Hquid Flows

Diffusional interception or Brownian motion, ie, the movement of particles resulting from molecular collisions, increases the probability of particles impacting the filter surface. Diffusional interception also plays a minor role in Hquid filtration. The nature of Hquid flow is to reduce lateral movement of particles away from the fluid flow lines. 

Since the total gas and Hquid flow rates per unit cross-sectional area vary throughout the tower (Fig. 5) rigorous material balances should be based on the constant iaert gas and solvent flow rates and respectively, and expressed ia terms of mole ratios and X. A balance around the upper... 

The principles outlined so far may be used to calculate the tower height as long as it is possible to estimate the temperature as a function of Hquid concentration. The classical basis for such an estimate is the assumption that the heat of solution manifests itself entirely in the Hquid stream. It is possible to relate the temperature increase experienced by the Hquid flowing down through the tower to the concentration increase through a simple enthalpy balance, equation 68, and thus correct the equiHbrium line in ajy—a diagram for the heat of solution as shown in Figure 9. 

The packing parameter ( ) (m) reflects the influence of the Hquid flow rate as shown in Figure 20. reflects the influence of the gas flow rate, staying at unity below 50% of the flooding rate but beginning to decrease above this point. At 75% of the flooding velocity, = 0.6. Sc is the Schmidt number of the Hquid. 

Pig. 22. Schematic representation of typical pressure drop as a function of superficial gas velocity, expressed in terms of G = /9q tiQ, in packed columns. O, Dry packing , low Hquid flow rate I, higher Hquid flow rate. The points do not correspond to actual experimental data, but represent examples. 

If, on the other hand, the Hquid flows in a plug-flow-like manner over the tray, but the vapor may be assumed to mix between the trays so that it enters each tray in uniform composition, the result maybe calculated according to (112). 

At high hquid flow, the hydrauHc gradient may become so large that the caps near the Hquid feed point will stop bubbling, and the efficiency will... 

Raffinate product, consisting of the less strongly adsorbed component B mixed with desorbent, is withdrawn from a position below the feed entry. Only a portion of the Hquid flowing in the bed is withdrawn at this point the remainder continues to flow into the next section of the bed. Extract product, consisting of the more strongly adsorbed component A mixed with desorbent, is withdrawn from the bed again, only a portion of the flowing Hquid in the bed is withdrawn, and the remainder continues to flow into the next bed section. 

To complete the simulation, the Hquid-flow rate relative to the soHd must be the same in both the moving-bed and simulated moving-bed operations. Because the soHd is physically stationary in the simulated moving-bed operation, the Hquid velocity relative to the vessel wall must be higher than in an actual moving-bed operation. 

The primary control variables at a fixed feed rate, as in the operation pictured in Figure 8, are the cycle time, which is measured by the time required for one complete rotation of the rotary valve (this rotation is the analog of adsorbent circulation rate in an actual moving-bed system), and the Hquid flow rate in Zones 2, 3, and 4. When these control variables are specified, all other net rates to and from the bed and the sequence of rates required at the Hquid... 

Equation 36 must be corrected for changes in the drop shape and for the effects of the inertia of Hquid flowing through the orifice, viscous drag, etc (64). As the orifice or aperture diameter is increased, d has less effect on the drop diameter and the mean drop si2e then tends to become a function only of the system properties ... 

This equation is the basis of cake filtration analysis. Feed Hquid flow rate and filtrate volume Dare usually assumed to be related as... 

Head-Area Meters. The Bernoulli principle, the basis of closed-pipe differential-pressure flow measurement, can also be appHed to open-channel Hquid flows. When an obstmction is placed in an open channel, the flowing Hquid backs up and, by means of the Bernoulli equation, the flow rate can be shown to be proportional to the head, the exact relationship being a function of the obstmction shape. 

Vortex precession meters feature no moving parts and a relatively high frequency digital output. They are used in the measurement of gas and Hquid flows, generally in pipe sizes 80 mm and smaller. 

Doppler Flow Meters. Doppler flow meters sense the shift in apparent frequency of an ultrasonic beam as it is reflected from air bubbles or other acoustically reflective particles that ate moving in a Hquid flow. It is essential for operation that at least some particles ate present, but the concentration can be low and the particles as small as ca 40 p.m. CaUbration tends to be influenced by particle concentration because higher concentrations result in mote reflections taking place neat the wall, in the low velocity portion of the flow profile. One method used to minimize this effect is to have separate transmitting and receiving transducers focused to receive reflections from an intercept zone neat the center of the pipe. 

