Plugs flow field

Macromixing is estabflshed by the mean convective flow pattern. The flow is divided into different circulation loops or zones created by the mean flow field. The material is exchanged between zones, increasing homogeneity. Micromixing, on the other hand, occurs by turbulent diffusion. Each circulation zone is further divided into a series of back-mixed or plug flow cells between which complete intermingling of molecules takes place. 

Welschof (1962) carried out tests on dense phase plugs having a low velocity of 1 m/s. Later Lippert (1965) did an systematic analysis of the plug flow behavior. Following these researchers in the plug field were Weber (1973), Konrad et al. (1980) and Legel and Schwedes (1984). In... 

Our treatment of Chemical Reaction Engineering begins in Chapters 1 and 2 and continues in Chapters 11-24. After an introduction (Chapter 11) surveying the field, the next five Chapters (12-16) are devoted to performance and design characteristics of four ideal reactor models (batch, CSTR, plug-flow, and laminar-flow), and to the characteristics of various types of ideal flow involved in continuous-flow reactors. Chapter 17 deals with comparisons and combinations of ideal reactors. Chapter 18 deals with ideal reactors for complex (multireaction) systems. Chapters 19 and 20 treat nonideal flow and reactor considerations taking this into account. Chapters 21-24 provide an introduction to reactors for multiphase systems, including fixed-bed catalytic reactors, fluidized-bed reactors, and reactors for gas-solid and gas-liquid reactions. 

The complexity of the turbulent reacting flow problem is such that it is best to deal first with the effect of a turbulent field on an exothermic reaction in a plug flow reactor. Then the different turbulent reacting flow regimes will be described more precisely in terms of appropriate characteristic lengths, which will be developed from a general discussion of turbulence. Finally, the turbulent premixed flame will be examined in detail. 

Kramer et al. [272] used this same technique to compare two different flow field designs— inferdigifafed and serpentine— and their interactions with the cathode diffusion layer. If was shown thaf the bottom of the interdigitated channels got plugged with liquid water that was not removed properly. On the other hand, the serpentine FF could transport the water inside the channels more effectively, but inside the cathode DL accumulation of wafer was still evident. 

Velocity Profile Effects Many variables can influence the accuracy of specific flow measurement methods. For example, the velocity profile in a closed conduit affects many types of flow-measuring devices. The velocity of a fluid varies from zero at the wall and at other stationary solid objects in the flow channel to a maximum at a distance from the wall. In the entry region of a conduit, the velocity field may approach plug flow and a constant velocity across the conduit, dropping to zero only at the wall. As a newtonian fluid progresses down a... 

As has been analyzed, the basic model for bubble column assumes complete mixed flow for the liquid phase and plug flow for the gas phase. The Deckwer el al. correlation (3.202) for the liquid phase and the Field and Davidson equation (3.206) for the gas phase can be used for the estimation of the dispersion coefficient. The resulting coefficients are Dll = 0.09 m2/s and DLG = 0.49 m2/s. 

Boundary-layer behavior is one of several potential simplifications that facilitate channel-flow modeling. Others include plug flow or one-dimensional axial flow. The boundary-layer equations, however, are the ones that require the most insight and effort to derive and to establish the ranges of validity. The boundary-layer equations retain a full two-dimensional representation of all the field variables as well as all the nonlinear behavior of Navier-Stokes equations. Nevertheless, when applicable, they provide a very significant simplification that can be used to great benefit in modeling. 

Most dispersed gas units contain three or four cells. Bulk water moves in series from one cell to the other by underflow baffles Field tests have indicated that the high intensity mixing in each cell creates the effect of plug flow of the bulk water from one cell to the next. That is, there is virtually no short-circuiting or breakthrough of a part of the inlet flow to the oudet wier box. 

The RTD obtained for this case is simply a straight line at 6 = 1 (Fig. 2). This assumes no dispersion occurs. In pracuce, even under the best of situations, a minimal amount of dispersion will occur and the closest approximation to plug flow that can be anticipated in any type of field unit will be represented by distribution about this Une. 

NMR imaging techniques were applied to the measurements of velocity field in opaque systems such as tomato juice and paper pulp suspensions [58-60]. In both cases, the particle concentrations are sufficiently high that widely applied techniques such as hot film and laser Doppler anemometry could not be used. The velocity profile for a 6 % tomato juice slurry clearly showed a power-law behavior [58, 59]. Row NMR images for a 0.5 % wood pulp suspension provided direct visual of three basic types of shear flow plug flow, mixed flow and turbulent flow as mean flow rate was increased. Detailed analysis of flow NMR image is able to reveal the complex interaction between the microstructure of suspensions and the flow [60]. 

