Flow pattern, determination

Fig. 4.59 illustrates the flow pattern determined by Eqs (4.45) and (4.47). The distribution of the velocity vectors is shown for the case when the axial velocity component equals (ux - 1). Eqs. (4.45) and (4.47) allow us to find temperature and degree of conversion distributions in the frontal zone based on the fundamental balance equations. These equations differ from Eqs. (4.36) and (4.47) because they take into account convective heat transfer along the z-direction. The dimensionless forms of the main determining equations are as follows energy balance... 

The SDF, like the RTD functions, can be calculated from the velocity distribution in the system that is, a certain flow pattern determines both functions. The reverse, however, does not necessarily apply. The calculation of the SDF requires a complete description of the flow pattern, whereas RTD functions often can be calculated from a less than complete flow pattern. For example, the RTD of axial annular flow between two rotating concentric cylinders (helical flow) of a Newtonian fluid depends only on the axial velocity, whereas the SDF depends on both the axial and the tangential velocity... 

Water/catalyst/light-contacting has an important influence on the reactor s performance. Flow patterns determine the extent of the segregation and the non-ideal mixing. 

Important characteristics of Mode I of operation closely relate to the bubble flow patterns which are coalesced bubble flow, dispersed bubble flow, slug flow, and transitional flow. The exact definition of these regimes is rather subjective and is frequently the result of visual observations. These flow patterns determine many of the properties of cocurrent three phase fluidized beds such as porosity, bubble characteristics, mixing, heat and mass transfer. The specific values of these properties, their changes and their interdependence with respect to the flow patterns is covered in the following sections of this review. 

On the basis of flow patterns determined simultaneously in both advancing and receding liquids it... 

In some cases, however, it is possible, by analysing the equations of motion, to determine the criteria by which one flow pattern becomes unstable in favor of another. The mathematical technique used most often is linearised stabiHty analysis, which starts from a known solution to the equations and then determines whether a small perturbation superimposed on this solution grows or decays as time passes. 

Fig. 13. Bubble column flow characteristics (a) data processing system for split-film probe used to determine flow characteristics, where ADC = automated data center (b) schematic representation of primary flow patterns.

For a given impeller and tank geometiy, the impeller Reynolds number determines the flow pattern in the tank ... 

Many times solids are present in one or more phases of a solid-hquid system. They add a certain level of complexity in the process, especially if they tend to be a part of both phases, as they normally will do. Approximate methods need to be worked out to estimate the density of the emulsion and determine the overall velocity of the flow pattern so that proper evaluation of the suspension requirements can be made. In general, the solids will behave as though they were a fluid of a particular average density and viscosity and won t care much that there is a two-phase dispersion going on in the system. However, if solids are being dissolved or precipitated by participating in one phase and not the other, then they will be affected by which phase is dispersed or continuous, and the process will behave somewhat differently than if the solids migrate independently between the two phases within the process. 

Caseade tests are useful in determining all aspeets of seeondary flow. For better visualization, tests have been eondueted in water easeades. The flow patterns are studied by injeeting globules of dibutyl phatalate and kerosene in a mixture equal to the density of water. The mixture is useful in traeing seeondary flow, sinee it does not eoagulate. 

This is the reaetion system used by Bourne et ai. [3] and Middleton et ai. [4]. The first reaetion is mueh faster than the seeond reaetion Kj = 7,300 m moie see versus Kj = 3.5 m moie see The experimental data published by Middleton et ai. [4] were used to determine tlie model eonstant Two reaetors were studied, a 30-i reaetor equipped with a D/T = 1/2 D-6 impeller and a 600-i reaetor with a D/T = 1/3 D-6 impeller. A small volume of reaetant B was instantaneously added just below the liquid surfaee in a tank otherwise eontaining reaetant A. A and B were added on an equimolar basis. The transport, mixing, and reaetion of the ehemieai speeies were then eaieuiated based on the flow pattern in Figure 10-3. Experimental data were used as impeller boundary eonditions. The produet distribution Xg is then eaieuiated as ... 

Wind tunnel A fan-assisted test rig used to determine the air forces and flow patterns acting on model buildings or components. 

Non-ideal reactors are described by RTD functions between these two extremes and can be approximated by a network of ideal plug flow and continuously stirred reactors. In order to determine the RTD of a non-ideal reactor experimentally, a tracer is introduced into the feed stream. The tracer signal at the output then gives information about the RTD of the reactor. It is thus possible to develop a mathematical model of the system that gives information about flow patterns and mixing. 

The overall nueleation rate in a erystallizer is determined by the interaetion of the seeondary nueleation eharaeteristies of the material being erystallized with the hydrodynamies of the erystal suspension. When erystallizing a given material, erystallizers of different size, agitation levels, flow patterns, ete. will... 

Performance of a cyclone separator is determined by flow pattern, pressure drop, and collection efficiency. 

General laws for the flow of fluids were determined by Reynolds, who recognized two flow patterns, laminar and turbulent. In laminar flow the fluid can be considered as a series of parallel strata, each moving at its own speed, and not mixing. Strata adjacent to walls of the duct will be slowed by friction and will move slowest, while those remote from the walls will move fastest. In turbulent flow there is a general forward movement together with irregular transfer between strata. 

When this type of flow pattern is impractical, an alternative may be a through hole or tube formation combined with a postmolding sealing or closing operation by spinning or ultrasonic welding. At the other extreme, consider a 1 /4 in. (0.6 cm) diameter core exposed to a pressure of 4,000 psi (28 MPa) with an allowance for deflection of 0.0001 in. (0.00025 cm) and determine how deep a blind hole can be molded under these conditions. 

Reynold s number It is a dimensionless number that is significant in the design of any system in which the effect of viscosity is important in controlling the velocities or the flow pattern of a fluid. It is equal to the density of a fluid, times its velocity, times a characteristic length, divided by the fluid viscosity. This value or ratio is used to determine whether the flow of a fluid through a channel or passage, such as in a mold, is laminar (streamlined) or turbulent. 

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. 

Gal-Or and Resnick (Gl) have developed a simplified theoretical model for the calculation of mass-transfer rates for a sparingly soluble gas in an agtitated gas-liquid contactor. The model is based on the average gas residencetime, and its use requires, among other things, knowledge of bubble diameter. In a related study (G2) a photographic technique for the determination of bubble flow patterns and of the relative velocity between bubbles and liquid is described. 

As mentioned in Section 11.3, fluidized-bed reactors are difficult to scale. One approach is to build a cold-flow model of the process. This is a unit in which the solids are fluidized to simulate the proposed plant, but at ambient temperature and with plain air as the fluidizing gas. The objective is to determine the gas and solid flow patterns. Experiments using both adsorbed and nonadsorbed tracers can be used in this determination. The nonadsorbed tracer determines the gas-phase residence time using the methods of Chapter 15. The adsorbed tracer also measures time spent on the solid surface, from which the contact time distribution can be estimated. See Section 15.4.2. 

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