Turbulence parameters, drag reduction

The main interest of this work, therefore, lay in the field of water-soluble polymers and their influence on drag reduction in turbulent pipe flow, as it is from this field that the major technological use is to be expected. The investigation of the influential parameters for this class of polymers, such as molecular weight and distribution thereof, thermodynamic quality of the solvent, to name but a few (see Sect. 6.3.3), must precede a clear-cut characterization (see Sect. 6.3.1) of the polymer used. 

A. N. Direct numerical simulation of viscoelastic turbulent channel flow exhibiting drag reduction effect of the variation of rheological parameters. J. Non-Newton. Fluid 1998, 79 (2-3), 433-468. 

Kobets, G.F. Matjukhov, A.P. The influence of physical parameters of polymer solutions on drag reduction in a turbulent flow. IFZh, vol. 25, N 6, 1973. 

Equation (10) cannot be applied until A, the equivalent relaxation time for the fluid, is known. However, A is defined by the linear Maxwell model, and actual polymer solutions exhibit marked nonlinear viscoelastic properties [5,6,7]. For both fresh and shear degraded solutions of Separan AP 30 polyacrylamide, which exhibit pronounced drag reduction in turbulent flow, Chang and Darby [8] have measured the nonlinear viscosity and first normal stress functions, and Tsai and Darby [6] have reported transient elastic properties of similar solutions, A nonlinear hereditary integral function containing six parameters has been proposed to represent the measured properties [8], The apparent viscosity function predicted by this model is ... 

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. 

Drag reduction can be achieved by direct injection of microbubbles through slots or porous skin (193-196) or the generation of hydrogen by electrolysis at the wall (197). The primary parameters, independent of gas type and Reynolds number, appear to be the actual gas flow rate referenced to injector conditions of temperature and pressure (198-200) and the location of the bubbles in the turbulent boundary layer (198,199,201-203). Merkle and Deutsch (196) have provided a comprehensive review on skin friction reduction by microbubble injection. Mahadevan and co-workers (204) postulated that microbubbles like polymer solution destroy turbulence production by selectively increasing the viscosity near the buffer region. They increase the local dynamic viscosity. Pal and co-workers (205) demonstrated that microbubble and polymer solution shear stress statistics as measured by flush moimted hot film sensors are similar at equivalent value of drag reduction. 

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