The designer usually has control over the size of a droplet. As discussed below, several of the correlations show that droplet diameter varies with turbulent energy dissipation. For example, Eqs. (14-190) and (14-201) suggest that in droplet systems
D j1/(gas velocity)]12
and hence from Eq. (14-178)
However, just looking at the impact of velocity on droplet size underestimates the velocity impact because turbulence gives higher transfer than Eq. (14-183) predicts. Transfer coefficients increase as the mixing adjacent to the surface increases. This mixing depends on the energy dissipated into the phases. To a first approximation this transfer from droplets increases with local power dissipation raised to the 0.2 power.
^ (power dissipated)02
and since power dissipation per unit volume increases with (velocity)3, hG,turbulent <* (velocity)06 (14-185)
The combined effect on interfacial area and on the transfer coefficient is that the effective transfer increases greatly with gas velocity. From Eqs. (14-178) and (14-185)
hGaturbulent ~ (velocity)18 (14-186)
For quenching operations, this means that even though residence time is cut as gas velocity goes up, the effective approach to equilibrium increases. Since the volume for a given length of pipe falls with (velocity)-1, the expected number of transfer units NG in a given length of pipe increases with (velocity)08.
NG ,turbulent ~ (hGaturbulent)(volume) <* (velocity)08 (14-187) See Example 21.
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