PFC regime

For solving the EMMS model, the saturation carrying capacity K has to be determined to ascertain whether Nn should be minimized or maximized in Model LG, that is, to identify the transition from the PFC regime to the FD regime. This transition is characterized by the following equality (Li et al, 1992) ... 

Figure 4 shows the changes of Wu calculated with respect to Nsl = min for the PFC regime and to Nsl = max for the FD regime, respectively. The two curves cross each other at point B ... 

According to the preceding definition, the relationship between the saturation carrying capacity K and fluid velocity Ut can be calculated, as shown in Fig. 5, which defines the transition from the PFC regime to the FD regime, that is, from fast fluidization to dilute transport, as corroborated by the experimental points (the data at high velocities was transported from Fig. 7). 

Beyond l/pt, the FD regime replaces the PFC regime which becomes unstable at Gs < K, resulting in Mode FC, showing a dilute region only,... 

In theory, given the required boundary conditions, it is possible to calculate the radial profiles of all parameters with Model OR from the specified operating variables, Ut and Gs. An approximate solution to the simplest case of the PFC regime, for example, that is, Nst = min, is possible by simplifying Model OR with experimental results, for calculating Ud(r) from Ut(r) and e(r). 

At any radial position r, l/d(r) can be calculated from l/g(r) and e(r) by using Model LR through a trial /(A, r), which may be approximated by polynomials or other adequate functions with the parameter vector A, to be optimized with respect to Nst = min. Now, the problem becomes how to find K(r), that is, how to determine A, in order to satisfy energy minimization, force balance, continuity and the given boundary conditions. Therefore, Model OR is simplified for the PFC regime as the K-Radial (KR) model ... 

Because of this, the Type I ELMy H-mode regime has been chosen as the reference operating regime for high fusion gain experiments in next step devices, such as ITER and FIRE [23], despite the drawbacks associated with the large energy and particle fluxes on the PFCs inherent to the Type I ELMs themselves. 

Fig. 4. Definition of saturation carrying capacity and transition from PFC to FD regime...

For instance, if the solids flow rate is specified at Gs = 50 kg/(m2s), choking will take place at Ug = 3.21 m/s for system FCC/air as indicated in the figure. Throughout the entire regime spectrum, only at this unique point (l/pl, K ) can both dense-phase fluidization and dilute-phase transport coexist. At velocities higher than Upt, only dilute transport can exist, shown as Mode FD in Fig. 4 at velocities lower than l/pt, only dense-phase fluidization can take place, shown as Mode PFC in Fig. 4. The transition point at l/pt identifies the unique Mode PFC/FD on the curve of Fig. 5 for the coexistence of both modes, the relative proportion of which depends on other external conditions such as the imposed pressure APimp as reported by Weinstein et al. (1983). 

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