Time Scales for Dispersed Multiphase Flows

APPENDIX 4.1. TIME SCALES FOR DISPERSED MULTIPHASE FLOWS (FROM PEIRANO AND LECKNER, 1998) 

Eddy lifetime or the integral time scale of turbulence can be expressed in the framework of the k-s model as 

Subscript 1 indicates continuous phase and 2 indicates dispersed phase. Cd is a parameter of the standard k-s model (0.09), k is turbulent kinetic energy and si is turbulent energy dissipation rate. The eddy lifetime seen by dispersed phase particles will in general be different from that for continuous phase fluid particles due to the so-called crossing-trajectory effect (Csnady, 1963). This can be expressed in the form  

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