A multiphase turbulence theory for gas–solid flows: I. Continuity and momentum equations with Favre-averaging

CFD calculations for multiphase gas-particle flows would benefit from a multiphase turbulence theory which would allow the direct calculation of an average solution. A slightly truncated form of the two fluid equations, which are the basis of the MFIX code, have been formally averaged, introducing Favre-like averages for the phasic velocities. This process results in a set of equations which can be solved directly for the average variables describing the flow. This equation set has significantly fewer closure terms than would have occurred using standard Reynolds averaging. The full set of required closure relations is enumerated. Some simple forms for these closures are suggested, although no attempt is made to establish their validity.