By Sreekanth Pannala
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Extra info for Computational gas-solids flows and reacting systems : theory, methods and practice
1990; Lundgren, 1972; Saffman, 1971). 8) In addition, let us define an averaging operator ‹› that represents the ensemble average over many independent trials: consider conducting an experiment many times (N) starting from the same initial conditions and recording a certain quantity at the same location and time evolution. The operator ‹› stands for the average of that quantity as we let N → ∞. 9) and of the solids (considering only one solids-phase—M=1): . 12) 9 Multiphase Continuum Formulation for Gas-Solids Reacting Flows where U(x,t) is the true velocity of the mixture.
Khan, Pirie, & Richardson, 1987). In a multi-particle system, the nearness of other particles makes the drag force on each particle significantly greater than that given by the single-particle drag formula. Thus, the formula for multi-particle drag force must include at least the fluid-volume fraction as an additional parameter to account for the effect of neighboring particles. The drag formula must also be a linear function of the volume fraction of the solids phase, the linearity ensuring that the equations correctly satisfy the following requirement (Syamlal, 1985).
2006) have proposed an additive approach for collisional-frictional stress in the intermediate dense regions based on the results of Patil et al. (2005a; 2005b) and Tardos et al. (2003). A method for describing the continuous transition from the collisional to the frictional regime is to replace the step-function used by Syamlal et al. , 2008; Xie, Battaglia, & Pannala, 2008a, 2008b). This model is based on using a weighted averaging function that smoothly bridges the limiting modes. To better understand the physical motivation, consider the schematic in Figure 4 where the viscous regime (dilute) and the plastic regime (dense) are depicted as functions of void fraction, εg.