Bed scale modeling

GTVEN Commercial Bed Scale Model, full scaling laws... 

In this study, we have shown how gas-liquid flow through a random packing may be represented by a percolation process. The main concepts of percolation theory allow us to account for the random nature of the packing and to derive a theoretical expression of the liquid flow distribution at the bed scale. This flow distribution allows us to establish an averaging formula between the particle and bed scales. Using this formula, we propose the bed scale modelling of some transport processes previously modelled at the particle scale. 

A technique which can assist in the scale-up of commercial plants designs is the use of scale models. A scale model is an experimental model which is smaller than the hot commercial bed but which has identical hydrodynamic behavior. Usually the scale model is fluidized with air at ambient conditions and requires particles of a different size and density than those used in the commercial bed. The scale model relies on the theory of similitude, sometimes through use of Buckingham s pi theorem, to design a model which gives identical hydrodynamic behavior to the commercial bed. Such a method is used in the wind tunnel testing of small model aircraft or in the towing tank studies of naval vessels. 

Figure 20. Use of scale models with different bed diameters to simulate the influence of diameter on the hydrodynamics of a hot commercial reactor.

In later sections, the use of the scaling relationships to design small scale models will be illustrated. For scaling to hold, all of the dimensionless parameters given in Eqs. (36), (37) or (39) must be identical in the scale model and the commercial bed under study. If the small scale model is fluidized with air at ambient conditions, then the fluid density and viscosity are fixed and it will be shown there is only one unique modeling condition which will allow complete similarity. In some cases this requires a model which is too large and unwieldy to simulate a large commercial bed. 

Using these Reynolds number scale factors, the errors in the dimensionless drag coefficient j3L/psua using the simplified scaling models are shown in Figs. 24 and 25 for u0/umf of 10 and 1000, respectively, plotted as a function of Rep, based on parameters for the exact scaled bed. For a particle Reynolds number of 1000 or less, which corresponds to... 

Table 1 gives the values of design and operating parameters of a scale model fluidized with air at ambient conditions which simulates the dynamics of an atmospheric fluidized bed combustor operating at 850°C. Fortunately, the linear dimensions of the model are much smaller, roughly one quarter those of the combustor. The particle density in the model must be much higher than the particle density in the combustor to maintain a constant value of the gas-to-solid density ratio. Note that the superficial velocity of the model differs from that of the combustor along with the spatial and temporal variables. 

The simplified scaling relationships, Eq. (53), offer some flexibility in the model design since fewer parameters must be matched than with the full set of scaling relationships. When the fluidizing gas, the pressure and temperature of the scale model are chosen, the gas density and viscosity for the scale model are set. The model must still be geometrically similar to the commercial bed. There is still one free parameter. Generally this will be the linear scale of the model. For the simplified scaling relationships, the gas-to-solid density ratio must be maintained constant... 

Table 4. Scale Models of Atmospheric Commercial Hot Bed Using the Simplified Scaling Relationship...

Glicksman and Farrell (1995) constructed a scale model of the Tidd 70 MWe pressurized fluidized bed combustor. The scale model was fluidized with air at atmospheric pressure and temperature. They used the simplified set of scaling relationships to construct a one-quarter length scale model of a section of the Tidd combustor shown in Fig. 34. Based on the results of Glicksman and McAndrews (1985), the bubble characteristics within a bank of horizontal tubes should be independent of wall effects at locations at least three to five bubble diameters away from the wall. Low density polyurethane beads were used to obtain a close fit with the solid-to-gas density ratio for the combustor as well as the particle sphericity and particle size distribution (Table 6). 

Figure 42. Bed expansion for TVA 20 MWe FBC and for scale model, shown in Fig. 39. (From Glicksman etal., 1989.)...

The heat transfer from tubes in the freeboard was also measured for the 20 MW model. Figure 45 shows a comparison of the measured overall heat transfer coefficient in the 20 MW pilot plant versus that predicted from the scale model test. When the bed height is lowered, uncovering some tubes, the heat transfer is reduced because there are fewer particles contacting the tube surface. Although the scale model did not include proper scaling for convective heat transfer, the rate of change of the overall heat transfer should be a function of the hydrodynamics. 

Ackeskog et al. (1993) made the first heat transfer measurements in a scale model of a pressurized bubbling bed combustor. These results shed light on the influence of particle size, density and pressure levels on the fundamental mechanism of heat transfer, e.g., the increased importance of the gas convective component with increased pressure. 

Figure 46. Expanded bed height model data compared to field data for multisolids fluidized bed for properly scaled steel pellets and mis-scaled gravel particles. (From Ake and Glicksman, 1989.)...

Small, properly scaled laboratory models operated at ambient conditions have been shown to accurately simulate the dynamics of large hot bubbling and circulating beds operating at atmospheric and elevated pressures. These models should shed light on the overall operating characteristics and the influence of hydrodynamics factors such as bubble distribution and trajectories. A series of different sized scale models can be used to simulate changes in bed behavior with bed size. 

Figure 54. Solid fraction profile comparison between pressurized circulating fluidized bed combustor and one-half size scale model based on simplified scaling law. (Glicksman et al., 1995.)...

The scale models must be carefully designed. Failure to match the important dimensionless parameters will lead to erroneous simulation results. Modeling can be extended to particle convective heat transfer. Wear or erosion of in-bed surfaces can be qualitatively studied, although quantitative assessment requires the identification and simulation of additional wear-related parameters. 

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