Fluidised Systems

As noted in Section 6.1.3 of Volume 2, the Carman-Kozeny equation applies only to conditions of laminar flow and hence to low values of the Reynolds number for flow in the bed. In practice, this restricts its application to fine particles. Approaches based on both the Carman-Kozeny and the Ergun equations are very sensitive to the value of the voidage and it seems likely that both equations overpredict the pressure drop for fluidised systems. 

Because equation 4.18 is applicable to low Reynolds numbers at which the flow is streamline, it appears that the flow of fluid at high concentrations of particles in a sedimenting or fluidised system is also streamline. The resistance to flow in the latter case appears to be about 30 per cent lower, presumably because the particles are free to move relative to one another. 

In order to understand the properties of a fluidised system, it is necessary to study the flow patterns of both the solids and the fluid. The mode of formation and behaviour of fluid bubbles is of particular importance because these usually account for the flow of a high proportion of the fluid in a gas-solids system. 

In any study of the properties of a fluidised system, it is necessary to select conditions which are reproducible and the lack of agreement between the results of many workers, particularly those relating to heat transfer, is largely attributable to the existence of widely different uncontrolled conditions within the bed. The fluidisation should be of... 

As already indicated, when a liquid is the fluidising agent, substantially uniform conditions pervade in the bed, although with a gas, bubble formation tends to occur except at very low fluidising velocities. In an attempt to improve the reproducibility of conditions within a bed, much of the earlier research work with gas fluidised systems was carried out at gas velocities sufficiently low for bubble formation to be absent. In recent years, however, it has been recognised that bubbles normally tend to form in such systems, that they exert an important influence on the flow pattern of both gas and solids, and that the behaviour of individual bubbles can often be predicted with reasonable accuracy. 

It is probable that the Ergun equation, like the Carman-Kozeny equation, also overpredicts pressure drop for fluidised systems, although no experimental evidence is available on the basis of which the values of the coefficients may be amended. 

An alternative way of calculating the index n in equation 6.31 for the expansion of particulately fluidised systems is now considered. Neglecting effects due to the container wall then ... 

The importance of particle density in determining the nature of fluidised systems is well established, and increase in density generally results in a less uniform fluidised system. 

In general, the behaviour of gas-fluidised systems is considerably more complex than that of liquid-fluidised systems which exhibit a gradual transition from fixed bed to fluidised bed followed by particle transport, without a series of transition regions, and with bed expansion and pressure drop conforming reasonably closely to values calculated for ideal... 

The differences between liquid and gas fluidised systems have also been studied theoretically by Jackson121 who showed that small discontinuities tend to grow in a fluidised bed, although the rate of growth is greater in a gas-solids system. 

The hydrodynamics of three-phase fluidised systems is complex and reference should be made to specialised publications for a detailed treatment(87 91). Only a brief summary of their characteristics is given here. 

The good heat transfer properties of fluidised systems have led to their adoption in circumstances where close control of temperature is required. The presence of the particles in a fluidised system results in an increase of up to one-hundredfold in the heat transfer coefficient, as compared with the value obtained with a gas alone at the same velocity. In a liquid-fluidised system the increase is not so marked. 

The heat transfer characteristics of liquid-solid fluidised systems, in which the heat capacity per unit volume of the solids is of the same order as that of the fluid are of considerable interest. The first investigation into such a system was carried out by Lemlich and Caldas193, although most of their results were obtained in the transitional region between streamline and turbulent flow and are therefore difficult to assess. Mitson194 and Smith(20) measured heat transfer coefficients for systems in which a number of different solids were fluidised by water in a 50 mm diameter brass tube, fitted with an annular heating jacket. 

The maximum value of the ratio of the coefficient for the fluidised system to that for liquid alone at the same velocity is about 3. 

In a modified system in which a suspension of solids is conveyed through the heat transfer section, the heat transfer coefficient is greater than that obtained with liquid alone, though lower than that obtained at the same concentration in a fluidised system. Similar conclusions have been reached by Jepson, Poll, and Smith(95) who measured the heat transfer to a suspension of solids in gas. 

Figure 6.22. Data for heat transfer to fluidised systems...

The importance of the flow pattern on the experimental data is clearly apparent, and the reasons for discrepancies between the results of different workers are largely attributable to the rather different characters of the fluidised systems. It is of particular interest to note that, at high values of the Reynolds number when the effects of back-mixing are unimportant, similar results are obtained in fixed and fluidised beds. This conclusion was also reached by Mullin and Treleaven 116 1 in their tests with models. 

Cornish(128) considered the minimum possible value of the Nusselt number in a multiple particle system. By regarding an individual particle as a source and the remote fluid as a sink, it was shown that values of Nusselt number less than 2 may then be obtained. In a fluidised system, however, the inter-particle fluid is usually regarded as the sink and under these circumstances the theoretical lower limit of 2 for the Nusselt number applies. Zabrodsky 1 291 has also discussed the fallacy of Cornish s argument. 

Data on, and the understanding of, fluidised systems are increasing at a very high rate, with as many as a hundred papers appearing in any given year. 

It appears likely that fluidised bed combustion of coal may, in the near future, be one of the most important applications of fluidised systems and it may well be that many new coal-fired generating stations will incorporate fluidised bed combustors. 

Richardson, 1. F. and Smith, 1. W. Trans. Inst. Chem. Eng. 40 (1962) 13. Heat transfer to liquid fluidised systems and to suspensions of coarse particles in vertical transport. 

SZEKELY, J. Third Congress of the European Federation of Chemical Engineering (1962). The Interaction between Fluids and Particles 197. Mass transfer between the dense phase and lean phase in a gas-solid fluidised system. 

Richardson, J. F. and Mitson, A. E. Trans. Inst. Chem. Eng. 36 (1958) 270. Sedimentation and fluidisation. Part II. Heat transfer from a tube wall to a liquid-fluidised system. 

Discuss the variation of the index n with flow conditions, indicating why this is independent of the Reynolds number Re with respect to the particle at very low and very high values of Re. When are appreciable deviations from this relation observed with liquid fluidised systems ... 

Liquid-solid fluidised systems are generally characterised by the regular expansion of the bed which takes place as the liquid velocity increases from the minimum fluidisation velocity to a value approaching the terminal falling velocity of the particles. The general form of relation between velocity and bed voidage is found to be similar for both Newtonian and inelastic power-law liquids. For fluidisation of uniform spheres by Newtonian liquids, equation (5.21), introduced earlier to represent hindered settling data, is equally applicable ... 

Instantaneous local solids densities have been successfully measured in fluidised systems using capacitance probes or fibre optic sensors, e.g. Hartge et al (1988), Herb et al (1989). The fibre optic systems can also be used to measure local solids velocities, although the interpretation is not entirely unambiguous. 

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