Time averaging, Favre

For flows in which density fluctuations are negligible, the formulations become identical. Favre-averaged quantities are not easily comparable with experimentally measured quantities, which are normally non-weighted time averages. For most chemical reactor engineering applications (except maybe combustion processes), classical Reynolds averaging is suitable. 

The relationship between the conventional Re3Tiolds time average in (3.323) and the weighted Favre time average variables in (3.324) follows directly from their definitions [131] ... 

Besides, multipl3dng both sides of the expression (3.384) by and thereafter time averaging the resulting equation, we get a relation between the Favre and Re3molds averaged variables ... 

In analogy to the conventional Favre decomposition and time averaging procedure we let ip l denote the temporal fluctuation of the instantaneous variable -ipk about the... 

For multiphase flows perturbed by the presence of particles to obtain a turbulence like behavior the local instantaneous velocity of the continuous phase can for example be decomposed adopting the Reynolds averaging procedure (i.e., other methods including time-, volume-, ensemble-, and Favre averaging have been used as well) and expressed as Vg = Vg- - < v >g, where v(. is the fluctuating component of the continuous phase velocity. Introducing the peculiar velocity for the dispersed phase this relation can be re-arranged as ... 

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