Full Set of Scaling Relationships

We will first consider the steps to design a model which is similar to another bed based on the full set of scaling parameters, Eqs. (37) or (39). 

To construct a model which will give behavior similar to another bed, for example, a commercial bed, all of the dimensionless parameters listed in Eqs. (37) or (39) must have the same value for the two beds. The requirements of similar bed geometry is met by use of geometrically similar beds the ratio of all linear bed dimensions to a reference dimension such as the bed diameter must be the same for the model and the commercial bed. This includes the dimensions of the bed internals. The dimensions of elements external to the bed such as the particle return loop do not have to be matched as long as the return loop is designed to provide the proper external solids flow rate and size distribution and solid or gas flow fluctuations in the return loop do not influence the riser behavior (Rhodes and Laussman, 1992). 

All of the linear dimensions of the model are scaled to the corresponding dimensions of the commercial bed by the ratio of the kinematic viscosities of the gas raised to the two-thirds power. By taking the ratio of Reynolds number based on the particle diameter to Reynolds number based on the bed diameter 

the velocity scales are the square root of the linear dimension scale. 

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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... 

Most early experiments devoted to verifying the scaling relationships have dealt with the full set of scaling relationships. Several more recent experiments have dealt with a reduced set of dimensionless parameters. In some experiments, additional scaling parameters were unintentionally matched. 

For scaling to hold with the full set of scaling relationships, all of the dimensionless parameters given in Eqs. (6) or (7) 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 there is only one unique modeling condition that will allow complete similarity. In some cases, this requires a model that is too large and unwieldy or will not permit simulation of a very large bed. 

As a full-scale family classification system, more than 1200 MOTIFIND neural networks were implemented, one for each ProSite protein group. The training set for the neural networks consisted of both positive (ProSite family members) and negative (randomly selected non-members) sequences at a ratio of 1 to 2. ProClass groups non-redundant SwissProt and PIR protein sequence entries into families as defined collectively by PIR superfamilies and ProSite patterns. By joining global and motif similarities in a single classification scheme, ProClass helps to reveal domain and family relationships, and classify multi-domained proteins. 

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