Dispersive flow

In the Davy-Powergas unit (118—120), shown in Figure 13c, the Hquids mn through a draft tube and are pumped by an impeller mnning directly above the draft tube. The dispersion flows out from the top of the mixer and down through a channel into a rectangular settler. Large units of this type are used for copper extraction (7). 

Resin Viscosity. The flow properties of uncured compounded plastics is affected by the particle loading, shape, and degree of dispersion. Flow decreases with increased sphericity and degree of dispersion, but increases with increased loading. Fillers with active surfaces can provide thixotropy to filled materials by forming internal network stmctures which hold the polymers at low stress. 

Droplet Dispersion. The primary feature of the dispersed flow regime is that the spray contains generally spherical droplets. In most practical sprays, the volume fraction of the Hquid droplets in the dispersed region is relatively small compared with the continuous gas phase. Depending on the gas-phase conditions, Hquid droplets can encounter acceleration, deceleration, coUision, coalescence, evaporation, and secondary breakup during thein evolution. Through droplet and gas-phase interaction, turbulence plays a significant role in the redistribution of droplets and spray characteristics. 

Boundary Conditions In normal operation with closed ends, reactant is brought in by bulk flow and carried away by both bulk and dispersion flow. At the inlet where L = 0 or r = 0,... 

Open end vessel One in which there are no discontinuities (abrupt changes) in concentration at die inlet and outlet where bodi bulk and dispersion flow occur. The boundary condidons are C = when z = 0 and 6C/6z = 0 when z =... 

A hydrodynamic characterization of the micro reactor is given in [12], A flow-pattem map reveals the existence of dispersed flow, annular flow, slug-dispersed... 

This example models the dynamic behaviour of an non-ideal isothermal tubular reactor in order to predict the variation of concentration, with respect to both axial distance along the reactor and flow time. Non-ideal flow in the reactor is represented by the axial dispersion flow model. The analysis is based on a simple, isothermal first-order reaction. 

As discussed in Sec. 4.3.6, the axial dispersion flow model is given by... 

From the axial dispersion flow model the component balance equation is 9Ca 9Ca 3 Ca, p... 

The washing of filter cake is carried out to remove liquid impurities from valuable solid product or to increase recovery of valuable filtrates from the cake. Wakeman (1990) has shown that the axial dispersion flow model, as developed in Sec. 4.3.6, provides a fundamental description of cake washing. It takes into account such situations as non-uniformities in the liquid flow pattern, non-uniform porosity distributions, the initial spread of washing liquid onto the topmost surface of the filter cake and the desorption of solute from the solid surfaces. 

Boiling, by G. Leppert and C. C. Pitts, and Two-Phase Annular-Dispersed Flow, by Mario Silvestri, in Advances in Heat Transfer 1, edited by T. F. Irvine, Jr., and J. H. Hartnett, Academic Press (1964). 

The second term on the right-hand side of Eq. (3-95) represents the effect of the wall-drop heat transfer. The heat transfer analysis of dispersed-flow film boiling is discussed in Section 4.4.3. 

Henry and Fauske (1971) developed a model for critical flow in nozzles and short tubes, which allows for nonequilibrium effects and considers a two-phase mixture upstream of the break by using an empirical correlation to relate actual dXIdp to the value (flXJdp) under equilibrium conditions. For a dispersed flow, they assumed that... 

Annular flow, smooth interface (Henry et al., 1969) Since the interface is relatively small compared to dispersed flow and assumed to be smooth, there is no significant momentum transfer or mass transfer between phases. Under such conditions, the change of slip ratio with pressure is... 

Figure 4.17 Droplet formation in dispersed flow (a) in annular flow dryout (b) in inverted annular dryout. (From Varone and Rohsenow, 1990. Reprinted with permission of Massachusetts Institute of Technology, Cambridge, MA.)...

Dispersed flow model. To calculate the actual quality, vapor temperature, and wall temperature, or heat flux, as functions of axial position beyond dryout... 

Andreani, M., and G. Yadigaroglu, 1992, Difficulties in Modeling Dispersed Flow Boiling, War me und Stoffubertragung 27 37-49. (4)... 

Forslund, R. P, and W. M. Rohsenow, 1966, Thermal Non-Equilibrium in Dispersed Flow Film Boiling in a Vertical Tube, MIT Heat Transfer Lab. Rep. 75312-44, Massachusetts Institute of Technology, Cambridge, MA. (4)... 

Serizawa, A., I. Kataoka, and L. Van Wijngaarden, 1992, Dispersed Flow, 3rd Int. Workshop on Two-Phase Fundamentals, London, June. (3)... 

As 100% vaporization is approached, there is not sufficient liquid flowing in the system to continuously wet the entire tube wall, and thus dry spots appear. Transition Zone III is characterized by the initial appearance of these dry spots, and Region IV is characterized by a completely dry tube wall and a dispersed flow pattern. Due to the effects of gravity, dry spots... 

Macbeth (M5) has recently written a detailed review on the subject of burn-out. The review contains a number of correlations for predicting the maximum heat flux before burn-out occurs. These correlations include a dependence upon the tube geometry, the fluid being heated, the liquid velocity, and numerous other properties, as well as the method of heating. Sil-vestri (S6) has reviewed the fluid mechanics and heat transfer of two-phase annular dispersed flows with particular emphasis on the critical heat flux that leads to burn-out. Silvestri has stated that phenomena responsible for burn-out, due to the formation of a vapor film between the wall and the liquid, are believed to be substantially different from phenomena causing burn-out due to the formation of dry spots that produce the liquid-deficient heat transfer region. It is known that the value of the liquid holdup at which dry spots first appear is dependent on the heat flux qmi. The correlations presented by Silvestri and Macbeth (S6, M5) can be used to estimate the burn-out conditions. 

Three main flow patterns exist at various points within the tube bubble, annular, and dispersed flow. In Section I, the importance of knowing the flow pattern and the difficulties involved in predicting the proper flow pattern for a given system were described for isothermal processes. Nonisother-mal systems may have the added complication that the same flow pattern does not exist over the entire tube length. The point of transition from one flow pattern to another must be known if the pressure drop, the holdups, and the interfacial area are to be predicted. In nonisothermal systems, the heat-transfer mechanism is dependent on the flow pattern. Further research on predicting flow patterns in isothermal systems needs to be undertaken... 

The flow regime can be determined from Fig.l5-16a, using an ordinate of 1 and an abscissa of 2635 kg/(m2 s) to be well in the dispersed flow regime, so each of these methods should be applicable. 

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