Polymer solutions drag reduction

Fig. 4 shows Toms / - data for both a Newtonian solvent and a DR polymer solution. Drag reduction onset occurs at 10,000 in the 0.202 cm tube, while the critical conditions for DR are reached in the laminar region for the 0.0645 cm tube and there is no apparent onset. Rather, friction factors depart gradually from the laminar equation as A Re increases (see also the section Concentration). Virk proposed that onset of DR in turbulent pipe flows, at which the friction factor departs abruptly from Eq. (4), occurs at a distinct wall-shear stress, which does not depend on the pipe size and is only weakly dependent on concentration for a given polymer-solvent combination, but depends strongly on the radii of gyration, Rq, of the polymer molecules ... 

On the other side, extricates factors, such as solution concentration, are very important. One can note that in the case of polymer solutions, drag reduction occurs in the range of extremely small polymer concentrations. Figure 3.382. Thus in the case of poly(ethylene oxide) the optimal concentration is about 7500 ppm [1084], but not below 0.02 ppm [1085]. 

The novel polymer slurry drag reduction method used by Little et al. [2] has been recently researched by Mamonov et al. [25]. Mamonov et al. [25] were able to prepare poly(ethylene oxide) solutions in less than 2 seconds using a special mixer and injected into the flow in a non-fu ly dissolved state. The reported results indicate that more drag reduction occurs when quickly prepared solutions have more time to dissolve. However, no data were reported for drag reduction effects with respect to time,... 

Dimitropoulos, C.D., Dubief, Y., Shaqfeh, E.S.G., and Moin, P. (2006) Direct numerical simulations of polymer-induced drag reduction in turbulent boimdary layer flow of inhomogeneous polymer solutions. /. Fluid Mech., 566, 153-166. 

Aggregation in dilute solutions of high molar mass poly(ethylene) oxide and its effect on polymer turbulent drag reduction. Polymer, 50, 261-270. 

Kulicke, W.-M., Kotter, M. and Grager, H. Drag Reduction Phenomenon with Special Emphasis on Homogeneous Polymer Solutions. Vol. 89, pp. 1—68. 

The presence of small amounts of dissolved polymer can alter sizably the aerosol particle dimensions when the solutions are sprayed. This antimisting property has received special attention in an effort to develop additives for jet fuel to prevent accidental ignition following crash landing. As in drag reduction, the polymer... 

The effect of polymer additives on turbulent flow is at the origin of the important phenomenon of drag reduction and has found other industrial applications such as oil recovery and antimisting action. Drag reduction in dilute polymer solutions... 

In the extensive literature on polymer drag reduction, it has occasionally been reported that a continuous thread of a high-concentration polymer solution injected into the axis of a pipe produces a drag-reduction effect on the water flow in the pipe [856]. The thread seems to persist through the length of the pipe and little, if any, diffusion of polymer to the walls of the pipe is apparent. 

A polymer of the polyacrylamide type was injected as a 0.5% solution from an axially-placed nozzle at the bellmouth entrance. The experiments showed that the central thread provided drag reduction almost equivalent to premixed solutions of the same total polymer concentration flowing in the pipe. Overall concentrations of 1, 2, 4, and 20 ppm were used. Moreover, the effects were additive 2 ppm thread overall concentration plus 2 ppm premixed gave drag reductions equivalent to 4 ppm of either type. Reynolds numbers of up to 300,000 were investigated. In other experiments, a number of different polymer fluids were injected on the centerline of a water pipe-flow facility [857]. Two distinct flow regions were identified ... 

S. Malik, S. N. Shintre, and R. A. Mashelkar. Process for the preparation of a new polymer useful for drag reduction in hydrocarbon fluids in exceptionally dilute polymer solutions. Patent US 5080121, 1992. 

Although the exact mechanism is debatable, Darby and Chang (1984) and Darby and Pivsa-Art (1991) have presented a model for turbulent drag reduction based on the fact that solutions of very high polymers are visco-... 

Drag reduction is caused by the viscoelasticity of polymer solutions (61). PIB is oil soluble and is thus interesting as a drag reducing additive for the transport of crude oil in pipelines (62). 

Universal drag reduction curves can be obtained in several ways, for example, by normalizing the hydrodynamic volume fraction of the polymer in solution (63). Further, a three-parameter empirical relationship between the drag reduction and concentration has been introduced (64). 

Drag Reduction Phenomenon with Special Emphasis on Homogeneous Polymer Solutions... 

Goren found asymptotic behaviour, which is higher for this heterogeneous drag reduction than for a premixed homogeneous solution, whereas Tullis, Ramu, and Maus reported only little influence of the concentration of the injected polymer solution on this asymptotic value. Walters and McComb (1982) found no such influence. 

McComb (1982) investigated both types of injection namely at the wall and at the center line of the flow. In their apparatus the injection point was situated where the flow was well developed. These experiments led to the following conclusions when polymer solution was injected at the center line of the pipe, the local drag reduction... 

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