$\mathsf{\rho }$	density of the fluid
p	static pressure
v	kinematic viscosity
ui	the instantaneous velocity associated with the ${\mathrm{x}}_{\mathrm{i}}$ coordinate direction
Ui	mean flow velocity
ui′	turbulent velocity fluctuation
ui	Ui+ ui′
$\overline{{\mathrm{u}}_{\mathrm{i}}^{\prime }{\mathrm{u}}_{\mathrm{j}}^{\prime }}$	determined with a turbulence closure model
u	velocity of the fluid phase
up	velocity of the particle phase
μ	hydrodynamic viscosity
ρp	density of the particles
dP	diameter of the particles
Re	relative Reynolds number
Gk	the generation rate of turbulence kinetic energy due to mean velocity gradients
Gb	the generation rate of turbulence kinetic energy due to buoyancy
ak	the inverse effective Prandtl numbers for k
aε	the inverse effective Prandtl numbers for ε
µeff	effective viscosity
C1ε, C2ε and C3ε	turbulence model constants