Reynolds number and drag

This result can also be applied directly to coarse particle swarms. For fine particle systems, the suspending fluid properties are assumed to be modified by the fines in suspension, which necessitates modifying the fluid properties in the definitions of the Reynolds and Archimedes numbers accordingly. Furthermore, because the particle drag is a direct function of the local relative velocity between the fluid and the solid (the interstitial relative velocity, Fr), it is this velocity that must be used in the drag equations (e.g., the modified Dallavalle equation). Since Vr = Vs/(1 — Reynolds number and drag coefficient for the suspension (e.g., the particle swarm ) are (after Barnea and Mizrahi, 1973) ... 

Fig. 10. Normalized drag force at arbitrary Reynolds numbers and gas fractions. The symbols represent the simulation data, the solid line the Ergun correlation Eq. (18), the dashed line the Wen-Yu correlation Eq. (46) for e = 0.8, and the grey line the correlation by Hill et al. (2001a,b) Eq. (47) and the long-dashed line Eq. (19), both for e = 0.5.

Fd was evaluated from the drag coefficient at bubble Reynolds number and the projected area of the bubble. As the Reynolds number varied from 2 to 700, the drag coefficient CD was evaluated by the Schiller and Naumann (S4) equation ... 

Equation 3.1, which is known as Stokes law is applicable only at very low values of the particle Reynolds number and deviations become progressively greater as Re increases. Skin friction constitutes two-thirds of the total drag on the particle as given by equation 3.1. Thus, the total force F is made up of two components ... 

The vaporization rates and drag coefficients for 2,2,4-trimethylpentane (iso-octane) sprays in turbulent air streams were determined experimentally by Ingebo (40), who reported that the effect of relative velocity on the evaporation rate was represented by the 0.6 power of the Reynolds number and that the drag coefficient varied inversely with the relative velocity of the drops in the spray. By assuming that the evaporation rate was independent of velocity and the drag coefficient for droplets obeyed Stokes s law, the present author derived a mathematical theory for the ballistics of droplets injected into an air stream for which the velocity varied linearly with distance (57) and... 

H.A. Becker, The effects of shape and Reynolds number on drag in the motion of a freely orientated body in an infinite fluid, Can. J. Chem. Eng., 37 (1959) 85—91. 

At low Reynolds number and with convex particles, the drag diameter equals the surface diameter and Stokes diameter may be defined as ... 

Fig. 6.6 Comparison between equations relating drag coefficient to Reynolds number and experimental data...

Within the precipitation field, a particle experiences the following forces acting upon it a momentum force, /v = ma an electrical force, = QpE and a drag force, Ed = ReACo (Re is the Reynolds number and Co the Cunningham coefficient). 

Swanson [145] reviewed the investigations of the Magnus force, and presented experimental drag and lift coefficients for an infinite, rotating cylinder at different Reynolds numbers and velocity ratios. For velocity ratios less than 0.55, and Reynolds numbers between 12.8 x 10 and 50.1 x 10 the cylinder would experience negative lift. 

The curves for the drag coefficient and the terminal velocity converge for small and large bubbles. This is likely to be because there is always some surface active contaminants present, even in distilled water, that will prevent the internal circulation of the smallest bubbles. For the large bubbles the surface tension forces are not important. Several different drag formulations are given based on the Reynolds number and the density ratio of the gas and liquid [54, 163, 78]. 

Benyahia S, Syamlal M, O Brien T (2006) Extension of Hih-Koch-Ladd drag correlation over all ranges of Reynolds number and solids volume fraction. Powder Technology 162 166-174... 

The drag coefficient is a variable depending on the flow conditions represented by the particle Reynolds number and is given in Table 9.6 or Figure 9.25. 

From dimensional analysis, the drag coefficient of a smooth solid in an incompressible fluid depends upon a Reynolds number and the necessary shape... 

The Reynolds number at which the attached boundary layer becomes turbulent is called the critical Reynolds number for drag. The curve for spheres shown in Fig. 7.3 applies only when the fluid approaching the sphere is non-turbulent or when the sphere is moving through a stationary static fluid. If the approaching fluid is turbulent, the critical Reynolds number is sensitive to the scale of turbulence and becomes smaller as the scale increases. For example, if the scale of turbulence, defined as is 2 percent, the critical Reynolds... 

At low Reynolds numbers, the drag coefficient varies inversely with and the equations for C, Fj, and u, are... 

In steady pipe flow it was found experimentally that / depends on only the Reynolds number and the relative roughness. It has been found similarly that the drag coefficient for smooth spheres in steady motion depends on only the Reynolds number. Here we must redefine the Reynolds number, which previously included the pipe diameter. The common practice is to define a particle Reynolds number, in which the particle diameter takes the place of the pipe diameter ... 

For a sphere, Ap = nDl /4, where Dp is the sphere diameter. A correlation of the Reynolds number and the drag coefficient can be observed, moreover, in the laminar region, for low Reynolds numbers (Re < 1) ... 

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