Electrodriven separations, such as capillary electrophoresis (CE) and capillary electrochromatography (CEC), are based on the different electrophoretic mobilities in an electric field of the molecules to be separated. They provide a higher separation efficiency then conventional HPLC since the electrophoretic flow (EOF) has a plug-flow profile. Whereas the mobile phase in CE is driven only by the electro-osmotic flow, it is generated in CEC by a combination of EOF and pressure. CEC has a high sample capacity which favours its hyphenation with NMR. 

Fluorescence burst analysis, a variation of FCS procedures that has an optimum configuration for simple presentation, uses a uniform nanoscopic flow channel with an optically perfect ceiling, uniform cross section, and periodic electrodes that can now be constructed by careful electron lithography techniques.55 By application of controlled electric fields, uniform plug flow of solution through... 

Fig. 11.9 Types of linear continuous-flow reactors (LCFRs). (a) Continuous plug flow reactor (CPFR) resembling a batch reactor (BR) with the axial distance z being equivalent to time spent in a BR. (b) A tabular flow reactor (TFR) with (tq) miscible thin disk of reactive component deformed and distributed (somewhat) by the shear field over the volume, and (b2) immiscible thin disk is deformed and stretched and broken up into droplets in a region of sufficiently high shear stresses, (c) SSE reactor with (cj) showing laminar distributive mixing of a miscible reactive component initially placed at z = 0 as a thin slab, stretched into a flat coiled strip at z L, and (c2) showing dispersive mixing of an immiscible reactive component initially placed at z — 0 as a thin slab, stretched and broken up into droplets at z — L.

In the literature many studies on LDPE tubular reactors are found (2-6).All these studies present models of the tubular reactor, able to predict the influence, on monomer conversion and temperature profiles, of selected variables such as initiator concentration and jacket temperature. With the exception of the models of Mullikin, that is an analog computer model of an idealized plug-flow reactor, and of Schoenemann and Thies, for which insufficient details are given, all the other models developed so far appear to have some limitations either in the basic hypotheses or in the fields of application. 

There appear to have been few modelling efforts for hot-wall LPCVD reactors. Gieske et al. (28) and Hitchman et al. (29) present experimental data and discuss flow fields, mass transfer effects, and possible kinetics in rather general terms. A recent model by Kuiper et al. (30) cannot account for diffusion in the spaces between the wafers and the significant volume expansion commonly associated with LPCVD processes. Furthermore, it is restricted to isothermal conditions and plug flow in the main flow region in spite of the large diffusivities associated with LPCVD. 

The complexity of the turbulent reacting flow problem is such that it is best to deal first with the effect of a turbulent field on an exothermic reaction in a plug flow... 

In addition to the CSTR and batch reactors, another type of reactor commonly used in industry is the tubular reactor. It consists of a cylindrical pipe and is normally operated at steady state, as is the CSTR. For the purposes of the material presented here, we consider systems in which the flow is highly turbulent and the flow field may be modeled by that of plug flow. That is, there is no radial variation in concentration and the reactor is referred to as a plug-flow reactor (PFR). (The laminar flow reactor is discussed in Chapter 13.)... 

The mechanics and applications of multiphase flow has been an area of continuing interest to chemical, environmental, and civil engineers (23,77). The multiphase flow patterns may be classified as bubble flow, plug flow, stratified flow, wave flow, slug flow, annular flow, spray flow, and froth flow. Typical sketches of these various flow patterns are shown in Fig. 3. They are self-explanatory. In the field of absorptive bubble separation processes, only multiphase bubble flow and froth flow are of interest to the process engineer. 

Many types of reactors have entered the field of petroleum refining, but they can be roughly divided into three types 1) batch 2) continuous stirred tank reactor (CSTR) and 3) continuous plug flow. In small-scale studies, the researcher may use a simple pipe reactor, which is operated batchwise. The CSTR reactor is used in small-scale studies for kinetic studies... 

The main contribution from the work of Luo [95, 96] was a closure model for binary breakage of fluid particles in fully developed turbulence flows based on isotropic turbulence - and probability theories. The author(s) also claimed that this model contains no adjustable parameters, a better phrase may be no additional adjustable parameters as both the isotropic turbulence - and the probability theories involved contain adjustable parameters and distribution functions. Hagesaether et al [49, 50, 51, 52] continued the population balance model development of Luo within the framework of an idealized plug flow model, whereas Bertola et al [13] combined the extended population balance module with a 2D algebraic slip mixture model for the flow pattern. Bertola et al [13] studied the effect of the bubble size distribution on the flow fields in bubble columns. An extended k-e model was used describing turbulence of the mixture flow. Two sets of simulations were performed, i.e., both with and without the population balance involved. Four different superficial gas velocities, i.e., 2,4,6 and 8 (cm/s) were used, and the superficial liquid velocity was set to 1 (cm/s) in all the cases. The population balance contained six prescribed bubble classes with diameters set to = 0.0038 (m), d = 0.0048 (m), di = 0.0060 (m), di = 0.0076 (m), di = 0.0095 (m) and di = 0.0120 (m). 

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