Development of Scaling Parameters

There are several approaches to developing the correct scaling relationships. Probably the most straightforward is the nondimensional-ization of the governing equations. If we can write the proper equations governing the fluid and particle dynamic behavior, we can develop the proper scaling relationships even if we can t solve the equations (at present we can t). In essence, if a model is designed which follows the 

It is important to include all of the relevant physical effects in the equations to be nondimensionalized. This can be difficult because there isn t always consensus about which effects are important. Moreover, there is controversy over how to properly represent these effects in equation form. For our purposes the question is Have all of the important parameters been included in the nondimensional equations Pragmatically, the success to date of the scaling experiments using the formulation as presented adds confidence to the use of these simplifications which will be employed. Also, a limited number of tests have verified the omission of parameters specifically related to several phenomena. 

In some cases, if we are too precise and include effects of marginal significance, the resulting modeling rules may be overly restrictive, limiting the choice of models or requiring the models which are too big. These questions are most expeditiously settled by experiments since an exact theoretical answer is not presently available. 

The equations of motion can either be formulated for individual particles and the surrounding fluid, or the fluid and the particulate phases can each be considered a continuum. Both approaches yield identical results, see Glicksman et al. (1994) for a complete derivation. For our purposes, we will base the derivation on the continuum model formulated by Jackson. 

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Although general treatments of the flow in fluidized beds of coarse particles, in view of the difficulty of the problem, will only evolve slowly, there have been some promising developments. These include the success achieved in correlating heat transfer data (7, 113., 114) and the development of scaling parameters that permit the use of cold flow models to study many of the characteristics of AFBC s (114%115). 

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