Onset of entrainment

Reentrainment is generally reduced by lower inlet gas velocities. Calvert (R-12) reviewed the hterature on predicting the onset of entrainment and found that of Chien and Ibele (ASME Pap. 62-WA170) to be the most reliable. Calvert applies their correlation to a liquid Reynolds number on the wall of the cyclone, Nrcl = 4QilhjVi, where is the volumetric liquid flow rate, cmVs hj is the cyclone inlet height, cm and Vi is the Idnematic liquid viscosity, cmVs. He finds that the onset of entrainmeut occurs at a cyclone inlet gas velocity V i, m/s, in accordance with the relationship in = 6.516 — 0.2865 lu A Re,L ... 

Fig. 10. Correlation of film thickness with gas and liquid flow rates for air-water system in vertical flow, according to Zhivaikin (Zl). 1, 2 limits for onset of entrainment in downward and upward flow, respectively. 3, 3 limits for small effect of gas velocity on liquid flow (smooth wetted wall operation). 4, 4 region of film suspension. 5 limit for existence of film flow.

Entrainment Limitation. As a result of the high vapor velocities, liquid droplets may be picked up or entrained in the vapor flow and cause excess liquid accumulation in the condenser and hence dryout of the evaporator wick [14]. This phenomenon requires that, for proper operation, the onset of entrainment in countercurrent two-phase flow be avoided. The most commonly quoted criterion to determine this onset is that the Weber number We, defined as the ratio of the viscous shear force to the force resulting from the liquid surface tension,... 

The transition to annular flow either from the stratified wavy or slug flow is determined by the entrainment process. Thus if the gas (or relative) velocity exceeds the onset of entrainment velocity, the entrainment of wave crests or liquid slugs occurs. In case of slug flow, this leads to the elimination of liquid slugs. Since the part of entrained droplets are deposited on the wall surface, the onset of entrainment leads to the formation of annular flow with liquid wetting the whole surface. However, due to the gravity effect it is expected that the liquid film thickness at... 

The most likely flow regime in the cavity is the film flow. In this case the droplet entrainment becomes the most important mechanisms to disperse the molten corium mass. The onset of entrainment, entrainment rate and entrained droplet size ate discussed below. The onset of entrairunent criteria is given (Ishii and Grolmes [10]) by... 

When the liquid starts to flow as a film, three different regimes are possible as discussed previously. The stratified to slug flow transition criterion gives the required gas velocity of 300 m/s, which is about twice the expected gas velocity. However, the more important transition is that to the annular flow, which is determined by the entrainment process. As shown below, for the case of the sample calculation the onset of entrainment velocity is exceeded by the expected gas... 

The entrainment of liquid from the film is governed by the relative velocity and film Reynolds number. The minimum relative velocity required for the onset of the entrainment is given by V . in Table I. The steam velocity in the cavity of 192 m/s far exceeds this onset of entrainment velocity of 89 m/s at the assumed cavity pressure of 0.2 MPa. Thus significant entrainment of the film into droplets is expected. The calculated entrainment rate is 12.6 g/cm sec. At this rate, the characteristic time constant is 5.3 seconds. This value should be compared with the film residence time of 3.6 seconds. The two characteristic time constants indicate that the film transport and entrainment mechanisms are in the same order of magnitude. A little less than one half of the molten corium is expected to be entrained by the streaming gas and the remaining mass discharged from the cavity to the lower compartment as a liquid film. 

The mean droplet size from the entrainment is 3.9 mm, which is rather large. The subsequent disintegration due to the relative motion between the droplets and gas flow may be possible. When the free stream gas velocity and Weber munber of 12 to 2 are used, the droplet stability criterion gives a diameter of about 0.6 to 0.1 mm. The very high entrainment rate shown above will certainly slow down the gas flow, specially in the boundary layer region, since the entrainment process and subsequent acceleration of droplets require considerable momentum transfer from the gas to liquid. When the onset of entrainment gas velocity is used as a mean gas velocity in the droplet boundary layer, the criterion gives the droplet the size of 2.4 to 0.4 nun. Thus it is expected that the size of droplets is in the range of 0.4 to 3.9 mm. 