If the gas-flow rate is increased, one eventuaHy observes a phase transition for the abovementioned regimes. Coalescence of the gas bubbles becomes important and a regime with both continuous gas and Hquid phases is reestabHshed, this time as a gas-flUed core surrounded by a predominantly Hquid annular film. Under these conditions there is usuaHy some gas dispersed as bubbles in the Hquid and some Hquid dispersed as droplets in the gas. The flow is then annular. Various qualifying adjectives maybe added to further characterize this regime. Thus there are semiannular, pulsing annular, and annular mist regimes. Over a wide variety of flow rates, the annular Hquid film covers the entire pipe waH. For very low Hquid-flow rates, however, there may be insufficient Hquid to wet the entire surface, giving rise to rivulet flow. 

In inclined or vertical pipes, the flow regimes are similar to those described for horizontal pipes when both gas- and Hquid-flow rates are high. At lower flow rates, the effects of gravity are important and the regimes of flow are quite different. For Hquid velocities near 30 cm/s and gas velocities near... 

The upward flow of gas and Hquid in a pipe is subject to an interesting and potentially important instabiHty. As gas flow increases, Hquid holdup decreases and frictional losses rise. At low gas velocity the decrease in Hquid holdup and gravity head more than compensates for the increase in frictional losses. Thus an increase in gas velocity is accompanied by a decrease in pressure drop along the pipe, a potentially unstable situation if the flows of gas and Hquid are sensitive to the pressure drop in the pipe. Such a situation can arise in a thermosyphon reboiler, which depends on the difference in density between the Hquid and a Hquid—vapor mixture to produce circulation. The instabiHty is manifested as cycHc surging of the Hquid flow entering the boiler and of the vapor flow leaving it. 

Measurement by Liquid Level. The flow rate of Hquids flowing in open channels is often measured by the use of weirs (see Liquid-LEVEL measurement). The most common type is the rectangular weir shown in Figure 22e. The flow rate across such a weir varies approximately with the quantity. Other shapes of weirs are also employed. Standard civil engineering handbooks describe the precautions necessary for constmcting and interpreting data from weirs. 

In addition to the reduction in performance, flow maldistribution may result in increased corrosion, erosion, wear, fouling, fatigue, and material failure, particularly for Hquid flows. This problem is even more pronounced for multiphase or phase change flows as compared to single-phase flows. Flow distribution problems exist for almost all types of exchangers and can have a significant impact on energy, environment, material, and cost in most industries. 

Several wick stmctures are in common use. First is a fine-pore (0.14—0.25 mm (100-60 mesh) wire spacing) woven screen which is roUed into an annular stmcture consisting of one or more wraps inserted into the heat pipe bore. The mesh wick is a satisfactory compromise, in many cases, between cost and performance. Where high heat transfer in a given diameter is of paramount importance, a fine-pore screen is placed over longitudinal slots in the vessel wall. Such a composite stmcture provides low viscous drag for Hquid flow in the channels and a small pore size in the screen for maximum pumping pressure. 

The cross-sectional area of the wick is deterrnined by the required Hquid flow rate and the specific properties of capillary pressure and viscous drag. The mass flow rate is equal to the desired heat-transfer rate divided by the latent heat of vaporization of the fluid. Thus the transfer of 2260 W requires a Hquid (H2O) flow of 1 cm /s at 100°C. Because of porous character, wicks are relatively poor thermal conductors. Radial heat flow through the wick is often the dominant source of temperature loss in a heat pipe therefore, the wick thickness tends to be constrained and rarely exceeds 3 mm. 

The hquid flow rate is adjusted to prevent resia from passiag through the openings ia either directioa. Liquid flow is stopped for a short period to allow resia to drop through openings to the chamber below. Liquid flow resumes before resia can drop through more than one chamber. 

The pressure drop for gas—Hquid flow is deterrnined by the Lockhart-MartineUi method. It is assumed that the AP for two-phase flow is proportional to that of the single phase times a function of the single-phase pressure drop ratio P. 

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