Drag reduction

It is recognized that within the range where drag reduction occurs, the solids concentration is so dilute that the averaged distance between particles is usually 10 or more particle diameters. Therefore, under this flow condition, interparticle effects can be neglected. Consider the case of a fully developed horizontal pipe flow with negligible electrostatic effects. From Eq. (11.6), the pressure drop depends only on the wall friction, as given by 

The equation indicates that rwp can be estimated from the particle volume fraction, the particle velocity, and the intensity of the turbulent motion of particles at the wall. If we approximate rgp by the friction due to the gas flow without particles, the ratio of rwp to rgp can be roughly estimated by 

For the Reynolds number range typical of drag reduction (Re 105), / is about 0.02 from the Moody chart (see Fig. 11.7). The typical turbulent intensity of gas in a pipe flow is about 5 percent. Using the Hinze-Tchen model (see 5.3.4.1), the ratio of the velocity fluctuation of the particles to that of the gas may be given by Eq. (5.196) as 

It is noted from measurements that within the range of particle loading where the drag reduction takes place, the velocity profile of the gas phase is nearly unaltered by the presence 

For case (2), Re can be calculated as 105, which gives rise to / of 0.018. Thus, on the basis of a similar procedure to case (1), rwp/rgp is obtained as 0.34. Both cases show that Tgp plays a dominant role in the determination of rwp. 

Equations 14.30 and 14.31 apply to all fluids in both laminar and turbiflent flow. 

The next question is, how do you define a Reynolds number for a fluid that has a variable viscosity Metzner and Reed [16] proposed that the known relation between the friction factor and the Reynolds number for the laminar flow of Newtonian fluids may be applied to the laminar flow of non-Newtonians as well  

Since Equation 14.32 has been defined to apply to all fluids in laminar flow, it may now be used to obtain a generalized Reynolds number—applicable to all fluids in both laminar and turbulent flow— by combining it with Equation 14.31 as follows  

Equations 14.30-14.33 by definition should describe the behavior of all fluids in steady-state laminar viscous flow. They do so, provided that the true steady-state pressure gradient is used in Equation 14.30 [17]. Approximation of the steady-state gradient by APIL can sometimes cause considerable error. 

FIGURE 14.13 Turbulent drag reduction as evidenced by a drop in friction factors with the addition of polysaccharides to water [18]. Copyright 1972 by the American Chemical Society. Reprinted with permission of the copyright owner. 

This phenomenon has important practical applications. Pressure drops, and therefore pumping costs, can be reduced for a given flow rate, or the capacity of a pumping system (e.g., the Trans-Alaska pipeline) can be increased by the 

As with Newtonians, it s a pretty safe bet that flow is laminar for Re 2100, but drag-reducing additives often seem to delay the laminar-turbulent transition to higher Re s. The friction factor-Reynolds Number relation remains a function of pipe roughness. Unlike the Newtonian case, however, the Re curve seems to depend on pipe diameter when drag reduction is observed. 

Van Wazer, et al, Viscosity and Flow Measurement A Laboratory Handbook of Rheology, Interscience, New York, 1963. 

Sellin, R. H. J., and R, T. Moses, Drag Redxin on in Fluid Flows. Techniques for Friction Control, Ellis Horwood, Chichester (distributed by Wiley, NY), 1989. 

The following data were obtained by Dr. N. D. Sylvester (PhD. thesis, Carnegie Institute of Technology, 1968) in the world s largest capillary viscometer, an 8-ft long, -iiL-i.d. tube equipped with pressure taps to measure the pressure gradient down the tube. The fluid was a 1.34% solution of poly(ethylene oxide) in water. 

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Drag reduction has been reported for low loadings of small diameter particles (<60 [Lm diameter), ascribed to damping of turbulence near the wall (Rossettia and Pfefl er, AIChE J., 18, 31-39 [1972]). 

Evolution of drag reduction for airplanes, drag coefficient versus years. 

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... 

Chain degradation in turbulent flow has been frequently reported in conjunction with drag reduction and in simple shear flow at high Reynolds numbers [187], Using poly(decyl methacrylate) under conditions of turbulent flow in a capillary tube, Muller and Klein observed that the hydrodynamic volume, [r ] M, is the determining factor for the degradation rate in various solvents and at various polymer concentrations [188], The initial MWD of the polymers used in their experiments are, however, too broad (Mw/Iiln = 5 ) to allow for a precise... 

The concepts of boiling in micro-channels and comparison to conventional size channels are considered in Chap. 6. The mechanism of the onset of nucleate boiling is treated. Specific problems such as explosive boiling in parallel micro-channels, drag reduction and heat transfer in surfactant solutions are also considered. 

Laminar Drag Reduction in Micro-Channels Using Ultrahydrophobic Surfaces... 

A series of experiments was presented by Ou et al. (2004), which demonstrate significant drag reduction for the laminar flow of water through micro-channels using hydrophobic surfaces with well-defined micron-sized surface roughness. 

Fig. 3.16 Schematic diagram of a model for ultrahydrophobic drag reduction. A combination of surface hy-drophobicity and roughness combine to allow water to stand away from the solid surface. Reprinted from Ou et al. (2004) with permission...

Hetsroni G, Gurevich M, Mosyak A, Rozenblit R (2004) Drag reduction and heat transfer of surfactants flowing in a capillary tube. Int J Heat Mass Transfer 47 3797-3869... 

Loitsianskii LG (1966) Mechanics of liquid and gases. Pergamon, Oxford Lumley JL (1969) Drag reduction by additives. Ann Rev Fluid Mech 1 367-384 Ma HB, Peterson GP (1997) Laminar friction factor in microscale ducts of irregular cross section. Microscale Thermophys Eng 1 253-265... 

Ou J, Perot B, Rothstein JP (2004) Laminar drag reduction in microchannels using ultrahydrophobic surfaces. Phys Fluids 16(12) 4635 643... 

Watanabe K, Udagawa Y, Udagawa H (1999) Drag reduction of Newtonian fluid in a circular pipe with a highly water-repellent wall. J Fluid Mech 381 225-238 White FM (1994) Fluid mechanics, 3rd edn. McGraw-HiU, New York... 

The average Nusselt number, Nu, is presented in Fig. 4.10a,b versus the shear Reynolds number, RCsh- This dependence is qualitatively similar to water behavior for all surfactant solutions used. At a given value of Reynolds number, RCsh, the Nusselt number, Nu, increases with an increase in the shear viscosity. As discussed in Chap. 3, the use of shear viscosity for the determination of drag reduction is not a good choice. The heat transfer results also illustrate the need for a more appropriate physical parameter. In particular. Fig. 4.10a shows different behavior of the Nusselt number for water and surfactants. Figure 4.10b shows the dependence of the Nusselt number on the Peclet number. The Nusselt numbers of all solutions are in agreement with heat transfer enhancement presented in Fig. 4.8. The data in Fig. 4.10b show... 

Hetsroni G, Gurevich M, Mosyak A, Rozenblit R (2003) Surface temperature measurement of a heated capillary tube by means of an infrared technique. Meas Sci Technol 14 807-814 Hetsroni G, Gurevich M, Mosyak A, RozenbUt R (2004) Drag reduction and heat transfer of surfactants flowing in a capillary tube. Int J Heat Mass Transfer 47 3797-3809 Hetsroni G, Mosyak A, Pogrebnyak E, Yaiin LP (2005) Eluid flow in micro-channels Int J Heat Mass Transfer 48 1982-1998... 

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