻型纳米流体在圆管内的流动和换热特性

实验测定了在Reynolds数4000～16000范围内,质量分数0～0.5%的石墨、多壁碳纳米管、Al₂O₃、Cu、Al、Fe₂O₃、Zn纳米粒子加入到100～400 mg·kg^-1浓度的十六烷基三甲基氯化铵(CTAC)减阻剂中所制备的减阻型纳米流体的摩擦阻力系数和对流传热系数。结果表明:在CTAC中加入水杨酸钠(NaSal)与去离子水所配制的减阻剂具有一定的稳定性和很强的减阻特性,当减阻剂浓度为200 mg·kg^-1时其减阻特性最优。石墨纳米粒子在增强对流换热和减少流动阻力方面具有较佳的综合性能,当石墨纳米颗粒质量分数为0.4%时,其综合性能因子K是去离子水的5倍。最后给出了减阻型石墨纳米流体在圆管内的流动阻力和换热关联式,其计算值和实验值吻合良好。     

Drag reduction effectiveness of macromolecules

A working hypothesis has been developed to account for observed drag reduction properties of dilute polymer solutions. Drag reduction effectiveness of polymer solutes is attributed to their ability to form a deformable network structure which inhibits the formation of microvortices in the solvent and retards their ability to migrate through the fluid, coalesce, and result in fully developed turbulence centres. The size of microvortex precursors is tentatively set in the range of 100 Å, and it is assumed that the damping (drag reduction) effect of macromolecules is due to strong association between solvent molecules and polymer chains, immobilizing many of these active precursors. The hypothesis indicates that drag reduction effectiveness of polymers should depend strongly on polymer/solvent interactions in addition to the recognized variables of molecular weight, concentration and geometry of the flow-system. The hypothesis accounts for a number of published anomalous observations and leads to new predictions of drag reduction variations with polymer molecular weight distribution, and temperature. These and related predictions are the focal points of new experimental research studies of the drag reduction phenomenon.     

Degradation of drag reducing polymers in aqueous solutions

The performance of drag reducing polymers in turbulent flow is restricted by their mechanical degradation. This study examines how the working fluid can affect the degradation behavior of diluted drag reducing polymeric solutions. Solutions having different proportions of tap water and de-ionized water served as the working fluids. Three commercially available water soluble polymeric agents, namely, an anionic copolymer of polyacrylamide, xanthan gum, and polyethylene oxide, were then added to these solutions. All experiments had identical flow rates corresponding to turbulent conditions in a laboratory scale pipe line. Variation of pressure drop in the pipe line was then measured for 2 hours. It was found that polymer degradation is accelerated in tap water solutions compared to that in de-ionized water solutions. However, this is dependent on the specification of the polymer used, namely, the molecular weight of the polymer and the rigidity of its molecular backbone. Furthermore, a new mathematical relation has been developed to investigate degradation of the polymers over time.     

Diameter dependence of the cutoff molecular weights of drag-reducing polymers

Drag reduction data of poly(ethylene oxide) obtained in turbulent pipe flows were analyzed. A cutoff molecular weight for drag reduction was determined by correlating the drag reduction effectiveness with polymer molecular weight. Based on a time-correlation onset concept, this critical molecular weight was found to depend on the pipe diameter and Reynolds number. This effect is examined using available experimental data.     

Drag reduction and molecular structure. The interaction of polyethylenimine with some linear high polymers

The structure of polyethylenimine in aqueous and ethanolic solutions was investigated by measuring the fluorescence polarization of dansyl conjugates. In aqueous solutions, all polyethylenimines, whatever their molecular weight, are associated into large aggregates containing rotating units having rotary relaxation times corresponding to spherical particles of molecular weight about 3–6 × 10³. The interaction of polyethylenimine with very dilute solutions of linear high polymers has been investigated by fluorescence polarization measurements and by the measurement of turbulent drag. Addition of polyethylenimine causes the solutions of anionic polymers to lose their capability of reducing turbulent drag. The results are discussed in relation to the proposed structure of the anionic–cationic complexes formed in the mixtures.     

Biodegradable drag reducing agents and flocculants based on polysaccharides: Materials and applications

Organic and inorganic flocculants are used in treatment of water and industrial effluents. Polymeric flocculants, synthetic as well as natural, because of their natural inertness to PH changes, low dosage, and easy handling, have become very popular in industrial effluent treatment. It has been established in the authors' laboratory that by grafting polyacrylamide branches on rigid backbone of polysaccharides, the dangling grafted chains have easy approachability to contaminants in effluents. Thus grafted polysaccharides are very efficient, shear stable and biodegradable flocculants. They also exhibit turbulent drag reducing characteristics. Among grafted guar gum, xanthan gum, carboxymethyl cellulose, and starch, grafted starch performs the best. Starch consists of amylose (a low molecular weight linear polymer) and amylopectin (a high molecular weight, branched polymer). The grafted amylopectin is found to be the best flocculant for various kinds of industrial effluents, providing credibility to the above‐cited model. In the present paper, the details about grafted polysaccharides as turbulent drag reducers and flocculants are given, along with their applications.     

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.     

长链α-烯烃本体聚合制备油溶性减阻剂的研究

以负载型TiCl4/MgCl2为引发体系,在微正压条件下采用本体聚合法引长链α-烯烃聚合,制备高减阻性能的油溶性减阻剂(DRA).采用正交试验法考察了各项因素对聚合反应的影响,最终确定最优化的工艺条件.聚合物环道减阻测试的结果表明,在环道中添加的质量浓度为0.01 kg/m3时,减阻率高达55％.用乌氏粘度计测定了特性...     

