Types of flow

Flow in separation systems can be divided into the following four categories  

Parasitic Flow How often assumes a destructive role, despite efforts to prevent it. Convective currents frequently lead to the remixing of separated components. Electroosmotic flow (see Section 4.9) is destructive in some (not all) electrophoretic systems and is difficult to eliminate because of the ubiquitous presence of surface charges. These unintended and generally unproductive forms of flow can be termed parasitic flow. The following discussion serves to distinguish parasitic flows from nonparasitic flow processes. 

Anywhere a chemical potential increment or gradient exists, an elementary separation step can occur. Anywhere random flow currents exist, separation is dissipated. Thus random flow currents are parasitic in regions where incremental chemical potential is used for separation. These currents should thus be eliminated, insofar as possible, in regions where electrical, sedimentation, and other continuous (c) fields are generating separations. Likewise, they should not be allowed to transport matter over discontinuous (d) separative interfaces such as phase boundaries or membrane surfaces. However, they are nonparasitic in bulk phases (removed from the separative interface) where only diffusion occurs. Here, in fact, they aid diffusion and speed the approach to equilibrium. This positive role is recognized in the following category of flow. 

Integral Flow In many systems flow plays an integral role in structuring the separation process. The essential character of the separation method therefore hinges on the existence, orientation, and nature of flow. Most commonly the flow—which is inherently nonselective—serves to magnify a local enrichment induced by the selective forces underlying /i.  

The term flow system, designated in our classification scheme by the letter F, is reserved for those methods employing integral flow because in no other case does flow alter the basic nature of separation. Two distinct classes of integral flow can be identified, F(=) and F( + ), as noted in our classification of Section 7.3. These classes are discussed separately below. 

Three types of flow are mainly encountered in vacuum technology viscous or continuous flow, molecular flow and - at the transition between these two - the so-called Knudsen flow. 

This will be found almost exclusively in the rough vacuum range. The character of this type of flow is determined by the interaction of the molecules. Consequently Internal friction, the viscosity of the flowing substance. Is a major factor. If vortex motion appears In the streaming process, one speaks of turbulent flow. If various layers of the flowing medium slide one over the other, then the term laminar flow or layer flux may be applied. 

Laminar flow In circular tubes with parabolic velocity distribution Is known as Poiseuille flow. This special case is found frequently in vacuum technology. Viscous flow will generally be found where the molecules mean free path is considerably shorter than the diameter of the pipe X d. 

A characteristic quantity describing the viscous flow state is the dimensionless Reynolds number Re. 

Re is the product of the pipe diameter, flow velocity, density and reciprocal value of the viscosity (internal friction) of the gas which is flowing. Flow is turbulent where Re 2200, laminar where Re 2200. 

A number of types of flow have been found to occur in capillary systems, each of which is observed in the appropriate region of pressure difference, absolute pressure, and pore size. Each kind of flow may be characterised by different permeability constants, a fact which has often led to confusion in expressing the data. The nature of gas flow in single capillaries teaches a great deal concerning the more complex permeation processes through porous plates, refractories, and consolidated and unconsolidated sands, so that before discussing flow in these systems the different types of capillary flow will be discussed. 

The researches of Warburg(i), Knudsen(2), Gaede(3), Smoluchowski(4), Buckingham (5), and others (6,7) have demonstrated the properties of the following types of flow (1) Molecular effusion (2) Molecular streaming, or Emudsen flow (3) Poiseuille or stream-line flow (4) Turbulent flow (5) Orifice flow. These may now be considered in turn. 

If one has an orifice of area A in a thin plane wall such that its diameter is small compared with the mean free path of the gas the number of molecules N effusing up to it in unit time is given by the well-known kinetic theory equations 

In these expressions, Nq is the Avogadro number, C the concentration, w the mean velocity, k the Boltzmann 

When the orifice is of considerable length molecules will collide with its walls on their way through. If the collisions are elastic the flow through a smooth tube will be identical with the effusion velocity through the hole in the thin plane wall, since no molecules will be turned back in the original direction by collision with the wall. For such a tube therefore the equations of flow are, as before, 

There ate therefore three types of flow to consider. In the flrst the flow is viscous and equation (1.10) may be applied in the transitional region, in which the mean free path X of the gas molecules is of the 

If water is caused to flow steadily through a transparent tube and a dye is continuously injected into the water, two distinct types of flow may be 

In turbulent flow, properties such as the pressure and velocity fluctuate rapidly at each location, as do the temperature and solute concentration in flows with heat and mass transfer. By tracking patches of dye distributed across the diameter of the tube, it is possible to demonstrate that the liquid s velocity (the time-averaged value in the case of turbulent flow) varies across the diameter of the tube. In both laminar and turbulent flow the velocity is zero at the wall and has a maximum value at the centre-line. For laminar flow the velocity profile is a parabola but for turbulent flow the profile is much flatter over most of the diameter. 

Flow regimes in a pipe shown by dye injection (a) Laminar flow (b) Turbulent flow 

The relationship between pressure drop and flow rate in a pipe 

Measurements with different fluids, in pipes of various diameters, have shown that for Newtonian fluids the transition from laminar to turbulent flow takes place at a critical value of the quantity pudjp in which u is the volumetric average velocity of the fluid, dt is the internal diameter of the pipe, and p and p. are the fluid s density and viscosity respectively. This quantity is known as the Reynolds number Re after Osborne Reynolds who made his celebrated flow visualization experiments in 1883  

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As mentioned in Chapter 1, in general, the solution of the integral viscoelastic models should be based on Lagrangian frameworks. In certain types of flow... 

