Time flow pattern

The advantage of single-pass over cross-flow filtration is that it is an easier system to operate and can be cost effective, particularly if the product to be filtered is expensive, because very tittle of the initial fluid is lost during filtration. However, because the flow pattern of the fluid is directly through the filter, filter life maybe too short for the fluid being filtered. The minimum flow rate needed downstream of the filter must also be considered, especially when there are time constraints to the process. In some situations it may be more advantageous to use a cross-flow system where higher flow rates may be easier to obtain. 

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. 

The factors which govern the efficiency of waste destmction iaclude atomi2ation, ie, mean drop si2e, and si2e distribution temperature residence time O2 concentration and flow patterns. 

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). 

Fresh butane mixed with recycled gas encounters freshly oxidized catalyst at the bottom of the transport-bed reactor and is oxidized to maleic anhydride and CO during its passage up the reactor. Catalyst densities (80 160 kg/m ) in the transport-bed reactor are substantially lower than the catalyst density in a typical fluidized-bed reactor (480 640 kg/m ) (109). The gas flow pattern in the riser is nearly plug flow which avoids the negative effect of backmixing on reaction selectivity. Reduced catalyst is separated from the reaction products by cyclones and is further stripped of products and reactants in a separate stripping vessel. The reduced catalyst is reoxidized in a separate fluidized-bed oxidizer where the exothermic heat of reaction is removed by steam cods. The rate of reoxidation of the VPO catalyst is slower than the rate of oxidation of butane, and consequently residence times are longer in the oxidizer than in the transport-bed reactor. 

Because mass flow bins have stable flow patterns that mimic the shape of the bin, permeabihty values can be used to calculate critical, steady-state discharge rates from mass flow hoppers. Permeabihty values can also be used to calculate the time required for fine powders to settle in bins and silos. In general, permeabihty is affected by particle size and shape, ie, permeabihty decreases as particle size decreases and the better the fit between individual particles, the lower the permeabihty moisture content, ie, as moisture content increases, many materials tend to agglomerate which increases permeabihty and temperature, ie, because the permeabihty factor, K, is inversely proportional to the viscosity of the air or gas in the void spaces, heating causes the gas to become more viscous, making the sohd less permeable. 

Nonintrusive Instrumentation. Essential to quantitatively enlarging fundamental descriptions of flow patterns and flow regimes are localized nonintmsive measurements. Early investigators used time-averaged pressure traverses for holdups, and pilot tubes for velocity measurements. In the 1990s investigators use laser-Doppler and hot film anemometers, conductivity probes, and optical fibers to capture time-averaged turbulent fluctuations (39). 

This gives two choices ia interpreting calculated NRR values, ie, a direct comparison of NRR values for different options or a comparison of the NRR value of each option with a previously defined NRR cutoff level for acceptabiUty. The NPV, DTC, and NRR can be iaterpreted as discounted measures of the return, iavestment, and return rate, analogous to the parameters of the earher example. These three parameters characterize a venture over its entire life. Additional parameters can be developed to characterize the cash flow pattern duting the early venture years. Eor example, the net payout time (NPT) is the number of operating years for the cumulative discounted cash flow to sum to zero. This characterizes the early cash flow pattern it can be viewed as a discounted measure of the expected operating time that the investment is at risk. 

FIG. 6-39 Typical stirred tank configurations, showing time-averaged flow patterns for axial flow and radial flow impellers. From Oldshue, Fluid Mixing Technology, McGraw-Hill, New Yo7 k, 1983.)... 

In another land of ideal flow reactor, all portions of the feed stream have the same residence time that is, there is no mixing in the axial direction but complete mixing radially. It is called a.plugflow reactor (PFR), or a tubular flow reactor (TFR), because this flow pattern is characteristic of tubes and pipes. As the reaction proceeds, the concentration falls off with distance. 

Type T is the spiraf-spiral flow pattern. It is used for all heating and cooling seiwices and can accommodate temperature crosses such as lean/rich seiwices in one unit. The removable covers on each end allow access to one side at a time to perform maintenance on that fluid side. Never remove a cover with one side under pressure as the unit will telescope out hke a collapsible cup. 

In the region of laminar flow (Vr < 10), the same power is consumed by the impeller whether baffles are present or not, and they are seldom required The flow pattern may be affected by the baffles, but not always advantageously. When they are needed, the baffles are usually placed one or two widths radially off the tank wall, to allow fluid to circulate behind them and at the same time produce some axial deflection of flow. 

Solid-Liquid Mass Transfer There is potentially a major effect of both shear rate and circulation time in these processes. The sohds can either be fragile or rugged. We are looking at the slip velocity of the particle and also whether we can break up agglomerates of particles which may enhance the mass transfer. When the particles become small enough, they tend to follow the flow pattern, so the slip velocity necessary to affect the mass transfer becomes less and less available. 

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. 

Relatively uncomphcated transparent tank studies with tracer fluids or particles can give a similar feel for the overall flow pattern. It is important that a careful balance be made between the time and expense of calculating these flow patterns with computational flirid dynamics compared to their apphcabihty to an actual industrial process. The future of computational fluid dynamics appears very encouraging and a reasonable amount of time and effort put forth in this regard can yield immediate results as well as potential (or future process evaluation. 

A distinc tion is to be drawn between situations in which (1) the flow pattern is known in detail, and (2) only the residence time distribution is known or can be calculated from tracer response data. Different networks of reactor elements can have similar RTDs, but fixing the network also fixes the RTD. Accordingly, reaction conversions in a known network will be unique for any form of rate equation, whereas conversions figured when only the RTD is known proceed uniquely only for hnear kinetics, although they can be bracketed in the general case. 

FIG. 23-13 The two limiting flow patterns with the same RTD. a) Segregated flow, in which all molecules of any exit stream have the same residence time, (h) Maximum mixed flow, in which all molecules of an external stream with a certain life expectation are mixed with all molecules of the internal stream that have the same life expectation. 

This chapter reviews the various types of impellers, die flow patterns generated by diese agitators, correlation of die dimensionless parameters (i.e., Reynolds number, Froude number, and Power number), scale-up of mixers, heat transfer coefficients of jacketed agitated vessels, and die time required for heating or cooling diese vessels. 

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. 

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,... 

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