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.     

SOLID-LIQUID MASS TRANSFER AT THE WALLS OF A RECTANGULAR AGITATED VESSEL

Rates of mass transfer between the walls of a rectangular agitated vessel and solution were studied by measuring the limiting current of the cathodic reduction of ferricyanide ion at the vessel wall. Variables studied were rotation speed of 45° pitched blade turbine impeller, physical properties of the solution and the presence of drag reducing polymer in lhe solution (Polyox WSR-301). The data were correlated for polymer free solution by the equation:

Sh= 1.925 Sc^0.33 Re^0.5

Comparison of the present data with previous heat and mass transfer studies conducted in cylindrical vessels has shown that the mass transfer behaviour of agitated rectangular vessels lie between baffled and unbaffled agitated cylindrical vessels. Polyox addition was found to reduce the mass transfer coefficient by an amount ranging from 5.6 to 37% depending on polymer concentration. Practical implications of using drag reducing polymers in agitated vessels were discussed.     

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     

Pipeline scale-up in drag reducing turbulent flow

Models available in literature for predicting drag reduction scale-up are inadequate as they have been successful only over a narrow range of diameters. A new scale-up model is presented which equates dampening of turbulent velocity fluctuations by drag reducing additives to a reduction in the Prandtl mixing length. Flow and pressure drop data from a laboratory scale pipe along with shear viscosity measurements are sufficient to predict drag reduction scale-up in bigger diameter pipes. Using this approach, scale-up was successfully predicted over a diameter range of 7 to 154 mm for a surfactant-water system and 26.6 to 1194 mm for a polymer-oil system.     

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.     

油溶性减阻剂三元共聚物的合成和表征

在管输油品中加入减阻剂是提高管线输送能力的有效方法。利用本体聚合法,在齐格勒 纳塔催化体系下,对1 辛烯/1 癸烯/1 十二烯进行三元共聚,用室内模拟环道评价装置测定了聚合物的减阻率,采用正交试验法考察了不同的聚合条件对减阻率的影响。结果表明,最适宜的反应条件如下：V（1 辛烯）∶V（1 癸烯）∶V（1 十二烯）为1∶4∶5,主催化剂TiCl4/MgCl2用量015 g,助催化剂三异丁基铝（TIBA）用量15 mL时,减阻率达到5325％。用乌氏黏度计测定聚合物的特性黏数并关联Mark Houwink方程计算出黏均相对分子质量为6 629 759,通过IR、XRD和1H NMR对聚合物进行表征,证明该方法所得聚合物聚合度较高,具有工业价值。     

On the real molecular weight of polyethylene oxide of high molecular weight in water

It is shown that water is close to being a theta solvent for polyethylene oxide which is highly aggregated in this solvent. This result is in agreement with the behaviour observed by hydrodynamic measurements (turbulent drag reduction and concentration and shear dependence of the viscosity). With the molecular weight correction proposed in this work, the onset drag reduction data obtained with Polyox agree well with Virk's theory.     

高分子减阻剂减阻性能的影响因素研究

对减阻剂减阻性能的影响因素进行了系统讨论,阐述了聚合物相对分子质量及相对分子质量分布、聚合物空间结构、聚合物抗剪切降解、聚合物后处理等因素对减阻性能的影响,并提出我国应加大对减阻剂的生产及利用研究。     

Wasserlösliche hochpolymere als strömungsbeschleuniger

Soluble high polymers drastically reduce the friction or drag of turbulent wall flows; this effect is widely known as drag reduction. In practical applications drag reducing polymers also bring about an increase in flow rate. That is why we have introduced the term flow enhancer for this type of polymer. Drag reduction by polymers was discovered in 1948. The addition of very small amounts (ppm) of a high polymer reduces the pressure drop in turbulent pipe flow by up to 80 % or increases the flow rate by up to 100 %. These rheological effects are demonstrated with the aid of laboratory experiments. A physical model is presented which describes the interference of the coiled macromolecule in turbulent boundary layers with elongational velocity gradients. From this theory are derived a number of requirements for particularly effective macromolecules, such as molar mass, conformation, linearity and electrical charges in the molecule. The well-known water soluble drag reducing polymers are presented and the influence of pH, electrolytes and temperature described. Finally a survey of practical applications with experiments describing the operation of a specially designed flow enhancer for hydrotransport of sand slurries is given.     

Review on the applications and developments of drag reducing polymer in turbulent pipe flow

Drag reduction phenomenon in pipelines has received lots of attention during the past decades due to its potential engineering applications, especially in fluid transporting industries. Various methods to enhance drag reduction have been developed throughout the years and divided into two categories;non-additives method and additives method. Both categories have different types of methods, with different formulations and applications which will generally be discussed in this review. Among all the methods discussed, drag reduction using polymer additive is as one of the most enticing and desirable methods. It has been the subject of research in this field and has been studied extensively for quite some time. It is due to its ability to reduce drag up to 80% when added in minute concentrations. Reducing drag in the pipe will require less pumping power thus offering economic relieves to the industries. So, this paper will be focusing more on the use of polymer additives as drag reducing agent, the general formulations of the additives, major issues involving the use of drag reducing polymers, and the potential applications of it. However, despite the extensive works of drag reduction polymer, there are still no models that accurately explain the mechanism of drag reduction. More studies needed to be done to have a better understanding of the phenomenon. Therefore, future research areas and potential approaches are proposed for future work.