Fluid Davidson model

The analysis of fluidized-bed reactors is based largely on the fluid mechanical model first described fully by Davidson and Harrison (1963) and modified later by a number of investigators (e.g., Jackson, 1963 Murray, 1965 Pyle and Rose, 1965 Kunii and Levenspiel, 1968a,b Rowe, 1971 Orcutt and Carpenter, 1971 Davidson and Harrison, 1971 Davidson et al., 1978 Van Swaaij, 1985). Our description of fluidized-bed reactor modeling will be based on the Kunii-Levenspiel adaptation (see Levenspiel, 1993). 

Davidson, L. Turbulence modelling and calculation of ventilation parameters in ventilated rooms. Lie. thesis. Report 86/10, Dept, of Thermo and Fluid Dynamics, Chalmers Universirv of Technology, Gothenburg, 1986. 

The two-phase theory of fluidization has been extensively used to describe fluidization (e.g., see Kunii and Levenspiel, Fluidization Engineering, 2d ed., Wiley, 1990). The fluidized bed is assumed to contain a bubble and an emulsion phase. The bubble phase may be modeled by a plug flow (or dispersion) model, and the emulsion phase is assumed to be well mixed and may be modeled as a CSTR. Correlations for the size of the bubbles and the heat and mass transport from the bubbles to the emulsion phase are available in Sec. 17 of this Handbook and in textbooks on the subject. Davidson and Harrison (Fluidization, 2d ed., Academic Press, 1985), Geldart (Gas Fluidization Technology, Wiley, 1986), Kunii and Levenspiel (Fluidization Engineering, Wiley, 1969), and Zenz (Fluidization and Fluid-Particle Systems, Pemm-Corp Publications, 1989) are good reference books. 

The direct contact model has some difiiculties, however. In fluidized beds, gas bubbles of very low solid content are usually considered to exist in the dense phase (H14, K13, T19). Also, the cloud layer is negligibly thin, due to small (/ r for the usual fluid catalyst beds, according to equa-ticMis of Davidson and Harrison (D3) and Murray (M47). The streamlines of gas phase through a bubble have been observed to pass through the cloud, but not through the bubble wake (R17). Thus there seems little possibility of believing that the bubble gas is in direct contact with a substantial amount of catalyst in the bubble phase (see also Secticxi VI,A). Furthermore, the direct contact model is applied to the data by Gilliland and Knudsen, and v in Eq. (7-9) is calculated to fit the data. Calculation (M26) shows that the volume of catalyst, with an apparent density the same as for the emulsion, which contacts the bubble gas freely exceeds the volume of bubble gas itself (v/ib = 3.3, 2.0, and 1.5, respectively, for Uc. = 10, 20, and 30 cm/sec). This seems to be unsound physically. 

Johansson SH, Davidson L, Olsson E (1993) Numerical Simulation of Vortex Sheadding Past Triangular Cylinders at High Reynolds Number Using a k-e Turbulence Model. Int J Numer Methods Fluids 16 859-878... 

The first hydrodynamic model proposed for fluid-bed reactor design (see Davidson and Harrison, 1963) is simple but is the basis of most models developed since. A sketch of the model appears in Figure CS5.1a. Three main groups are involved U for fluidization, for reaction, and Y for mass transfer. Equations can be derived both for plug flow and mixed flow of emulsion gas. The simpler mixed-flow model is usually adequate (with predictions close to those of the plug-flow model) and is given by... 

As a first approximation, the analysis in reference [68] uses the well-known model of Davidson and Harrison [65] in which the bubble is assumed to be a spherical cavity without particles and in which the dispersed phase is characterized by uniform concentration < )o everywhere outside the bubble. Relative interstitial fluid velocity, u, and mean particle velocity, w, can then be found on the basis of 1) a simple filtration flow model for a homogeneous porous body containing a spherical cavity, and 2) an ideal fluid model for flow around a sphere. In particular, the vertical components of these velocities along vertical axis z of the coordinate system having its origin at the bubble center are ... 

Number of FEM elements that constitute a part of the domain Parameter in bubble size model for bubbling beds (—) Permeability constant in the Davidson-Harrison model characteristic of the particles and the fluidizing fluid... 

Hq( is also influenced by gas velocity (slightly) particle size distribution (e.g. fines (particles with dp < 44y) percentage), temperature and pressure. Recommended values have been given elsewhere ( ), but more data are needed. Models of level I are flexible and ceui cope with the complex phenomena occuring in the fluid bed. The parameters should be measured separately which is costly emd time consuming but rell2tble (This was called "Cautious empirsm" by Davidson (55)). 

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