The effective clear liquid height is given by
The factor C is analogous to the Francis weir constant in Eq. (6.49) and is given by
The froth density <t> is estimated by an expression analogous to Fig. 6.22a
where Cs is the C-factor, given by Eq. (6.4), with Cs and us based on the tray bubbling area.
6.3.4 Head loss under downcomer apron
Ada should be taken as the most restrictive area in the downcomer outlet region. For instance, if an inlet weir is used and the area open for liquid flow between the segmental downcomer and the inlet weir is smaller than the area under the downcomer apron, the smaller area should be used in Eq. (6.59).
Equation (6.59) was derived from the orifice equation with an orifice coefficient of 0.6 (3), and assuming pure liquid is passing under the downcomer. Tests by Lockett and Gharani (43) showed that Eq. (6.59* gives conservative predictions, even under conditions of significant vapor entrainment in the downcomer underflow (Sec. 6.2.8).
The clear liquid height, or the liquid holdup, is the height to which the aerated mass would collapse in the absence of vapor flow. The clear liquid height gives a measure of the liquid level on the tray, and ■ used in efficiency, flooding, pressure drop, downcomer backup, weep ing, and entrainment calculations. The term hl in Eq. (6.41) is the clear liquid height derived from pressure drop data. It has, however, been shown (82,83) that an estimate of clear liquid height from pressure drop data is unsatisfactory for . other purposes. The clear liquid height is related to the froth density and froth height by kc = i>fhf (6.60)
Sieve trays, troth regime. Most clear liquid height and froth density correlations (35,68,81-86) are based on the Francis weir formula. A correlation by Colwell (68), based on a model of froth flow over the weir, was demonstrated to agree with experimental data better than other published correlations. Colwell's correlation is recommended by the author and by Lockett (12), and was successfully used as a building block in weeping correlations (56,63,69) and in froth regime entrainment correlation (40). Colwell's correlation is
where <ty is given by Eq. (6.60), and Cd is given by Eq. (6.62)
The froth density, <Jy, is calculated from
fw in Eq. (6.61) is calculated from the correlations in Sec. 6.2.12. Usually, the weeping fraction is small, and fw can be set to zero. The original Colwell correlation (68) did not contain the 1 ~ fw correction term; this term was added while adopting the correlation to perform weeping studies (56,58). This correction term must be applied when weeping is significant.
Some trial and error is required in this calculation, because the clear liquid height [Eq. (6.61)) and the froth density [Eqs. (6.64) to (6.66)3 depend on each other. Under weeping conditions, additional trial and error is required because the weep fraction fw depends on the clear liquid height (Sec. 6.2.12).
Hofhuis and Zuiderweg (85) presented an alternative correlation for predicting clear liquid height in the froth regime. It was shown (68) to be less accurate than Colwell's, and incorrectly predicts zero clear liquid height if either weir height or liquid flow rate drops to zero. Nevertheless, this correlation has been successful as a building block for the correlation for froth to emulsion regime transition (Sec. 6.4.3). This correlation is
Sieve trays, spray regime. Several correlations for clear liquid height in the spray regime were proposed (29,35,85,87-91). Lockett (12) recommended Stichlmair's (29) correlation. Since then Kister and Haas (36) modified an earlier correlation by Jeronimo and Sawistowski (35) and used it successfully as a building block for correlating entrain-ment flooding and spray regime entrainment. The modified Jeronimo and Sawistowski correlation is
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