Drag turbulent

Nepf, H. (1999) Drag, turbulence and diffusivity in flow through emergent vegetation, Water Resources Research 35(2), 479—489. 

Lateral Concentration Profiles in Horizontal Pipes. Previous theoretical studies for horizontal pipe and channel flow have concentrated on the variation of solids concentration in the vertical direction. In this case, gravity (including buoyancy), fluid-particle drag, turbulent diffusion, and particle-particle interaction effects must occur. In this section, the variation of solids concentration in a horizontal plane through the pipe axis is examined. 

Different values of would be obtained for another geometry, e.g. for a slab. The scale of eddies present in a turbulent fluid covers a wide range, but is bounded below (i.e. for eddies of small scale) by viscous drag. Turbulent velocity fluctuations are damped out rapidly at a scale smaller than the Kolmogoroff velocity microscale, given by equation (10.11) ... 

The basic concepts of a gas-fluidized bed are illustrated in Figure 1. Gas velocity in fluidized beds is normally expressed as a superficial velocity, U, the gas velocity through the vessel assuming that the vessel is empty. At a low gas velocity, the soHds do not move. This constitutes a packed bed. As the gas velocity is increased, the pressure drop increases until the drag plus the buoyancy forces on the particle overcome its weight and any interparticle forces. At this point, the bed is said to be minimally fluidized, and this gas velocity is termed the minimum fluidization velocity, The bed expands slightly at this condition, and the particles are free to move about (Fig. lb). As the velocity is increased further, bubbles can form. The soHds movement is more turbulent, and the bed expands to accommodate the volume of the bubbles. 

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]). 

Cylindrical Boundary Layer Laminar boundary layers on cylindrical surfaces, with flow parallel to the cylinder axis, are described by Glauert and LighthiU Proc. R. Soc. [London], 230A, 188-203 [1955]), Jaffe and Okamura (Z. Angety. Math. Phys., 19, 564—574 [1968]) and Stewartson ((J. Appl Math., 13, 113-122 [1955]). For a turbulent boundaiy layer, the total drag may be estimated as... 

For a turbulent boundary layer, the total drag may be roughly estimated using Eqs. (6-184) and (6-185) for finite cylinders. Measured forces by Kwon and Prevorsek ]. Eng. Jnd., 101, 73-79 [1979]) are greater than predicted this way. 

Between about Rop = 350,000 and 1 X 10 , the drag coefficient drops dramatically in a drag crisis owing to the transition to turbulent flow in the boundary layer around the particle, which delays aft separation, resulting in a smaller wake and less drag. Beyond Re = 1 X 10 , the drag coefficient may be estimated from (Clift, Grace, and Weber) ... 

Clift and Gauvin modified Schiller and Nauman s Eq. (14.26) to represent the drag force throughout the transitional and turbulent regimes ... 

Drag coefficient The coefficient relating to the influence of drag over a surface in either laminar or turbulent flow. 

Particles >200 pm are predicted by Synowiec etal. (1993) to be mainly affected by the drag component of the turbulent forces. For particles 200 pm, shear forces become more significant in the process of particle break-up. 

A dependence of both crystal and impeller material properties as well as the probability of crystal-impeller collision on fine particle generation rate has also been demonstrated. Thus the relative effects of impact, drag and shear forces responsible for crystal attrition have been identified. The contribution of shear forces to the turbulent component is predicted to be most significant when the parent particle size is smaller than a 200 pm while drag forces mainly affect larger crystals, the latter being consistent with the observations of Synowiec etal. (1993). 

This obviously implies that the skin friction exerted on an airplane wing or body will depend on whether the boundary layer on the surface is laminar or turbulent, with laminar flow yielding the smaller skin friction drag. 

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... 

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