Mixing in pipes

A system in which the liquid and gas/ vapour phases are uniformly mixed. In pipe flow, "homogeneous" also implies no slip between the phases and complete vapour/ liquid equilibrium (see 9 3 1)... 

R. D. Hawthorn, Effect of Radial Temperature Variation of Axial Mixing in Pipes, AJ.Ch,E, Journal, 6,443 (1960). 

Mixing in pipes is an important variant of stirring and is performed in different ways ... 

Another type of crystallizer is the Oslo-type unit shown in Figure 24. In units of this type, the object is to form a supersaturated solution in the upper chamber and then reHeve the supersaturation through growth in the lower chamber. The use of the downflow pipe in the crystallizer provides good mixing in the growth chamber. 

Other Flow Straightening Deviees Other devices designed to produce uniform velocity or reduce swirl, sometimes with reduced pressure drop, are available. These include both commercial devices of proprietaiy design and devices discussed in the hterature. For pipeline flows, see the references under flow inverters and static mixing elements previously discussed in the Tncompressible Flow in Pipes and Channels subsection. For large area changes, as at the... 

The universal turbulent velocity profile near the pipe wall presented in the preceding subsection Tncompressible Flow in Pipes and Channels may be developed using the Prandtl mixing length approximation for the eddy viscosity,... 

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. 

In some cases, it is impractical to use a plenum chamber under the constriction plate. This condition arises when a flammable or explosive mixture of gases is being introduced to the reactor. One solution is to pipe the gases to a multitude of individual gas inlets in the floor of the reactor. In this way it may be possible to maintain the gas velocities in the pipes above the flame velocity or to reduce the volume of gas in each pipe to the point at which an explosion can be safely contained. Another solution is to provide separate inlets for the different gases and depend on mixing in the fluidized bed. The inlets should be fairly close to one another, as lateral gas mixing in fluidized beds is poor. 

Modern central stations use the other burner-furnace configurations shown in Fig. 27-16, in which the coal and air are mixed rapidly in and close to the burner. The primary air, used to transport the pulverized coal to the burner, comprises 10 to 20 percent of the total combustion air. The secondary air comprises the remainder of the total air and mixes in or near the burner with the primary air and coal. The velocity of the mixture leaving the burner must be high enough to prevent flashback in the primaiy air-coal piping. In practice, this velocity is maintained at about 31 m/s (100 ft/s). 

Torbaeke and Rasmuson (2001) report the empirieal influenee of different seales of mixing in reaetion erystallization of benzole aeid in a loop reaetor. The authors infer that the proeess is mainly governed by mesomixing in terms of liquid eireulation rate but find anomalous behaviour in respeet of feed pipe diameter. 

Methods are to pre-cool the aggregate with cold air, to chill the mix water, and to provide part of the mix in the form of flake ice. Chilled water pipes may be buried in the concrete mass. 

Obtain m> expression for the concentration of gas A in that half of she pipe in which it is increasing, as a (unction of distance y from the valve and time t after opening. The whole system is at a constant pressure and the ideal gas law is applicable to both gases. It may be assumed that the rate of mixing in the vessels is high so that the gas concentration at the two ends of the pipe do not change. 

Almost all flows in chemical reactors are turbulent and traditionally turbulence is seen as random fluctuations in velocity. A better view is to recognize the structure of turbulence. The large turbulent eddies are about the size of the width of the impeller blades in a stirred tank reactor and about 1/10 of the pipe diameter in pipe flows. These large turbulent eddies have a lifetime of some tens of milliseconds. Use of averaged turbulent properties is only valid for linear processes while all nonlinear phenomena are sensitive to the details in the process. Mixing coupled with fast chemical reactions, coalescence and breakup of bubbles and drops, and nucleation in crystallization is a phenomenon that is affected by the turbulent structure. Either a resolution of the turbulent fluctuations or some measure of the distribution of the turbulent properties is required in order to obtain accurate predictions. 

The production of turbulence is maximum close to walls, where both shear rate and turbulent viscosity, ut, are high. In pipe flow, the maximum is close to y+ = 12. A proper design of a chemical reactor for efficient mixing at low Re should allow the generated turbulence to be transported with the mean flow from the region where it is produced to the bulk of the fluid where it should dissipate. 

Fig. 5. Mixing in the partitioned pipe mixer, (a) Schematic view of the mixer geometry one element of the mixer is shown, and the mixer comprises several such elements joined together, (b) KAM surfaces in flow bounding regions of regular flow, (c) A and B show examples of experimentally obtained streaklines undeformed streaklines pass through KAM tubes, whereas streaklines in the chaotic region are well mixed. The white arrows indicate the location of a companion streak-tube. (Khakhar, Franjione, and Ottino, 1987 Kusch and Ottino, 1992).

Khakhar, D. V., Franjione, J. G. and Ottino, J. M., A case study of chaotic mixing in deterministic flows the partitioned pipe mixer. Chem. Eng. ScL 42,2909-2926 (1987). 

Plug flow A simple convective flow pattern in pipes and tubes that is characterized by a fluid velocity independent of radial position, complete mixing in the radial direction, and no mixing in the axial direction. Also called the parallel tube model or tubular flow. See Eqs. (7) and (8) and Figure 3. 

If it is suspected (or known) that the plug flow assumption does not hold, a separate tracer study is needed to characterize the flow distribution within the pipes. These data are then used to adjust both the concentration and the sampling time, as required. If the nature of flow and mixing in the vessel is independent of the flow characteristics in the pipes, then the o1 curve for the vessel may be calculated from... 

Brodkey, R. S. (1966). Turbulent motion and mixing in a pipe. AIChE Journal 12, 403-404. 

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