A funnel flow bin typically exhibits a first-in/last-out type of flow sequence. If the material has sufficient cohesive strength, it may bridge over the outlet. Also, if the narrow flow channel empties out, a stable rathole may form. This stable rathole decreases the bin s five or usable capacity, causes materials to cake or spoil, and/or enhances segregation problems. Collapsing ratholes may impose loads on the stmcture that it was not designed to withstand. 

Many appHcations use screws with constant pitch to feed material from a slotted opening. The configuration shown in Figure 9a shows a constant pitch and constant diameter causing a preferential flow channel to form at the back (over the first flight) of the screw. This type of flow destroys the mass flow pattern and potentially allows some or all of the problems discussed about fiinnel flow. 

Flow. The principal types of flow rate sensors are differential pressure, electromagnetic, vortex, and turbine. Of these, the first is the most popular. Orifice plates and Venturi-type flow tubes are the most popular differential pressure flow rate sensors. In these, the pressure differential measured across the sensor is proportional to the square of the volumetric flow rate. 

A Hquid is a material that continues to deform as long as it is subjected to a tensile and/or shear stress. The latter is a force appHed tangentially to the material. In a Hquid, shear stress produces a sliding of one infinitesimal layer over another, resulting in a stack-of-cards type of flow (Fig. 1). 

Fig. 2. Flow curves (shear stress vs shear rate) for different types of flow behavior.

Laminar and Turbulent Flow, Reynolds Number These terms refer to two distinct types of flow. In laminar flow, there are smooth streamlines and the fuiid velocity components vary smoothly with position, and with time if the flow is unsteady. The flow described in reference to Fig. 6-1 is laminar. In turbulent flow, there are no smooth streamlines, and the velocity shows chaotic fluctuations in time and space. Velocities in turbulent flow may be reported as the sum of a time-averaged velocity and a velocity fluctuation from the average. For any given flow geometry, a dimensionless Reynolds number may be defined for a Newtonian fluid as Re = LU p/ I where L is a characteristic length. Below a critical value of Re the flow is laminar, while above the critical value a transition to turbulent flow occurs. The geometry-dependent critical Reynolds number is determined experimentally. 

A useful classification of lands of reaclors is in terms of their concentration distributions. The concentration profiles of certain limiting cases are illustrated in Fig. 7-3 namely, of batch reactors, continuously stirred tanks, and tubular flow reactors. Basic types of flow reactors are illustrated in Fig. 7-4. Many others, employing granular catalysts and for multiphase reactions, are illustratea throughout Sec. 23. The present material deals with the sizes, performances and heat effects of these ideal types. They afford standards of comparison. 

Maximum shell-side heat-transfer rates in forced convection are apparently obtained by cross-flow of the flmd at right angles to the tubes. In order to maximize this type of flow some heat exchangers are built with segmental-cut baffles and with no tubes in the window (or the baffle cutout). Maximum baffle spacing may thus equal maximum unsupported-tube span, while conventional baffle spacing is hmited to one-h f of this span. 

Not only is the type of flow related to the impeller Reynolds number, but also such process performance characteristics as mixing time, impeller pumping rate, impeller power consumption, and heat- and mass-transfer coefficients can be correlated with this dimensionless group. 

To understand the flow in turbomachines, an understanding of the basic relationships of pressure, temperature, and type of flow must be acquired. Ideal flow in turbomachines exists when there is no transfer of heat between the gas and its surroundings, and the entropy of the gas remains unchanged. This type of flow is characterized as a rever.sible adiabatic flow. To describe this flow, the total and static conditions of pressure, temperature, and the concept of an ideal gas must be understood. 

Cooling towers are broadly classified on the basis of the type of draft natural draft (natural convection), mechanical draft (forced convection) and mechanical and natural. Further distinction is made based on (1) the type of flow i.e. - crossflow, counterflow, cocurrent flow (2) the type of heat dissipation-wet (evaporative cooling), dry, wet-dry and (3) the type of application-industrial or power plant. Each of the major types of cooling towers has a distinct configuration. The major designs are summarized in Figures 1 through 8 and a brief description of each follows. 

The flow patterns typically encountered in vertical pipe flow are illustrated in Figure 23. The types of flow patterns encountered are as follows ... 

The forces applied by an impeller to the material contained in a vessel produce characteristic flow patterns that depend on the Impeller geometry, properties of the fluid, and the relative sizes and proportions of the tank, baffles and impeller. There are three principal types of flow patterns tangential, radial and axial. Tangential flow is observed when the liquid flows parallel to the path described by the mixer as illustrated in Figure 7. 

Figure 14.1 shows that the void fraction approaches zero, and, the smaller the mixture ratio /a, the greater the void fraction 4>. In some cases, the void fraction characteristic number for classification of the type of flow in pneumatic conveying. But generally speaking, the void fraction is not the only criterion that determines the behavior of the flow. 

One widely-used picture for illustrating the different types of flow in pneumatic conveying is the so-called state diagram, - in which the pressure drop is related to the air velocity. 

The way in which the force /j j is modeled clearly determines the type of the pneumatic flow this has been discussed earlier in Section 14.2.2, where we considered the classification of different types of flow. In the following we will give a detailed description for the force in a way that suits a particular type of flow. This approach will be adequate for so-called dilute-phase flow or, more generally speaking, for homogeneous flow where the particles move separately. 

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