D/T ratio

For straight metal pipe under internal pressure the formula for minimum reqiiired w thickness is applicable for D /t ratios greater than 6. Tme more conservative Barlow and Lame equations may also be used. Equation (10-92) includes a factor Y varying with material and temperature to account for the redistribution of circumferential stress which occurs under steady-state creep at high temperature and permits slightly lesser thickness at this range. 

The fluidfoil impellers in large tanks require only two baffles, but three are usually used to provide better flow pattern asymmetiy. These fluidfoil impellers provide a true axial flow pattern, almost as though there was a draft tube around the impeller. Two or three or more impellers are used if tanks with high D/T ratios are involved. The fluidfoil impellers do not vortex vigorously even at relatively low coverage so that if gases or solids are to Be incorporated at the surface, the axial-flow turbine is often required and can be used in combination with the fluidfoil impellers also on the same shaft. 

As the flow from an impeller is increased from a given power level, there will be a higher fluid velocity and therefore a shorter circulation time. This holds true when dealing with any given impeller. This is shown in Fig. 18-18, which shows that circulation time versus D/T decreases. A major consideration is when increasing D/T becomes too large and actually causes the curve to reverse. This occurs somewhere around 0.45, 0.05, so that using impellers of D/T ratios of 0.6 to 0.8... 

FIG. 18-18 Effect of D/T ratio on two different impellers on the circulation time and the hlend time. 

It turns out that in low-viscosity blending the acdual result does depend upon the measuring technique used to measure blend time. Two common techniques, wliich do not exhaust the possibilities in reported studies, are to use an acid-base indicator and inject an acid or base into the system that will result in a color change. One can also put a dye into the tank and measure the time for color to arrive at uniformity. Another system is to put in a conductivity probe and injecl a salt or other electrolyte into the system. With any given impeller type at constant power, the circulation time will increase with the D/T ratio of the impeller. Figure 18-18 shows that both circulation time and blend time decrease as D/T increases. The same is true for impeller speed. As impeller speed is increased with any impeller, blend time and circulation time are decreased (Fig. 18-19). 

Axial-flow turbines are often used in blendiug pseudoplastic materials, and they are often used at relatively large D/T ratios, from 0.5 to 0.7, to adequately provide shear rate in the majority of the batch particularly in pseudoplastic material. These impellers develop a flow pattern which may or may not encompass an entire tank, and these areas of motion are sometimes referred to as caverns. Several papers describe the size of these caverns relative to various types of mixing phenomena. An effec tive procedure for the blending of pseudoplastic fluids is given in Oldshue (op. cit.). 

Some Observations on the Use of Nys With D/T ratios of less than 0.4, uniformity throughout the rest of the tank is minimal. In D/T ratios greater than 0.4, the rest of the tank has a very vigorous fluid motion with marked approach to complete uniformity before Njs is reached. 

Figure 5-30. Effect of power on process result with constant D/T ratio. By permission. Fluid Mixing, Lightnin (formerly Mixing Equipment Co.), a unit of General Signal.

Emulsions require high shear in the mixing operation with high speed and low D/T ratio. 

The applicable D/t ratios for yield strength collapse are shown in Table 4-151. 

The analysis proceeds as follows. First, determine the D/T ratio of the tank, based on the largest impeller, in which the original (usually research and development) batches had been compounded. It is also necessary to know the rotational speed and the horsepower of the mixer used. 

Mixing achieved in the initial research and development processing must be in turbulent range. If the impeller Reynolds number is <2000, then mixing in the pilot tank was either inadequate or represented some other special case such as moderately viscous fluids. In these situations, another D/T ratio curve must be used. 

Equation 13 is the empirical relationship obtained by the linear regression between D/T and terminal pumping numbers (4). It is important to note that a family of curves exists for each D/T ratio when Nq (pumping number) is plotted versus the impeller Reynolds number (5). In the turbulent range (iVRe > 2000), the Nq curves flatten out and thus are independent of the Reynolds number. 

The terminal pumping number, iVq/Re > 2000, plotted against the D/T ratio results in Equation (13). 

The agitation was accomplished with the turbine-type mixer and the largest axial impeller was 40.64 cm. The pilot batch was mixed at 90rpm (1.5/sec). From the initially known data, the D/T ratio was determined. 

For example, it is found that the mass transfer coefficient, Kca, for gas-liquid processes, is mostly a function of the linear superficial gas velocity and the power per unit volume with the constant D/T ratio for various size tanks. This is because the integrated volumetric mass transfer coefficient over the entire tank can be quite similar in large and small tanks even though the individual bubble size, interfacial area, and mass transfer coefficient can vary at specific points within the small and large tanks. 

All of these conditions can be met using smaller D/T ratios and narrower blade heights than are used normally in a pilot unit. If one uses the same impeller type in both the pilot and commercial units, however, it may not be possible to come close to the long blend time that will be obtained in the commercial unit. Radial flow impellers can be excellent models in a pilot plant unit for axial flow impellers in a commercial unit. 

Figure 1. Effect of D/T ratio on power required for a given process result...

For example, if the emulsion must settle in each stage, so that a clear hydrocarbon phase can be passed on to the subsequent stage, then the optimum requirement for mixer variables becomes quite unique. As the speed of the given impeller is increased, the interfacial area is increased, better mass transfer is produced, possibility of better uniformity is available, but difficulty in settling a clear hydrocarbon phase is increased. There is a definite optimum power level, D/T ratio and other parameters, that have been found to exist in these kinds of-processes. 

Axial-flow turbines are often used in blending pseudoplastic materials, and they are often used at relatively large D/T ratios, from 0.5 to 0.7, to adequately provide shear rate in the majority of the batch particularly in pseudoplastic material. These impellers develop a flow... 

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