Liquid radial flow

Use now this equation to describe liquid film flow in conical capillary. Let us pass to spherical coordinate system with the origin coinciding with conical channel s top (fig. 3). It means that instead of longitudinal coordinate z we shall use radial one r. Using (6) we can derive the total flow rate Q, multiplying specific flow rate by the length of cross section ... 

Separability. One of the greatest advantages of a solid catalyst is that it can be separated easily from the products of reaction. To do this successfully requires careful control of the process conditions so that exposure of the catalyst to nonreactant liquids capable of affecting or dissolving either the catalytic material or the support is prevented or rninimi2ed. Solid catalysts typically are used in axial or radial flow beds and multitubular reactors. Many successful commercial processes maintain the reactants and products in the gas phase while in contact with the catalyst to avoid catalyst degradation problems. 

Figure 5-5X. Type R-500. Very high shear radial flow impeller for particle size reduction and uniform dispersion in liquids. By permission, Lightnin, (Formerly Mixing Equipment Co.) a unit of General Signal.

E. Eor radial flow turbine, locate 1.5D to 2.0D apart, with liquid coverage over the top impeller of minimum M to 3.0D, depending on surface motion desired. 

The process consists of a reactor section, continuous catalyst regeneration unit (CCR), and product recovery section. Stacked radial-flow reactors are used to minimize pressure drop and to facilitate catalyst recirculation to and from the CCR. The reactor feed consists solely of LPG plus the recycle of unconverted feed components no hydrogen is recycled. The liquid product contains about 92 wt% benzene, toluene, and xylenes (BTX) (Figure 6-7), with a balance of Cg aromatics and a low nonaromatic content. Therefore, the product could be used directly for the recovery of benzene by fractional distillation (without the extraction step needed in catalytic reforming). 

Small blade high speed agitators are used to mix low to medium viscosity liquids. Two of the most common types are the six-blade flat blade turbine and the marine type propeller shown in Figures 5.1 and 5.2 respectively. Flat blade turbines used to mix liquids in baffled tanks produce radial flow patterns primarily perpendicular to the vessel wall as shown in Figure 5.3. In contrast marine type propellers used to mix liquids in baffled tanks produce axial flow patterns primarily parallel to the vessel wall as shown in Figure 5.4. Marine type propellers and flat blade turbines are suitable to mix liquids with dynamic viscosities up to 10 and 50 Pa s, respectively. 

Various correlations for mean droplet size generated by plain-jet, prefilming, and miscellaneous air-blast atomizers using air as atomization gas are listed in Tables 4.7, 4.8, 4.9, and 4.10, respectively. In these correlations, ALR is the mass flow rate ratio of air to liquid, ALR = mAlmL, Dp is the prefilmer diameter, Dh is the hydraulic mean diameter of air exit duct, vr is the kinematic viscosity ratio relative to water, a is the radial distance from cup lip, DL is the diameter of cup at lip, Up is the cup peripheral velocity, Ur is the air to liquid velocity ratio defined as U=UAIUp, Lw is the diameter of wetted periphery between air and liquid streams, Aa is the flow area of atomizing air stream, m is a power index, PA is the pressure of air, and B is a composite numerical factor. The important parameters influencing the mean droplet size include relative velocity between atomization air/gas and liquid, mass flow rate ratio of air to liquid, physical properties of liquid (viscosity, density, surface tension) and air (density), and atomizer geometry as described by nozzle diameter, prefilmer diameter, etc. 

Axial-flow impellers generate currents parallel to the axis of the impeller shaft. Radial-flow impellers generate currents in a direction tangential or radial to the axis of the impeller shaft. Within the two classes of impellers, there are three main types of impeller design. These are propeller, turbine, and paddle. The three main types are utilized in about 95% of most batch liquid agitation systems. Standard propellers have three blades, but two-bladed, four-bladed, or impellers encased by a circular guard can also be used. 

A large number of impeller types have been studied over the years, but interest has centered on three designs marine-type propellers, flat-or curve-bladed turbines, and flat paddles, with the first two of greater interest than the third. Propellers produce axial flow of the liquids and are turned in such fashion as to direct flow against the bottom of the tank. Turbines provide radial flow, but in any case the presence of baffles strongly influences the flow pattern in the tank. The effectiveness of these in liquid extraction has not been well established, but it appears that there... 

Figure 7.7b shows a two-flat blade paddle. If the flat blades are pitched, then the liquid flow pattern becomes intermediate between axial and radial flows. Many other types of impellers are used in stirred tanks, but these are not described at this point. 

The cross-sectional area of the wick is determined by the required liquid 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 liquid (H20) flow of 1 cm3/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. 

