The Purpose of Averaging Procedures

From a mathematical point of view there are still no complete agreement on the properties of the different averaging operators and their suitability for deriving the macroscopic equations. In continuum mechanics a proper averaging procedure should lead to flow variables that are continuous [12]. Considering the pure time and space averages which were the first methods to appear around 1950 [58], some doubts or difficulties related to the continuity of the flow variables were pointed out by [12, 47, 51, 52, 219]. To deal with these matters the basic averages were thus 

FYom the preceding discussion in this chapter, one can conclude that the pertinent modeling approaches to be applied in practice must involve some kind of 

Prom a mathematical point of view there are still no complete agreement on the properties of the different averaging operators and their suitability for deriving the macroscopic equations. 

In the subsequent sections the averaging procedures most frequently used in multiphase reactor modeling are examined. Hence it follows that the basic principles of averaging are presented with emphasis on disperse two phase systems. 

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