Curved flow pattern

Fig. 5.91 A reflected light micrograph (A) shows the layered structures in a molded bar aligned parallel to the flow direction (arrow). Variation in density and color reflect variation in orientation from layer to layer. Lateral, curved flow patterns are seen in a polarized light micrograph overview of a thin section (B) (color section). The flow layers are nearly normal to the flow direction (arrow) in the center of the bar (C) (color section).

Fig. 5.91 Lateral, curved flow patterns are seen in a polarized light micrograph overview of a thin section (B). The flow layers are nearly normal to the flow direction (arrow) in the center of the bar (C).

Figure A.2 shows the cash-flow pattern for a typical project. The cash flow is a cumulative cash flow. Consider curve 1 in Fig. A.2. From the start of the project at A, cash is spent without any...

Radial-flow impellers include the flat-blade disc turbine, Fig. 18-4, which is labeled an RlOO. This generates a radial flow pattern at all Reynolds numbers. Figure 18-17 is the diagram of Reynolds num-ber/power number curve, which allows one to calculate the power knowing the speed and diameter of the impeller. The impeller shown in Fig. 18-4 typically gives high shear rates and relatively low pumping capacity. 

Fig ure 8-22. Curves for reaotors with idealized flow patterns. 

Figure 5-5C. Curved-blade turbine creates a dual suction flow pattern the same as the flat blade. This design is used when relatively low shear is a requirement, when abrasion must be considered, and when many other variables are of prime importance. Courtesy of Lightnin (formerly Mixing Equipment Co.), a unit of General Signal.

Mixing concepts, fundamentals, 297 Actual motor horsepower, 307 Axial flow, 291 Baffle diagrams, 318 Baffles, 311 Calculations, 297 Characteristic curves, 306 Draft lubes, 309, 312, 313 Entrainment, 309 Flow number, 298 Flow patterns, 309-313 Flow, 298... 

External jackets, 326-328 Helical coils, 312, 326, 327 Vertical coils, 326, 327 Mixing impellers, 290-297 Anchor, 290-329 Blending, 324, 326 Characteristic curves, 306 Chart to examine turbine applications, 296 Efficiency of propellers, 299 Flow of propellers. 298, 299 Flow patterns, 309-312 Gas-Liquid contacting, 324, 326 General list impellers, 291 Helical, 290, 329 Liquid-liquid dispersion, 326 Multiple, 297... 

Effects of performance changes, 201-203 Head curve for single pump, 198 Relations between head, horsepower, capacity and speed, 200 Temperature rise 207-209 Viscosity corrections, 203-207 Purging, flare stack systems, 535 Reciprocating pumps, 215—219 Flow patterns, 219 Specification form, 219 Relief areas, 437 External fires, 451, 453 Sizing, 434, 436... 

Total head, centrifugal pumps, 180, 183 Discharge, 205 Head curve, 198 Suction head, 184, 186 Suction lift, 184, 186 Type, 184 Tubing, 63, 64 Two-phase flow, 124 Calculations, 125-127 Flow patterns, chart, 124 System pressure drop, 125 Types of flow, 124, 125 Utilities check list, process design, 34 Vacuum,... 

As mentioned earlier, in curved channels a secondary flow pattern of two counter-rotating vortices is formed. Similarly to the situation depicted in Figrue 2.43, these vortices redistribute fluid volumes in a plane perpendicular to the main flow direction. Such a transversal mass transfer reduces the dispersion, a fact reflected in the dependence in Eq. (108) at large Dean numbers. For small Dean numbers, the secondary flow is negligible, and the dispersion in curved ducts equals the Taylor-Aris dispersion of straight ducts. 

To evaluate the true temperature difference (driving force) in a mixed vapour condenser a condensation curve (temperature vs. enthalpy diagram) must be calculated showing the change in vapour temperature versus heat transferred throughout the condenser, Figure 12.48. The temperature profile will depend on the liquid-flow pattern in the condenser. There are two limiting conditions of condensate-vapour flow ... 