Suspension of solids is maintained by upward movement of the liquid. In principle, use of a draft tube and an axial flow impeller will accomplish this flow pattern most readily. It turns out, however, that such arrangements are suitable only for low solids contents and moderate power levels. In order to be effective, the cross section of the draft tube must be appreciably smaller than that of the vessel, so that the solids concentration in the draft tube may become unpractically high. The usually practical arrangement for solids suspension employs a pitched blade turbine which gives both axial and radial flow. 

The problem to be solved in this paragraph is to determine the rate of spread of the chromatogram under the following conditions. The gas and liquid phases flow in the annular space between two coaxial cylinders of radii ro and r2, the interface being a cylinder with the same axis and radius rx (0 r0 < r < r2). Both phases may be in motion with linear velocity a function of radial distance from the axis, r, and the solute diffuses in both phases with a diffusion coefficient which may also be a function of r. At equilibrium the concentration of solute in the liquid, c2, is a constant multiple of that in the gas, ci(c2 = acj) and at any instant the rate of transfer across the interface is proportional to the distance from equilibrium there, i.e. the value of (c2 - aci). The dispersion of the solute is due to three processes (i) the combined effect of diffusion and convection in the gas phase, (ii) the finite rate of transfer at the interface, (iii) the combined effect of diffusion and convection in the liquid phase. In what follows the equations will often be in sets of five, labelled (a),..., (e) the differential equations expression the three processes (i), (ii) (iii) above are always (b), (c) and (d), respectively equations (a) and (e) represent the condition that there is no flow over the boundaries at r = r0 and r = r2. 

Fig. 7 shows the radial profiles of the bubble rise velocity at different axial positions. The radial profiles of bubble rise velocity become much more uniform after the gas-liquid mixture flowed through the internal, with an increase near the wall and a decrease in the central region compared with that below the internal. As the distance above the internal increases, the radial profile of the bubble rise velocity becomes more and more similar to that below the internal. At the axial position of 144 cm, the radial profile of the bubble rise velocity is about the same as that below the internal. 

Spiral vortex. So far the discussion has been confined to the rotation of all particles in concentric circles. Suppose there is now superimposed a flow with a velocity having radial components, either outward or inward. If the height of the walls of the open vessel were less than that of a liquid surface spread out by some means of centrifugal force, and if liquid were supplied to the center at the proper rate by some means, then it is obvious that liquid would flow outward, over the vessel walls. If, on the other hand, liquid flowed into the tank over the rim from some source at a higher elevation and were drawn out at the center, the flow would be inward. The combination of this approximately radial flow with the circular flow will result in path lines that are some form of spirals. 

Spiral vortex. If a radial flow is superimposed upon the concentric flow previously described, the path lines will then be spirals. If the flow goes out through a circular hole in the bottom of a shallow vessel, the surface of liquid takes the form of an empty hole, with an air core sucked down the hole. If an outlet symmetrical with the axis is provided, as in a pump impeller, we might have a flow either radially inward or radially outward. If the two plates are a constant distance B apart, the radial flow with a velocity Vr is then across a series of concentric cylindrical surfaces whose area is 0.2nrB. Thus Q = 2nrBVr is a constant, from which it is seen that rVr is a constant. Thus the radial velocity varies in the same way with r that the circumferential velocity did in the preceding discussion. Hence the pressure variation with the radial velocity is just the same as for pure rotation. Therefore the pressure gradient of flow applies exactly to the case of spiral flow, as well as to pure rotation. 

Radial flow impellers have a much lower pumping capacity and a much higher macroscale shear rate. Therefore they consume more horsepower for blending or solids suspension requirements. However, when used for mass transfer types of processes, the additional interfacial area produced by these impellers becomes a very important factor in the performance of the overall process. Radial flow turbines are primarily used in gas-liquid, liquid-solid, or liquid-liquid mass transfer systems or any combinations of those. 

For axial flow impellers, the ratio of mixer power to gas stream power for a mixer-controlled flow pattern is approximately 8-10. This means that radial flow impellers are more commonly used for gas-liquid dispersion than axial flow impellers. 

As mentioned previously, axial flow impellers are typically used for solids suspension. It is also typical to use radial flow impellers for gas-liquid mass transfer. In combination gas-liquid-solid systems, it is more common to use radial flow impellers because the desired power level for mass transfer normally accomplishes solids suspension as well. The less effective flow pattern of the axial flow impeller is not often used in high-uptake-rate systems for industrial mass transfer problems. There is one exception, and that is in the aeration of waste. The uptake rate in biological oxidation systems is on the order of 30 ppm/hr, which is about to the rate that may be required in industrial processes. In waste treatment, surface aerators typically use axial flow impellers, and there are many types of draft tube aerators that use axial flow impellers in a draft tube. The gas rates are such that the axial flow characteristic of the impeller can drive the gas to whatever depth is required and provide a very effective type of mass transfer unit. 

A new impeller is now being used for gas-liquid contacting, call the Smith Turbine. It is a radial flow turbine with blades as shown in Fig. 25. It is rotated in the concave... 

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