Drag coefficient turbulence effects

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. 

Henderson 575 presented a set of new correlations for drag coefficient of a single sphere in continuum and rarefied flows (Table 5.1). These correlations simplify in the limit to certain equations derived from theory and offer significantly improved agreement with experimental data. The flow regimes covered include continuum, slip, transition, and molecular flows at Mach numbers up to 6 and at Reynolds numbers up to the laminar-turbulent transition. The effect on drag of temperature difference between a sphere and gas is also incorporated. 

There has been relatively little work on the motion of bubbles and drops in well-characterized turbulent flow fields. There is some evidence (B3, K7) that mean drag coefficients are not greatly altered by turbulence, although marked fluctuations in velocity (B3) and shape (K7) can occur relative to flows which are free of turbulence. The effect of turbulence on splitting of bubbles and drops is discussed in Chapter 12. 

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... 

C What is the effect of surface roughness on the friction drag coefficient in laminar and turbulent flows ... 

However, there is generally considerable discrepancy in the data for the drag coefficient dependence on turbulence. The spread in the data obtained for the drag coefficient of a sphere in turbulent flows is indicated in Fig 5.6. For this reason the standard drag curve parameterizations are normally used and the effects of turbulence is disregarded. 

Fig. 5.6. Effect of relative turbulence intensity Ir on sphere drag coefficient Cd-Reprinted from Clift et al [22] with permission from Elsevier.

Clamen, a. Gauvdj, W. Ft. 1969 Effects of turbulence on the drag coefficients of spheres in a supercritical flow regime. AIChE Journal 15, 184-189. 

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. 

Shellside Forced Boiling. Additional turbulence effects, complex flow fields, and drag effects can significantly increase heat transfer coefficients on the shell side of a tube bundle. A detailed review of the topic is given in Ref. 68. 

Figure 3-3 Effect of relative intensity of turbulence Iji on the drag coefficients of spheres in the supercritical regime (Clift and Gauvin, 1970). Reproduced by permission of Butterworth Ltd.

In Newton s regime 700 < Rep < 2x 10 the (form) drag coefficient is normally approximated by a constant value Q> 0.44. Beyond Rep 3 x 10 Newton s drag law is not valid anymore as this value is considered a critical Reynolds number, where the boundary layer becomes turbulent reducing the (form) drag significantly. However, if the particle is not smooth, this transition effect is blurred and less well defined. 

Torobin LB, Gauvin WH Fundamental aspects of solids-gas flow— part V the effects offluid turbulence on the particle drag coefficient. Can J Chem Eng 39 189-200, 1960b. 

If the coolant entered at 13°C, T would equal 8-0 and the heat-cooling effect. The overall heat transfer coefficient H) is made up of the sum of the reciprocals of the heat resistances including those of (/) the thin liquid layer dragging on the surface of the plate, because the Reynolds number is low or the surface is rough, (h) the plate itself, and Hi) any scale deposited on the plate and derived from protein or water hardness. Very significant reductions in the coefficient arise from (/) and more so from Hi). Therefore, from this standpoint, it is desirable to have very turbulent flow and clean plates. 

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