Figure 2.2 shows the cash flow pattern for a typical project. The cash flow is a cumulative cash flow. Consider Curve 1 in Figure 2.2. From the start of the project at Point A, cash is spent without any immediate return. The early stages of the project consist of development, design and other preliminary work, which causes the cumulative curve to dip to Point B. This is followed by the main phase of capital investment in buildings, plant and equipment, and the curve drops more steeply to Point C. Working capital is spent to commission the plant between Points C and D. Production starts at D, where revenue from sales begins. Initially, the rate of production is likely to be below design conditions until full production is achieved at E. At F, the cumulative cash flow is again zero. This is the project breakeven point. Toward the end of the projects life at G, the net rate of cash flow may decrease owing to, for example, increasing maintenance costs, a fall in the market price for the product, and so on.

A variety of mechanisms have since been suggested to explain the physical basis for the observed transition between flow patterns (Ishii, 1975 Taitel and Dukler, 1976b Taitel et al., 1980 Barnea, 1987 Taitel and Barnea, 1990). Dukler and Taitel (1991b) summarized the various mechanisms to explain such flow pattern transitions (Table 3.1), where the letters in Table 3.1 identify the theoretical curves shown in the accompanied graphs (Fig. 3.7) for different flow directions. A word of caution was given in the reference ... 

An interwell chemical tracer study established fluid flow patterns within the pilot. Decline curve analysis showed that TFSA injection recovered more than 8150 +... 

The shape of the instantaneous yield curve determines the optimum reactor configuration and flow pattern for a particular reaction network. For cases where the instantaneous yield increases continuously with increasing reactant concentration, the optimum reactor configuration from a product selectivity viewpoint is a... 

For a few highly idealized systems, the residence time distribution function can be determined a priori without the need for experimental work. These systems include our two idealized flow reactors—the plug flow reactor and the continuous stirred tank reactor—and the tubular laminar flow reactor. The F(t) and response curves for each of these three types of well-characterized flow patterns will be developed in turn. 

The responses of this system to ideal step and pulse inputs are shown in Figure 11.3. Because the flow patterns in real tubular reactors will always involve some axial mixing and boundary layer flow near the walls of the vessels, they will distort the response curves for the ideal plug flow reactor. Consequently, the responses of a real tubular reactor to these inputs may look like those shown in Figure 11.3. 

The F(t) curve for a laminar flow tubular reactor with no diffusion is shown in Figure 11.6. Curves for the two other types of idealized flow patterns are shown for comparison. 

Different reactor networks can give rise to the same residence time distribution function. For example, a CSTR characterized by a space time Tj followed by a PFR characterized by a space time t2 has an F(t) curve that is identical to that of these two reactors operated in the reverse order. Consequently, the F(t) curve alone is not sufficient, in general, to permit one to determine the conversion in a nonideal reactor. As a result, several mathematical models of reactor performance have been developed to provide estimates of the conversion levels in nonideal reactors. These models vary in their degree of complexity and range of applicability. In this textbook we will confine the discussion to models in which a single parameter is used to characterize the nonideal flow pattern. Multiparameter models have been developed for handling more complex situations (e.g., that which prevails in a fluidized bed reactor), but these are beyond the scope of this textbook. [See Levenspiel (2) and Himmelblau and Bischoff (4).]... 

In a typical pulse experiment, a pulse of known size, shape and composition is introduced to a reactor, preferably one with a simple flow pattern, either plug flow or well mixed. The response to the perturbation is then measured behind the reactor. A thermal conductivity detector can be used to compare the shape of the peaks before and after the reactor. This is usually done in the case of non-reacting systems, and moment analysis of the response curve can give information on diffusivities, mass transfer coefficients and adsorption constants. The typical pulse experiment in a reacting system traditionally uses GC analysis by leading the effluent from the reactor directly into a gas chromatographic column. This method yields conversions and selectivities for the total pulse, the time coordinate is lost. 

An RTD curve, for instance, can be represented in algebraic form in more than one way and for different purposes. The characteristic bell shape of many RTDs is evident in the real examples of Figure 5.4. Such shapes invite comparison with some well-known statistical distributions and representation of the RTD by their equations. Or a realistic mechanism may be postulated, such as a network of reactor elements and a type of flow pattern, and the parameters of that mechanism evaluated from a measured RTD. 

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