Liquid velocity distribution

Fig.8 illustrates the liquid velocity distribution at the bottom section of the reactor when the draft-tube diameter is 0.45m, 1.05m and 1.45m respectively. Results show that the liquid velocity at the outlet of the draft-tube lowers when the draft-tube diameter is raised, to subsequently influence the shape and size of the vortex at the bottom of the gas sparger. 

To clarify the mutual interactions between the gas bubbles and its surrounding liquid flow (mostly turbulent) in a bubbly flow, information of bubble s shape and motion is one of the key issues as well as the surrounding liquid velocity distribution. Tokuhiro et al. (1998, 1999) enhanced the PIV/LIF combination technique proposed by Philip et al. (1994) with supplementation of SIT to simultaneously measure the turbulent flow velocity distribution in liquid phase around the gas bubble(s) and the bubble s shape and motion in a downward flow in a vertical square channel. The typical experimental setup of the combination of PIV, LIF, and SIT is shown in Figure 14. The hybrid measurement system consists of two CCD cameras one for PIV/LIF (rear camera) and the other for SIT (front). The fluorescent particles are Rhodamine-B impregnated, nominally 1-10 pm in diameter with specific density of 1.02, and illuminated in a light sheet of approximately 1 mm thickness (Tokuhiro et al., 1998,1999). The fluorescence is recorded through a color filter (to cut reflections) by the rear camera. A shadow of the gas bubble is produced from infrared LEDs located behind the gas bubble. A square "window" set within the array of LEDs provides optical access for... 

Improving liquid flow patterns. A number of special tray designs have been developed to improve liquid velocity distribution on large-diameter trays. Their main applications are vacuum distillation. In pressure distillation, liquid flows are usually high and multipass trays are used, so that stagnant zones are seldom a problem. Some means of improving the liquid flow patterns are... 

FIGURE 21.3 Schematic representation of liquid velocity distribution u x) (b) as well as potential distribution il/ x) (a) around a soft particle, and the electrophoretic mobibty /r as a function of electrolyte concentration n (c). 

FIGURE 21.5 Liquid velocity distribution across a polymer layer under constant velocity gradient field. 

Sato Y, Sekoguchi K (1975) Liquid velocity distribution in two-phase bubble flow. Int J Multiphase Flow 2 79-95... 

Usually flotation is carried out at not very small volume fractions (p of bubbles which results in a substantial deviation of the liquid velocity distribution in the neighbourhood of bubbles as compared with the case of individual bubble considered above. As a result of considering a system of bubbles, the following equation was obtained (Bogdanov Kiselwater, 1952)... 

Cij and Di represent the area-averaged concentration, the intersticial velocity and the dispersion coefficient, in channel i. It woiild be interesting to derive a similar equation for bed scale averaged variables. Unfortunately, it is impossible to derive such equation in an exact manner because diffusion and percolation processes are ruled by fundamentally different elementary mechanisms, (see e.g. Broadbent et al., 1957). Actually, the stochastic model defined by Eq.5 > describes the liquid velocity distribution and could also be used to characterize nximerically the distribution of residence times i.e., the dispersion process. Achwal et al. (1979) drew attention to a procedure using a Markov chain model which led to similar results for the velocity distribution. This model remained essentially numerical and rather cumbersome. Even if Eq.5 has a simple analytical form, its mamerical application to estimate the dispersion process is also too complex for practical purposes. 

It also gives a good description of important hydrodynamic features such as the existence of non irrigated zones and the liquid velocity distribution in the irrigated ones. The few examples analyzed above indicate also that the postulated model can describe many transport processes. In fact, the list of reported applications is not limitative. 

The discrete distribution described by Eq. 7 is characterized by a minimum non zero value of the density of connection - it equals 1. The actual velocity distribution observed in a trickle-bed reactor has a similar characteristic. There exist a minimum liquid velocity u below which the liquid film trickling over a solid surface becomes unstable. The smaller this minimum liquid velocity, the better the ability to spread over the packing surface. This parameter gives a physical meaning to the concept of packing accessibility. Accounting for the proportionality between the liquid flow velocity and the density of connection, Eq. 7 may be transformed in an actual liquid velocity distribution (Eq. 8). is proportional... 

Averaging formula. Two basic mechanisms drive dispersion at this level. The first one is static - streamtubes of the flow structures divide and rejoin repeatedly at the intersections of flow passages. This results in a variation of length and orientation of flow paths which induces dispersion of tracer. The second mechanism is dynamic - the residence time within a flow passage depends on the different local velocities encountered. The dispersion phenomenon depends thus also on the liquid velocity distribution. 

