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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-e model as

CDk1

1 e1

Subscript 1 indicates continuous phase and 2 indicates dispersed phase. CD is a parameter of the standard k-e model (0.09), k\ is turbulent kinetic energy and ei 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:

where Ur is relative velocity and Cp is a constant which depends on the type of flow. The particle relaxation time, which represents entrainment of particles by the continuous phase, is defined by

4dp p2

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