Flow patterns models

The above differential and algebraic equations may be solved numerically to calculate the separation in these flow pattern models. 

The analysis of flow pattern models occurring inside the radial distribution of the velocity vector components and the pressure at swirl generator exit are nonuniform the same burner equipped with an annular vane swirl generator in the same furnace can produce different velocity vector components, when the quarl geometry is changed (dQ/di, = 2-3.5) the shape and size of CRZ are primarily a function of quarl geometry and not of vane swirler diameter. 

Flow models Flow number FLOWPACK Flow patterns Flow-sheet models FlowSorb 2300 FLOWIRAN... 

Computer Models, The actual residence time for waste destmction can be quite different from the superficial value calculated by dividing the chamber volume by the volumetric flow rate. The large activation energies for chemical reaction, and the sensitivity of reaction rates to oxidant concentration, mean that the presence of cold spots or oxidant deficient zones render such subvolumes ineffective. Poor flow patterns, ie, dead zones and bypassing, can also contribute to loss of effective volume. The tools of computational fluid dynamics (qv) are useful in assessing the extent to which the actual profiles of velocity, temperature, and oxidant concentration deviate from the ideal (40). 

Fig. 15. (a) Values of the flow-pattern efficiency for the two-sheU model, (b) The dependence of the flow-pattern efficiency on the dimensionless... 

These simple velocity profiles do not indicate directly any dependence of the flow pattern efficiency upon the rotational speed of the centrifuge. A dependence on speed is to be expected on the basis of the argument that at high speeds the gas in the centrifuge is crowded toward the periphery of the rotor and that the effective distance between the countercurrent streams is thereby reduced. It can be seen from the two-sheU model that, as the position of upflowing stream approaches the periphery, the flow pattern efficiency drops off from its maximum value. 

Approximate prediction of flow pattern may be quickly done using flow pattern maps, an example of which is shown in Fig. 6-2.5 (Baker, Oil Gas]., 53[12], 185-190, 192-195 [1954]). The Baker chart remains widely used however, for critical calculations the mechanistic model methods referenced previously are generally preferred for their greater accuracy, especially for large pipe diameters and fluids with ysical properties different from air/water at atmospheric pressure. In the chart. 

Rhodes, and Scott Can. j. Chem. Eng., 47,445 53 [1969]) and Aka-gawa, Sakaguchi, and Ueda Bull JSME, 14, 564-571 [1971]). Correlations for flow patterns in downflow in vertical pipe are given by Oshinowo and Charles Can. ]. Chem. Eng., 52, 25-35 [1974]) and Barnea, Shoham, and Taitel Chem. Eng. Sci, 37, 741-744 [1982]). Use of drift flux theoiy for void fraction modeling in downflow is presented by Clark anci Flemmer Chem. Eng. Set., 39, 170-173 [1984]). Downward inclined two-phase flow data and modeling are given by Barnea, Shoham, and Taitel Chem. Eng. Set., 37, 735-740 [1982]). Data for downflow in helically coiled tubes are presented by Casper Chem. Ins. Tech., 42, 349-354 [1970]). 

Dispersion In tubes, and particiilarly in packed beds, the flow pattern is disturbed by eddies diose effect is taken into account by a dispersion coefficient in Fick s diffusion law. A PFR has a dispersion coefficient of 0 and a CSTR of oo. Some rough correlations of the Peclet number uL/D in terms of Reynolds and Schmidt numbers are Eqs. (23-47) to (23-49). There is also a relation between the Peclet number and the value of n of the RTD equation, Eq. (7-111). The dispersion model is sometimes said to be an adequate representation of a reaclor with a small deviation from phig ffow, without specifying the magnitude ol small. As a point of superiority to the RTD model, the dispersion model does have the empirical correlations that have been cited and can therefore be used for design purposes within the limits of those correlations. 

Numerical solutions of the maximum mixedness and segregated flow equations for the Erlang model have been obtained by Novosad and Thyn (Coll Czech. Chem. Comm., 31,3,710-3,720 [1966]). A few comparisons are made in Fig. 23-14. In some ranges of the parameters n or fte ihe differences in conversion or reaclor sizes for the same conversions are substantial. On the basis of only an RTD for the flow pattern, perhaps only an average of the two calculated extreme performances is justifiable. 

Coker, A. K., Mathematical Modelling and a Study of Flow Patterns in Cylindrical Nozzle, M.Sc. Tliesis, Aston University, 1979. 

The objeetive of the following model is to investigate the extent to whieh Computational Fluid Mixing (CFM) models ean be used as a tool in the design of industrial reaetors. The eommereially available program. Fluent , is used to ealeulate the flow pattern and the transport and reaetion of ehemieal speeies in stirred tanks. The blend time predietions are eompared with a literature eonelation for blend time. The produet distribution for a pair of eompeting ehemieal reaetions is eompared with experimental data from the literature. 

The flow pattern is ealeulated from eonservation equations for mass and mometum, in eombination with the Algebraie Stress Model (ASM) for the turbulent Reynolds stresses, using the Fluent V3.03 solver. These equations ean be found in numerous textbooks and will not be reiterated here. Onee the flow pattern is known, the mixing and transport of ehemieal speeies ean be ealeulated from the following model equation ... 

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 ... 