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

Ross (R2) measured liquid-phase holdup and residence-time distribution by a tracer-pulse technique. Experiments were carried out for cocurrent flow in model columns of 2- and 4-in. diameter with air and water as fluid media, as well as in pilot-scale and industrial-scale reactors of 2-in. and 6.5-ft diameters used for the catalytic hydrogenation of petroleum fractions. The columns were packed with commercial cylindrical catalyst pellets of -in. diameter and length. The liquid holdup was from 40 to 50% of total bed volume for nominal liquid velocities from 8 to 200 ft/hr in the model reactors, from 26 to 32% of volume for nominal liquid velocities from 6 to 10.5 ft/hr in the pilot unit, and from 20 to 27 % for nominal liquid velocities from 27.9 to 68.6 ft/hr in the industrial unit. In that work, a few sets of results of residence-time distribution experiments are reported in graphical form, as tracer-response curves. 

Ross (R2) reported measurements of desulfurization efficiency of fixed-bed pilot and commercial units operated under trickle-flow conditions. The percentage of retained sulfur is given as a function of reciprocal space velocity, and the curve for a 2-in. diameter pilot reactor was found to lie below the curves for commercial units it is argued that this is proof of bad liquid distribution in the commercial units. The efficiency of the commercial units increased with increasing nominal liquid velocity. This may be an effect either of mass-transfer resistance or liquid distribution. 

From the assumption that liquid volume elements travel as bubble wakes at velocities higher than the average liquid velocity, it follows that the bubble movement must influence the residence-time distribution of the liquid phase. However, no work on this subject has come to the author s attention. 

Assuming that the velocity distribution for flow past a gas bubble differs relatively little from the velocity distribution in an ideal liquid, and neglecting the curvature of the boundary layer, Levich finds that... 

In any liquid flowing down a surface, a velocity profile is established with the velocity increasing from zero at the surface itself to a maximum where it is in contact with the surrounding atmosphere. The velocity distribution may be obtained in a manner similar to that used in connection with pipe flow, but noting that the driving force is that due to gravity rather than a pressure gradient. 

The velocity of the liquid varies over the cross-section and is usually a maximum at a depth of between 0.05 D and 0.25 D below the surface, at the centre line of the channel. The velocity distribution may be measured by means of a pitot tube as described in Chapter 6. 

Figure 9.25. Effect of heat transfer on the velocity distribution for a liquid...

Figure 5.37a-d illustrates a typical temperature distribution in the range of the angle 0 < 0 < 180° (where 0 = 0° is at the top of the tube). The heat flux was q = 8,000 W/m, the superficial gas velocity was Uqs = 36 m/s. The superficial liquid velocities were 0.016, 0.027, 0.045 and 0.099 m/s, respectively. The flow moves from the right to the left. The color shades are indicative of the wall temperature. Comparison to simultaneous visual observations shows that the distribution of heat transfer coefficient at Uls = 0.0016 m/s corresponds to dryout on the upper part of the pipe. 

The results of numerical calculations of the velocity distribution within the vapor and liquid domains for two values of the difference between wall and saturation temperatures are shown in Fig. 10.17. It is seen that the vapor velocity reaches 100-150 m/s in the region of micro-film. The liquid velocity is much smaller than those in vapor. 

Fig.2 and Fig.3 show the typical liquid velocity and gas hold up distribution in the ALR. From the figures, one notices that the cyclohexane circulates in the ALR under the density difference between the riser and the downcomer. An apparent large vortex appears near the air sparger when the circulating liquid flows fi om the downcomer to the riser at the bottom. In the riser, liquid velocity near the draft-tube is much larger than that near the reactor wall, the latter moved somewhat downward. The gas holdup is nonuniform in the reactor, most gas exists in the riser while only a little appears in the dowmcomer. 

Eulerian two-fluid model coupled with dispersed itequations was applied to predict gas-liquid two-phase flow in cyclohexane oxidation airlift loop reactor. Simulation results have presented typical hydrodynamic characteristics, distribution of liquid velocity and gas hold-up in the riser and downcomer were presented. The draft-tube geometry not only affects the magnitude of liquid superficial velocity and gas hold-up, but also the detailed liquid velocity and gas hold-up distribution in the reactor, the final construction of the reactor lies on the industrial technical requirement. The investigation indicates that CFD of airlift reactors can be used to model, design and scale up airlift loop reactors efficiently. 

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