Particles drag coefficient

In the limit of very high voidage, the drag coefficient can be related to the single particle drag coefficient. For the case of spherical particles,... 

In some way, introducing an increased particle drag by means of Eq. (17) resembles the earlier proposal raised by Bakker and Van den Akker (1994b) to increase viscosity in the particle Reynolds number due to turbulence (in agreement with the very old conclusion due to Boussinesq, see Frisch, 1995) with the view of increasing the particle drag coefficient and eventually the bubble holdup in the vessel. Lane et al. (2000) compared the two approaches for an aerated stirred vessel and found neither proposal to yield a correct spatial gas distribution. 

In addition, it is dubious whether this new correlation due to Brucato et al. (1998) should be used in any Euler-Lagrangian approach and in LES which take at least part of the effect of the turbulence on the particle motion into account in a different way. So far, the LES due to Derksen (2003, 2006a) did not need a modified particle drag coefficient to attain agreement with experimental data. Anyhow, the need of modifying particle drag coefficient in some way illustrates the shortcomings of the current RANS-based two-fluid approach of two-phase flow in stirred vessels. 

A glass sphere, of diameter 6 mm and density 2600 kg/m3, falls through a layer of oil of density 900 kg/m3 into water. If the oil layer is sufficiently deep for the particle to have reached its free falling velocity in the oil, how far will it have penetrated into the water before its velocity is only 1 per cent above its free falling velocity in water It may be assumed that the force on the particle is given by Newton s law and that the particle drag coefficient R /pu2 = 0.22. 

Terminal falling velocity and particle drag coefficient... 

A particle drag coefficient Cd can now be defined as the drag force divided by the product of the dynamic pressure acting on the particle (i.e. the velocity head expressed as an absolute pressure) and the cross-sectional area of the particle. This definition is analogous to that of a friction factor in conventional fluid flow. Hence... 

Cdo = single particle drag coefficient at culated from Cdo = Ns. A Usuper cal- m... 

Cd = particle drag coefficient dso = mass median diameter of -I- 74 pm particles (m)... 

Torobdj, L. B. Gauvdj, W. H. 1960 Fundamental aspects of solids-gas flow. Part V the effects of fluid turbulence on the particle drag coefficient. Canadian Journal of Chemical Engineering 38, 189-200. 

Let us emphasise that the non-linearity in the particle drag coefficient is caused by the particle movement relative to the liquid. Its manifestation in the condition of particle rebound is weak and can be neglected. Let us estimate the effect for the onset of the recoil of the particle... 

CD is the particle drag coefficient for a spherical particle and is expressed as (92)... 

There is no analytic nor numerical model available, which provides the particle drag coefficient for particles over all the regimes of rarefied flows. The earlier methods to correct for rarefied flow effects were based on a correction to Stokes drag, derived by Basset to account for velocity slip at the surface. In that case, the drag coefficient can be expressed as... 

Crowe, C. T., Babcock, W., Willoughby, P. G., and Carlson, R. L., Measurement of particle drag coefficient m flow regimes encountered by particles m a rocket nozzle. United Technology Report 2296-FR, 1969. 

The conditions of flow around particles situated in the stream itself are not the same as the conditions of flow around particles attached to the walls. The air velocity in the main part of the stream is distributed more or less uniformly. In flow around adherent particles lying in the boundary layer, the flow velocity varies from zero up to a certain value. This variation has a substantial effect on the effective air-flow velocity, which determines the drag. Moreover, the particle drag coefficient Cx that appears in Eq. (X.3) depends on the Reynolds number, which in turn is a function of flow velocity, i.e., =/i(Re) and Re =f2(v). 

On the basis of experimental data, with the use of similitude theory, a relationship has been established between the drag coefficient Cx and the Reynolds number Re [273]. The particle drag coefficient Cx is the ratio of the dragF r to the product of the particle midsection S by the dynamic pressure... 

Vg is the average slurry velocity, and is the density ratio of the solids to that of the carrier liquid. Cp is the single particle drag coefficient and is given for spherical particles by [56]... 

Equation 27 indicates that the normalized hydraulic gradient, (i - i,)/i, is a function of the modified Froude number, the single particle drag coefficient and the delivered solids volume fraction. 

C Critical solids concentration, vol. % Cp Single particle drag coefficient, -... 

For other shapes of particles, drag coefficients will differ from those given in Fig. 14.3-1 and data are given in Fig. 3.1-2 and elsewhere(B2, L2, PI). In the turbulent Newton s law region above a Reynolds number of about 1000 to 2.0 x 10, the drag coefficient is approximately constant at Cj, = 0.44. 

Table 2.1 Reynolds number ranges for single particle drag coefficient correlations...

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