About the calculation of Re of particle in Heat transfer -CFD-DEM

MFiX
#1

Code: calc_gamma_des.f
N_Re = (2.0d0*DES_RADIUS(NP)SLIPRO_g(IJK)) / MU_g(IJK)
The Ranz and Mrshall, 1952 model is used in the code.

However, in J.Musser’s thesis, image
Re is defined as (epsilon_g2.0d0DES_RADIUS(NP)SLIPRO_g(IJK)) / MU_g(IJK)
It seems like that the voidage: epsilon_g is missed in the code. I was wondering which defination is right.
Thank you so much and hope to recieve your answer. Thank you.

#2

In the original Ranz and Marshall 1952 paper, the evaporation of single droplet was investigated. It is very dilute flow and epsilon_g=~1.0 and can be neglected. While for dense flow, I would add epsilon_g in calculating the Reynolds number. I would say, there is no general agreement in the literature on how to calculate Re for multiphase flow.