V3.03. The tank diameter was T = 1 m. Furthermore, Z/T = 1, D/T = 0.33, C/T = 0.32, and rpm = 58. The flow pattern in this tank is shown in Figure 10-9. Experimental data were used as impeller boundary eonditions. Figure 10-10 shows the uniformity of the mixture as a funetion of time. The model predietions are eompared with the results of the experimental blend time eorrelation of Fasano and Penny [6]. This graph shows that for uniformity above 90% there is exeellent agreement between the model predietions and the experimental eorrelation. Figure 10-1 la shows the eoneentration field at t = 0 see. Figures 10-1 lb through 10-1 Id show the eoneentration field at t = 0,... 

First we run the model so as to study the influenee of sereen resistanee on the overall flow patterns and on the maldistribution. The resulting profiles of inward radial veloeity at the inner sereen aeross the eatalyst bed appear in Figure 10-13 for different sereen resistanees. It ean be seen that higher sereen resistanee leads to more-uniform flow, as one would expeet. The existing sereens (with resistanee eoeffieients C2 of 2 X 10 /m) appear to be satisfaetory, sinee the deviations experieneed are less than 10%. 

Identify the flow pattern of the prototype system by subjecting it to an impulse, step, or sinusoidal disturbance by injection of a tracer material as reviewed in Chapter 8. The result is classified as either complete mixing, plug flow, and an option between a dispersion, cascade, or combined model. 

FIGURE iO.45 Capture of lime dust fram a clamshell unloading operation (three regions of lime drop flow patterns are modeled). 

A large one-sixth-scale model of the unloader hopper was selected so that flow patterns in the enclosure could be evaluated.Smoke was used to simulate the behavior of the lime dust in the enclosure. The lime drop from the clamshell was simulated by releasing coarse sand, thus modeling the flow patterns caused by the volume displacement and the air entrainment. The effects of local wind speed and direction on the enclosure were also simulated. 

Conclusions concerning the causes of the fugitive emissions were developed from extensive model testing. The emissions escaped from the enclosure by direct plume trajectory and wind flow patterns. Lime dropped into the back of the grizzly creates a plume towards the front of the enclosure, whereas a drop near the front produces a plume to the rear. The plume is caused by the rapid displacement of air and dust from the hopper. 

Fully developed nonisothermal flow may also be similar at different Reynolds numbers, Prandtl numbers, and Schmidt numbers. The Archimedes number will, on the other hand, always be an important parameter. Figure 12.30 shows a number of model experiments performed in three geometrically identical models with the heights 0.53 m, 1.60 m, and 4.75 m." Sixteen experiments carried out in the rotxms at different Archimedes numbers and Reynolds numbers show that the general flow pattern (jet trajectory of a cold jet from a circular opening in the wall) is a function of the Archimedes number but independent of the Reynolds number. The characteristic length and velocity in Fig. 12.30 are defined as = 4WH/ 2W + IH) and u = where W is... 

However, the correlation between and is essentially dependent on the flow pattern, and therefore the correlations, for example Eq. (14.72), are limited to distinctly specified cases. Figure 14.9 illustrates different types of vertical flow, each of which requires its own model for the correlation between and w so-... 

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

In these model equations it is assumed that turbulence is isotropic, i.e. it has no favoured direction. The k-e model frequently offers a good compromise between computational economy and accuracy of the solution. It has been used successfully to model stirred tanks under turbulent conditions (Ranade, 1997). Manninen and Syrjanen (1998) modelled turbulent flow in stirred tanks and tested and compared different turbulence models. They found that the standard k-e model predicted the experimentally measured flow pattern best. 

As the flow of a reacting fluid through a reactor is a very complex process, idealized chemical engineering models are useful in simplifying the interaction of the flow pattern with the chemical reaction. These interactions take place on different scales, ranging from the macroscopic scale (macromixing) to the microscopic scale (micromixing). 

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. 

As their name suggests, these models are based on the physical principles of diffusion and convection, which govern the mixing process. According to the flow pattern, the reactor is divided into different zones with different flow characteristics. 

The extension of generic CA systems to two dimensions is significant for two reasons first, the extension brings with it the appearance of many new phenomena involving behaviors of the boundaries of, and interfaces between, two-dimensional patterns that have no simple analogs in one-dimension. Secondly, two-dimensional dynamics permits easier (sometimes direct) comparison to real physical systems. As we shall see in later sections, models for dendritic crystal growth, chemical reaction-diffusion systems and a direct simulation of turbulent fluid flow patterns are in fact specific instances of 2D CA rules and lattices. 

Gas-liquid-particle operations are of a comparatively complicated physical nature Three phases are present, the flow patterns are extremely complex, and the number of elementary process steps may be quite large. Exact mathematical models of the fluid flow and the mass and heat transport in these operations probably cannot be developed at the present time. Descriptions of these systems will be based upon simplified concepts. 

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. 

Weekman and Myers (W3) measured wall-to-bed heat-transfer coefficients for downward cocurrent flow of air and water in the column used in the experiments referred to in Section V,A,4. The transition from homogeneous to pulsing flow corresponds to an increase of several hundred percent of the radial heat-transfer rate. The heat-transfer coefficients are much higher than those observed for single-phase liquid flow. Correlations were developed on the basis of a radial-transport model, and the penetration theory could be applied for the pulsing-flow pattern. 

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