Instantaneous flow pattern

Type 2 Characterized by slow change of Re with with the instantaneous flow pattern similar to that in steady motion at the instantaneous Re. 

The top figure to the right is a vector plot showing the time-mean flow pattern, and the bottom-right figure is a snapshot of an instantaneous flow pattern. Note the strong turbulence in the latter. 

Fig. 7.3.1. Velocity vectors from the simulations of Derksen (2003), reproduced with permission from Elsevier Science. Left the entire cyclone, top right the time-mean flow pattern bottom right an instantaneous flow pattern...

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 ... 

Stirred tank model A simple convective flow pattern in tanks, characterized by complete and instantaneous mixing in all directions. Also called the continuously stirred tank reaction or the mixing tank model. See Eqs. (3) and (4) and Figure 2. 

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... 

If the surface is first saturated with a monolayer of protein exposed to steady-state concentration cQ, and then is exposed to a second treatment at concentration 2c0, a second front emerges. The second profile represents the situation where no net protein is adsorbed and thus, in principle, is representative of the diffusion-shifted flow pattern of the nonadsorbed protein. Figure 7 shows both the initial (cQ) and second (2c0) fronts and the subtraction curve which is very close to the ideal step function. If the data are interpreted as solution-borne molecules passing over an inert surface, then (a) adsorption must be essentially instantaneous and (b) the surface must become covered by exhausting the concentration of solute at the front as it moves down the column. The slope of the difference profile should represent the rate of uptake of material on the column, and that is essentially infinite on the time scale of the experiment. The point of inflection of the subtracted front indicates the slowing of the sorption process due to filling of sites on the surface. 

Figure 10.10 shows the flow vectors and streamlines for a Triflat tool. These use the slip version of the model, so they may be compared directly with Fig. 10.8(b, d). Again, the broad pattern of flow around the probe is similar, but the detail is significantly altered. These figures also explore the variation in the flow as the tool orientation with respect to the translation direchon changes the two extreme posihons 60° apart are illustrated. The instantaneous flow path around the tool oscillates significantly be-... 

When a physical mass transfer experiment is carried out in the same equipment k[ A is obtained, so that both and A are known. For this purpose it is often preferable to exclusively use experiments involving mass transfer and reaction. This eliminates the problems associated with coming close to gas-liquid equilibrium and with nonideal flow patterns. k[ A can be obtained by using an instantaneous reaction in the liquid so that, according to the film theory. 

Fig. 35.1 Geometrical complexities of a real gas-turbine engine [1] (a) the cut section showing compressor, combustor, and turbine, (b) computational model of one section of the combustor, and (c) instantaneous snapshot of temperature distribution in the symmetry plane of the combustor showing complex flow patterns through various sections of the combustor...

Figure 17 Variation of instantaneous heat transfer rate with bubble passage synchronized with the visualization of flow patterns in the vicinity of the heat transfer probe in a liquid-solid fluidized bed of low-density gel beads. (From Kumar et al., 1993a.)...

In Fig. 4.1 lb instantaneous fields of the dry H2 mole fraction and the gas velocity vectors after 10 s simulation time are shown. That is, the reactions were turned on 5 s after the flow was initiated. The hydrogen production is fast in the inlet zone and the hydrogen produced are transported toward the exit. It is also seen that the gas bubbles created in the bottom of the vessel have a tendency to move toward the center of the tube and rise at a radial position halfway between the wall and the center. These bubbles carry some of the solids in their wakes producing the solids circulation pattern seen in (a). There are no experimental data available for this process yet, so no firm validation has been performed. Nevertheless, the flow pattern is deemed to be reasonable and the chemical conversion is in fair agreement with those obtained in fixed bed simulations [125]. 

The two last terms on the right-hand side of (2.2.1) relate to fast, unsteady motion. The added mass term accounts for the fact that when accelerating a particle from rest, the surrounding fluid must also be accelerated. This appears to add mass to the particle. The Basset integral says that the drag will, by rapidly changing motion, depend not only on its instantaneous velocity relative to the fluid, but also on the previous motion since the fluid flow pattern may not have had time to adjust, due to the fluid inertia. These two terms are zero in steady movement. 

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