Flow of gas-solids mixtures

D.J. Mason, A. Levy, P. Maijanovic, The influence of bends on the flow of gas-solids mixtures through pipelines, Proceedings of the 2nd Israel Conference for Conveying and Handling of Particulate Solids, Jerusalem, Israel, 1997, pp. 4.36 4.41. 

Leung, L. S. and Jones, P. J. (1978). Flow of Gas-Solid Mixture in Standpipes A Review. Powder Tech., 20,145. 

P. Maijanovic, An investigation of the behaviour of gas-solids mixture flow properties for vertical conveying in pipelines, Ph.D. Thesis, CNAA, Thames Polytechnic, London, UK, 1984. 

Gas-Solid Mixtures Carlson, Frazier, and Engdahl [Trans. Am. Soc. Mech. Eng., 70, 65-79 (1948)] describe the use of a flow nozzle and a square-edged orifice in series for the measurement of both the gas rate and the solids rate in the flow of a finely divided solid-in-gas mixture. The nozzle differential is sensitive to the flow of both phases, whereas the orifice differential is not influenced by the sohds flow. 

Farbar [Trans. Am. Soc. Mech. Eng., 75,943-951 (1953)] describes how a venturi meter can be used to measure solids flow rate in a gas-solids mixture when the gas rate is held constant. Separate calibration curves (solids flowversus differential) are required for each gas rate of interest. 

Cheng, Tung, and Soo [J. Eng. Power, 92, 135-149 (1970)] describe the use of an electrostatic probe for measurement of solids flow in a gas-solids mixture. 

I he mixture clement shown in Fig. 14.15 contains the flowing gas and solid particles. The partial densities of these two elements are pg and p. respectively. The void fraction is and this can be interpreted as the partial cross-sectional area for gas flow (see Eq. (14.13)). This means that if the pressure of the gas is p, then the pressure force per unit area of the total mixture affecting the flow of gas is (pp and the pressure force affecting the flow of solids is 1 -

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Tsuji et al. (1990) have modeled the flow of plastic pellets in the plug mode with discrete dynamics following the behavior of each particle. The use of a dash pot/spring arrangement to account for the friction was employed. Their results show remarkable agreement with the actual behavior of real systems. Figure 28 shows these flow patterns. Using models to account for turbulent gas-solid mixtures, Sinclair (1994) has developed a technique that could have promise for the dense phase transport. 

P. Maijanovic. Bends in gas-solids mixture flow in pipes — a view to the prediction of pressure loss, GAMM Congress, Vienna, Austria, 1988. 

This chapter describes the fundamental principles of heat and mass transfer in gas-solid flows. For most gas-solid flow situations, the temperature inside the solid particle can be approximated to be uniform. The theoretical basis and relevant restrictions of this approximation are briefly presented. The conductive heat transfer due to an elastic collision is introduced. A simple convective heat transfer model, based on the pseudocontinuum assumption for the gas-solid mixture, as well as the limitations of the model applications are discussed. The chapter also describes heat transfer due to radiation of the particulate phase. Specifically, thermal radiation from a single particle, radiation from a particle cloud with multiple scattering effects, and the basic governing equation for general multiparticle radiations are discussed. The discussion of gas phase radiation is, however, excluded because of its complexity, as it is affected by the type of gas components, concentrations, and gas temperatures. Interested readers may refer to Ozisik (1973) for the absorption (or emission) of radiation by gases. The last part of this chapter presents the fundamental principles of mass transfer in gas-solid flows. 

The analysis of a multiphase flow system is complex, in part because of the difficulties in assessing the dynamic responses of each phase and the interactions between the phases. In some special cases, the gas-solid mixture can be treated as a single pseudo-homogeneous phase in which general thermodynamic properties of a gas-solid mixture can be defined. This treatment provides an estimate for the bulk behavior of the gas-solid flow. The following treatment is based on the work of Rudinger (1980). 

One-dimensional flow models are adopted in the early stages of model development for predicting the solids holdup and pressure drop in the riser. These models consider the steady flow of a uniform suspension. Four differential equations, including the gas continuity equation, solids phase continuity equation, gas-solid mixture momentum equation, and solids phase momentum equation, are used to describe the flow dynamics. The formulation of the solids phase momentum equation varies with the models employed [e.g., Arastoopour and Gidaspow, 1979 Gidaspow, 1994], The one-dimensional model does not simulate the prevailing characteristics of radial nonhomogeneity in the riser. Thus, two- or three-dimensional models are required. 

The role of the pressure gradient may be shown in the momentum equation of a gas-solid mixture. Consider a steady pipe flow without mass transfer and with negligible interparticle collisions. From Eq. (5.170), the momentum equations for the gas and particle phases can be given by... 

Such questions are answered empirically all too often. A more fundamental approach is needed. In the area of gas-phase kinetics, the developments in the chemistry of large sets of elementary reactions and diffusion in multi-component mixtures in a combustion context are now finding applications in chemical engineering, as mentioned above. In the area of gas-solid reactions, the information flow will be in the opposite direction. A need exists... 

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