We have to refer to their paper for the details of the derivation, but their criterion for the onset of entrainment is ... 

The interfacial shear stress is influenced by both the interface velocity and the mixture side velocity. Moreover, the entrainment from a liquid film is associated with the onset of disturbance waves at the interface and, in general, depends on both the vapor and the liquid flow rates. In fully turbulent flow, above a film Reynolds number of 3000 the condition for the onset of entrainment depend mainly upon the vapor velocity [5]. For this reason, the fothers in Equation (2) is correlated as. 

Epstein, M., Fauske, H. K. and Hauser, G. M., The Onset of Two-Phase Venting Via Entrainment in Liquid-Filled Storage Vessels Exposed to Fire," Journal Loss Prevention Process Industries, 2 (1), 45-49, January 1989. 

An interesting study of entrainment from horizontal liquid films has also been carried out by Van Rossum (VI). On the basis of a liquid film in laminar flow with a flat and smooth surface, he found that the mean actual film thickness was about 0.6 times the theoretical one. The critical Weber number corresponding to the onset of atomization was determined for five different liquids, with Weber number defined as... 

Foster Simplistically, in entrainment the rods and cones provide transitional information at the sharp junction between a LD cycle, and the inner retinal opsins provide irradiance information. What was striking about that rodless-coneless mouse under dim LD cycles is that it was phase advanced and the onsets were bouncing all over the place. Something about the precision of entrainment is lost with the rods and cones under relatively low light conditions. 

If the roughness of the river bed increases even further, the water surface loses its intact form. Air bubbles are entrained into the water, water droplets are ejected into the air, and foam and spray are formed. The parameter which determines the onset of this kind of enhanced air-water exchange is the nondimensional element Froude... 

Zhivalkin (Z3), 1962 parabola with waves, profiles scattered about semiparabola. Entry effects also studied. Experimental work on film flow and upward and downward cocurrent gas/film flow (water and aqueous glycerol solutions). Data on onset of flooding and entrainment, effect of gas velocity. 

The onset of liquid reentrainment from tube banks can be predicted from Fig. 14-116. Reentrainment occurred at much lower velocities in vertical upflow than in horizontal gas flow through vertical tube banks. While the top of the cross-hatched line of Fig. 14-116a predicts reentrainment above gas velocities of 3 m/s (9.8 ft/s) at high liquid loading, most of the entrainment settled to the bottom of the duct in 1 to 2 m (3.3 to 6.6 ft), and entrainment did not carry significant distances until the gas velocity exceeded 7 m/s (23 ft/s). 

Figure 8. Regions of different behavior of the externally driven limit cycle of Model 2 (see Figures 5-7) (I) free oscillation (limit cycle with (II) quasi-peri-odic oscillation (III) entrainment (limit cycle with X) (IV) unstable region — onset of traveling waves.

To determine the effect of circadian rhythms on anticancer drug administration, it is important to incorporate the link between the circadian clock and the cell cycle. Entrainment by the circadian clock can be included in the automaton model by considering that the protein Weel undergoes circadian variation, because the circadian clock proteins CLOCK and BMAL1 induce the expression of the Weel gene (see Fig. 10.1b) [3-5]. Weel is a kinase that phosphorylates and thereby inactivates the protein kinase cdc2 (also known as the cyclin-dependent kinase Cdkl) that controls the transition G2/M and, consequently, the onset of mitosis. 

Figure 6.6 is a typical tray stability diagram. The area of satisfactory operation (shaded) is bound by the tray stability limits. These limits are discussed in the following sections. The upper capacity limit is the onset of flooding. At moderate and high liquid flow rates, the entrainment (jet) flooding limit is normally reached when vapor flow is raised, while the downcomer flooding limit is normally reached when liquid flow is raised. When flows are raised while the column operates at constant LIV (i.e., constant reflux ratio), either limit can be reached. At very low liquid rates, as vapor rate is raised, the limit of excessive entrainment is often reached. 

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